# Input Parameters

Note

WarpX input options are read via AMReX ParmParse.

Note

The AMReX parser (see Math parser and user-defined constants) is used for the right-hand-side of all input parameters that consist of one or more integers or floats, so expressions like `<species_name>.density_max = "2.+1."`

and/or using user-defined constants are accepted.

## Overall simulation parameters

`authors`

(string: e.g.`"Jane Doe <jane@example.com>, Jimmy Joe <jimmy@example.com>"`

)Authors of an input file / simulation setup. When provided, this information is added as metadata to (openPMD) output files.

`max_step`

(integer)The number of PIC cycles to perform.

`stop_time`

(float; in seconds)The maximum physical time of the simulation. Can be provided instead of

`max_step`

. If both`max_step`

and`stop_time`

are provided, both criteria are used and the simulation stops when the first criterion is hit.Note: in boosted-frame simulations,

`stop_time`

refers to the time in the boosted frame.

`warpx.used_inputs_file`

(string; default:`warpx_used_inputs`

)Name of a file that WarpX writes to archive the used inputs. The context of this file will contain an exact copy of all explicitly and implicitly used inputs parameters, including those extended and overwritten from the command line.

`warpx.gamma_boost`

(float)The Lorentz factor of the boosted frame in which the simulation is run. (The corresponding Lorentz transformation is assumed to be along

`warpx.boost_direction`

.)When using this parameter, the input parameters are interpreted as in the lab-frame and automatically converted to the boosted frame. (See the corresponding documentation of each input parameters for exceptions.)

`warpx.boost_direction`

(string:`x`

,`y`

or`z`

)The direction of the Lorentz-transform for boosted-frame simulations (The direction

`y`

cannot be used in 2D simulations.)

`warpx.zmax_plasma_to_compute_max_step`

(float) optionalCan be useful when running in a boosted frame. If specified, automatically calculates the number of iterations required in the boosted frame for the lower z end of the simulation domain to reach

`warpx.zmax_plasma_to_compute_max_step`

(typically the plasma end, given in the lab frame). The value of`max_step`

is overwritten, and printed to standard output. Currently only works if the Lorentz boost and the moving window are along the z direction.

`warpx.compute_max_step_from_btd`

(integer; 0 by default) optionalCan be useful when computing back-transformed diagnostics. If specified, automatically calculates the number of iterations required in the boosted frame for all back-transformed diagnostics to be completed. If

`max_step`

,`stop_time`

, or`warpx.zmax_plasma_to_compute_max_step`

are not specified, or the current values of`max_step`

and/or`stop_time`

are too low to fill all BTD snapshots, the values of`max_step`

and/or`stop_time`

are overwritten with the new values and printed to standard output.

`warpx.random_seed`

(string or int > 0) optionalIf provided

`warpx.random_seed = random`

, the random seed will be determined using std::random_device and std::clock(), thus every simulation run produces different random numbers. If provided`warpx.random_seed = n`

, and it is required that n > 0, the random seed for each MPI rank is (mpi_rank+1) * n, where mpi_rank starts from 0. n = 1 and`warpx.random_seed = default`

produce the default random seed. Note that when GPU threading is used, one should not expect to obtain the same random numbers, even if a fixed`warpx.random_seed`

is provided.

`warpx.do_electrostatic`

(string) optional (default none)Specifies the electrostatic mode. When turned on, instead of updating the fields at each iteration with the full Maxwell equations, the fields are recomputed at each iteration from the Poisson equation. There is no limitation on the timestep in this case, but electromagnetic effects (e.g. propagation of radiation, lasers, etc.) are not captured. There are several options:

`labframe`

: Poisson’s equation is solved in the lab frame with the charge density of all species combined. More specifically, the code solves:\[\boldsymbol{\nabla}^2 \phi = - \rho/\epsilon_0 \qquad \boldsymbol{E} = - \boldsymbol{\nabla}\phi\]`labframe-electromagnetostatic`

: Poisson’s equation is solved in the lab frame with the charge density of all species combined. Additionally the 3-component vector potential is solved in the Coulomb Gauge with the current density of all species combined to include self magnetic fields. More specifically, the code solves:\[\begin{split}\boldsymbol{\nabla}^2 \phi = - \rho/\epsilon_0 \qquad \boldsymbol{E} = - \boldsymbol{\nabla}\phi \\ \boldsymbol{\nabla}^2 \boldsymbol{A} = - \mu_0 \boldsymbol{j} \qquad \boldsymbol{B} = \boldsymbol{\nabla}\times\boldsymbol{A}\end{split}\]`relativistic`

: Poisson’s equation is solved**for each species**in their respective rest frame. The corresponding field is mapped back to the simulation frame and will produce both E and B fields. More specifically, in the simulation frame, this is equivalent to solving**for each species**\[\boldsymbol{\nabla}^2 - (\boldsymbol{\beta}\cdot\boldsymbol{\nabla})^2\phi = - \rho/\epsilon_0 \qquad \boldsymbol{E} = -\boldsymbol{\nabla}\phi + \boldsymbol{\beta}(\boldsymbol{\beta} \cdot \boldsymbol{\nabla}\phi) \qquad \boldsymbol{B} = -\frac{1}{c}\boldsymbol{\beta}\times\boldsymbol{\nabla}\phi\]where \(\boldsymbol{\beta}\) is the average (normalized) velocity of the considered species (which can be relativistic). See e.g. Vay et al., Physics of Plasmas 15, 056701 (2008) for more information.

See the AMReX documentation for details of the MLMG solver (the default solver used with electrostatic simulations). The default behavior of the code is to check whether there is non-zero charge density in the system and if so force the MLMG solver to use the solution max norm when checking convergence. If there is no charge density, the MLMG solver will switch to using the initial guess max norm error when evaluating convergence and an absolute error tolerance of \(10^{-6}\) \(\mathrm{V/m}^2\) will be used (unless a different non-zero value is specified by the user via

`warpx.self_fields_absolute_tolerance`

).

`warpx.self_fields_required_precision`

(float, default: 1.e-11)The relative precision with which the electrostatic space-charge fields should be calculated. More specifically, the space-charge fields are computed with an iterative Multi-Level Multi-Grid (MLMG) solver. This solver can fail to reach the default precision within a reasonable time. This only applies when warpx.do_electrostatic = labframe.

`warpx.self_fields_absolute_tolerance`

(float, default: 0.0)The absolute tolerance with which the space-charge fields should be calculated in units of \(\mathrm{V/m}^2\). More specifically, the acceptable residual with which the solution can be considered converged. In general this should be left as the default, but in cases where the simulation state changes very little between steps it can occur that the initial guess for the MLMG solver is so close to the converged value that it fails to improve that solution sufficiently to reach the

`self_fields_required_precision`

value.

`warpx.self_fields_max_iters`

(integer, default: 200)Maximum number of iterations used for MLMG solver for space-charge fields calculation. In case if MLMG converges but fails to reach the desired

`self_fields_required_precision`

, this parameter may be increased. This only applies when warpx.do_electrostatic = labframe.

`warpx.self_fields_verbosity`

(integer, default: 2)The vebosity used for MLMG solver for space-charge fields calculation. Currently MLMG solver looks for verbosity levels from 0-5. A higher number results in more verbose output.

`amrex.abort_on_out_of_gpu_memory`

(`0`

or`1`

; default is`1`

for true)When running on GPUs, memory that does not fit on the device will be automatically swapped to host memory when this option is set to

`0`

. This will cause severe performance drops. Note that even with this set to`1`

WarpX will not catch all out-of-memory events yet when operating close to maximum device memory. Please also see the documentation in AMReX.

`amrex.the_arena_is_managed`

(`0`

or`1`

; default is`0`

for false)When running on GPUs, device memory that is accessed from the host will automatically be transferred with managed memory. This is useful for convenience during development, but has sometimes severe performance and memory footprint implications if relied on (and sometimes vendor bugs). For all regular WarpX operations, we therefore do explicit memory transfers without the need for managed memory and thus changed the AMReX default to false. Please also see the documentation in AMReX.

### Signal Handling

WarpX can handle Unix (Linux/macOS) process signals. This can be useful to configure jobs on HPC and cloud systems to shut down cleanly when they are close to reaching their allocated walltime or to steer the simulation behavior interactively.

Allowed signal names are documented in the C++ standard and POSIX.
We follow the same naming, but remove the `SIG`

prefix, e.g., the WarpX signal configuration name for `SIGINT`

is `INT`

.

`warpx.break_signals`

(array of string, separated by spaces) optionalA list of signal names or numbers that the simulation should handle by cleanly terminating at the next timestep

`warpx.checkpoint_signals`

(array of string, separated by spaces) optionalA list of signal names or numbers that the simulation should handle by outputting a checkpoint at the next timestep. A diagnostic of type checkpoint must be configured.

Note

Certain signals are only available on specific platforms, please see the links above for details.
Typically supported on Linux and macOS are `HUP`

, `INT`

, `QUIT`

, `ABRT`

, `USR1`

, `USR2`

, `TERM`

, `TSTP`

, `URG`

, and `IO`

among others.

Signals to think about twice before overwriting in *interactive simulations*:
Note that `INT`

(interupt) is the signal that `Ctrl+C`

sends on the terminal, which most people use to abort a process; once overwritten you need to abort interactive jobs with, e.g., `Ctrl+\`

(`QUIT`

) or sending the `KILL`

signal.
The `TSTP`

(terminal stop) command is sent interactively from `Ctrl+Z`

to temporarily send a process to sleep (until send in the background with commands such as `bg`

or continued with `fg`

), overwriting it would thus disable that functionality.
The signals `KILL`

and `STOP`

cannot be used.

The `FPE`

and `ILL`

signals should not be overwritten in WarpX, as they are controlled by AMReX for debug workflows that catch invalid floating-point operations.

Tip

For example, the following logic can be added to Slurm batch scripts (signal name to number mapping here) to gracefully shut down 6 min prior to walltime.
If you have a checkpoint diagnostics in your inputs file, this automatically will write a checkpoint due to the default `<diag_name>.dump_last_timestep = 1`

option in WarpX.

```
#SBATCH --signal=B:1@360
srun ... \
warpx.break_signals=HUP \
> output.txt
```

For LSF batch systems, the equivalent job script lines are:

```
#BSUB -wa 'HUP' -wt '6'
jsrun ... \
warpx.break_signals=HUP \
> output.txt
```

## Setting up the field mesh

`amr.n_cell`

(2 integers in 2D, 3 integers in 3D)The number of grid points along each direction (on the

**coarsest level**)

`amr.max_level`

(integer, default:`0`

)When using mesh refinement, the number of refinement levels that will be used.

Use 0 in order to disable mesh refinement. Note: currently,

`0`

and`1`

are supported.

`amr.ref_ratio`

(integer per refined level, default:`2`

)When using mesh refinement, this is the refinement ratio per level. With this option, all directions are fined by the same ratio.

`amr.ref_ratio_vect`

(3 integers for x,y,z per refined level)When using mesh refinement, this can be used to set the refinement ratio per direction and level, relative to the previous level.

Example: for three levels, a value of

`2 2 4 8 8 16`

refines the first level by 2-fold in x and y and 4-fold in z compared to the coarsest level (level 0/mother grid); compared to the first level, the second level is refined 8-fold in x and y and 16-fold in z.

`geometry.dims`

(string)The dimensions of the simulation geometry. Supported values are

`1`

,`2`

,`3`

,`RZ`

. For`3`

, a cartesian geometry of`x`

,`y`

,`z`

is modeled. For`2`

, the axes are`x`

and`z`

and all physics in`y`

is assumed to be translation symmetric. For`1`

, the only axis is`z`

and the dimensions`x`

and`y`

are translation symmetric. For`RZ`

, we apply an azimuthal mode decomposition, with`warpx.n_rz_azimuthal_modes`

providing further control.Note that this value has to match the WarpX_DIMS compile-time option. If you installed WarpX from a package manager, then pick the right executable by name.

`warpx.n_rz_azimuthal_modes`

(integer; 1 by default)When using the RZ version, this is the number of azimuthal modes. The default is

`1`

, which corresponds to a perfectly axisymmetric simulation.

`geometry.prob_lo`

and`geometry.prob_hi`

(2 floats in 2D, 3 floats in 3D; in meters)The extent of the full simulation box. This box is rectangular, and thus its extent is given here by the coordinates of the lower corner (

`geometry.prob_lo`

) and upper corner (`geometry.prob_hi`

). The first axis of the coordinates is x (or r with cylindrical) and the last is z.

`warpx.do_moving_window`

(integer; 0 by default)Whether to use a moving window for the simulation

`warpx.moving_window_dir`

(either`x`

,`y`

or`z`

)The direction of the moving window.

`warpx.moving_window_v`

(float)The speed of moving window, in units of the speed of light (i.e. use

`1.0`

for a moving window that moves exactly at the speed of light)

`warpx.start_moving_window_step`

(integer; 0 by default)The timestep at which the moving window starts.

`warpx.end_moving_window_step`

(integer; default is`-1`

for false)The timestep at which the moving window ends.

`warpx.fine_tag_lo`

and`warpx.fine_tag_hi`

(2 floats in 2D, 3 floats in 3D; in meters) optional**When using static mesh refinement with 1 level**, the extent of the refined patch. This patch is rectangular, and thus its extent is given here by the coordinates of the lower corner (`warpx.fine_tag_lo`

) and upper corner (`warpx.fine_tag_hi`

).

`warpx.refine_plasma`

(integer) optional (default 0)Increase the number of macro-particles that are injected “ahead” of a mesh refinement patch in a moving window simulation.

Note: in development; only works with static mesh-refinement, specific to moving window plasma injection, and requires a single refined level.

`warpx.n_current_deposition_buffer`

(integer)When using mesh refinement: the particles that are located inside a refinement patch, but within

`n_current_deposition_buffer`

cells of the edge of this patch, will deposit their charge and current to the lower refinement level, instead of depositing to the refinement patch itself. See the mesh-refinement section for more details. If this variable is not explicitly set in the input script,`n_current_deposition_buffer`

is automatically set so as to be large enough to hold the particle shape, on the fine grid

`warpx.n_field_gather_buffer`

(integer, optional)Default:

`warpx.n_field_gather_buffer = n_current_deposition_buffer + 1`

(one cell larger than`n_current_deposition_buffer`

on the fine grid).When using mesh refinement, particles that are located inside a refinement patch, but within

`n_field_gather_buffer`

cells of the edge of the patch, gather the fields from the lower refinement level, instead of gathering the fields from the refinement patch itself. This avoids some of the spurious effects that can occur inside the refinement patch, close to its edge. See the section Mesh refinement for more details.

`warpx.do_single_precision_comms`

(integer; 0 by default)Perform MPI communications for field guard regions in single precision. Only meaningful for

`WarpX_PRECISION=DOUBLE`

.

`particles.deposit_on_main_grid`

(list of strings)When using mesh refinement: the particle species whose name are included in the list will deposit their charge/current directly on the main grid (i.e. the coarsest level), even if they are inside a refinement patch.

`particles.gather_from_main_grid`

(list of strings)When using mesh refinement: the particle species whose name are included in the list will gather their fields from the main grid (i.e. the coarsest level), even if they are inside a refinement patch.

## Domain Boundary Conditions

`boundary.field_lo`

and`boundary.field_hi`

(2 strings for 2D, 3 strings for 3D, pml by default)Boundary conditions applied to fields at the lower and upper domain boundaries. Options are:

`Periodic`

: This option can be used to set periodic domain boundaries. Note that if the fields for lo in a certain dimension are set to periodic, then the corresponding upper boundary must also be set to periodic. If particle boundaries are not specified in the input file, then particles boundaries by default will be set to periodic. If particles boundaries are specified, then they must be set to periodic corresponding to the periodic field boundaries.`pml`

(default): This option can be used to add Perfectly Matched Layers (PML) around the simulation domain. See the PML theory section for more details. Additional pml algorithms can be explored using the parameters`warpx.do_pml_in_domain`

,`warpx.pml_has_particles`

, and`warpx.do_pml_j_damping`

.`absorbing_silver_mueller`

: This option can be used to set the Silver-Mueller absorbing boundary conditions. These boundary conditions are simpler and less computationally expensive than the pml, but are also less effective at absorbing the field. They only work with the Yee Maxwell solver.`damped`

: This is the recommended option in the moving direction when using the spectral solver with moving window (currently only supported along z). This boundary condition applies a damping factor to the electric and magnetic fields in the outer half of the guard cells, using a sine squared profile. As the spectral solver is by nature periodic, the damping prevents fields from wrapping around to the other end of the domain when the periodicity is not desired. This boundary condition is only valid when using the spectral solver.`pec`

: This option can be used to set a Perfect Electric Conductor at the simulation boundary. Please see the PEC theory section for more details. Note that PEC boundary is invalid at r=0 for the RZ solver. Please use`none`

option. This boundary condition does not work with the spectral solver. If an electrostatic field solve is used the boundary potentials can also be set through`boundary.potential_lo_x/y/z`

and`boundary.potential_hi_x/y/z`

(default 0).`none`

: No boundary condition is applied to the fields with the electromagnetic solver. This option must be used for the RZ-solver at r=0.`neumann`

: For the electrostatic solver, a Neumann boundary condition (with gradient of the potential equal to 0) will be applied on the specified boundary.

`boundary.particle_lo`

and`boundary.particle_hi`

(2 strings for 2D, 3 strings for 3D, absorbing by default)Options are:

`Absorbing`

: Particles leaving the boundary will be deleted.`Periodic`

: Particles leaving the boundary will re-enter from the opposite boundary. The field boundary condition must be consistenly set to periodic and both lower and upper boundaries must be periodic.`Reflecting`

: Particles leaving the boundary are reflected from the boundary back into the domain. When`boundary.reflect_all_velocities`

is false, the sign of only the normal velocity is changed, otherwise the sign of all velocities are changed.

`boundary.reflect_all_velocities`

(bool) optional (default false)For a reflecting boundary condition, this flags whether the sign of only the normal velocity is changed or all velocities.

`boundary.verboncoeur_axis_correction`

(bool) optional (default true)Whether to apply the Verboncoeur correction on the charge and current density on axis when using RZ. For nodal values (rho and Jz), the cell volume for values on axis is calculated as \(\pi*\Delta r^2/4\). In Verboncoeur JCP 174, 421-427 (2001), it is shown that using \(\pi*\Delta r^2/3\) instead will give a uniform density if the particle density is uniform.

## Additional PML parameters

`warpx.pml_ncell`

(int; default: 10)The depth of the PML, in number of cells.

`do_similar_dm_pml`

(int; default: 1)Whether or not to use an amrex::DistributionMapping for the PML grids that is similar to the mother grids, meaning that the mapping will be computed to minimize the communication costs between the PML and the mother grids.

`warpx.pml_delta`

(int; default: 10)The characteristic depth, in number of cells, over which the absorption coefficients of the PML increases.

`warpx.do_pml_in_domain`

(int; default: 0)Whether to create the PML inside the simulation area or outside. If inside, it allows the user to propagate particles in PML and to use extended PML

`warpx.pml_has_particles`

(int; default: 0)Whether to propagate particles in PML or not. Can only be done if PML are in simulation domain, i.e. if warpx.do_pml_in_domain = 1.

`warpx.do_pml_j_damping`

(int; default: 0)Whether to damp current in PML. Can only be used if particles are propagated in PML, i.e. if warpx.pml_has_particles = 1.

`warpx.v_particle_pml`

(float; default: 1)When

`warpx.do_pml_j_damping = 1`

, the assumed velocity of the particles to be absorbed in the PML, in units of the speed of light c.

`warpx.do_pml_dive_cleaning`

(bool)Whether to use divergence cleaning for E in the PML region. The value must match

`warpx.do_pml_divb_cleaning`

(either both false or both true). This option seems to be necessary in order to avoid strong Nyquist instabilities in 3D simulations with the PSATD solver, open boundary conditions and PML in all directions. 2D simulations and 3D simulations with open boundary conditions and PML only in one direction might run well even without divergence cleaning. This option is implemented only for the Cartesian PSATD solver; it is turned on by default in this case.

`warpx.do_pml_divb_cleaning`

(bool)Whether to use divergence cleaning for B in the PML region. The value must match

`warpx.do_pml_dive_cleaning`

(either both false or both true). This option seems to be necessary in order to avoid strong Nyquist instabilities in 3D simulations with the PSATD solver, open boundary conditions and PML in all directions. 2D simulations and 3D simulations with open boundary conditions and PML only in one direction might run well even without divergence cleaning. This option is implemented only for the Cartesian PSATD solver; it is turned on by default in this case.

## Embedded Boundary Conditions

`warpx.eb_implicit_function`

(string)A function of x, y, z that defines the surface of the embedded boundary. That surface lies where the function value is 0 ; the physics simulation area is where the function value is negative ; the interior of the embeddded boundary is where the function value is positive.

`warpx.eb_potential(x,y,z,t)`

(string)Only used when

`warpx.do_electrostatic=labframe`

. Gives the value of the electric potential at the surface of the embedded boundary, as a function of x, y, z and time. This function is also evaluated inside the embedded boundary. For this reason, it is important to define this function in such a way that it is constant inside the embedded boundary.

## Distribution across MPI ranks and parallelization

`warpx.numprocs`

(2 ints for 2D, 3 ints for 3D) optional (default none)This optional parameter can be used to control the domain decomposition on the coarsest level. The domain will be chopped into the exact number of pieces in each dimension as specified by this parameter. If it’s not specified, the domain decomposition will be determined by the parameters that will be discussed below. If specified, the product of the numbers must be equal to the number of MPI processes.

`amr.max_grid_size`

(integer) optional (default 128)Maximum allowable size of each

**subdomain**(expressed in number of grid points, in each direction). Each subdomain has its own ghost cells, and can be handled by a different MPI rank ; several OpenMP threads can work simultaneously on the same subdomain.If

`max_grid_size`

is such that the total number of subdomains is**larger**that the number of MPI ranks used, than some MPI ranks will handle several subdomains, thereby providing additional flexibility for**load balancing**.When using mesh refinement, this number applies to the subdomains of the coarsest level, but also to any of the finer level.

`algo.load_balance_intervals`

(string) optional (default 0)Using the Intervals parser syntax, this string defines the timesteps at which WarpX should try to redistribute the work across MPI ranks, in order to have better load balancing. Use 0 to disable load_balancing.

When performing load balancing, WarpX measures the wall time for computational parts of the PIC cycle. It then uses this data to decide how to redistribute the subdomains across MPI ranks. (Each subdomain is unchanged, but its owner is changed in order to have better performance.) This relies on each MPI rank handling several (in fact many) subdomains (see

`max_grid_size`

).

`algo.load_balance_efficiency_ratio_threshold`

(float) optional (default 1.1)Controls whether to adopt a proposed distribution mapping computed during a load balance. If the the ratio of the proposed to current distribution mapping

*efficiency*(i.e., average cost per MPI process; efficiency is a number in the range [0, 1]) is greater than the threshold value, the proposed distribution mapping is adopted. The suggested range of values is`algo.load_balance_efficiency_ratio_threshold >= 1`

, which ensures that the new distribution mapping is adopted only if doing so would improve the load balance efficiency. The higher the threshold value, the more conservative is the criterion for adoption of a proposed distribution; for example, with`algo.load_balance_efficiency_ratio_threshold = 1`

, the proposed distribution is adopted*any*time the proposed distribution improves load balancing; if instead`algo.load_balance_efficiency_ratio_threshold = 2`

, the proposed distribution is adopted only if doing so would yield a 100% to the load balance efficiency (with this threshold value, if the current efficiency is`0.45`

, the new distribution would only be adopted if the proposed efficiency were greater than`0.9`

).

`algo.load_balance_with_sfc`

(0 or 1) optional (default 0)If this is 1: use a Space-Filling Curve (SFC) algorithm in order to perform load-balancing of the simulation. If this is 0: the Knapsack algorithm is used instead.

`algo.load_balance_knapsack_factor`

(float) optional (default 1.24)Controls the maximum number of boxes that can be assigned to a rank during load balance when using the ‘knapsack’ policy for update of the distribution mapping; the maximum is load_balance_knapsack_factor*(average number of boxes per rank). For example, if there are 4 boxes per rank and load_balance_knapsack_factor=2, no more than 8 boxes can be assigned to any rank.

`algo.load_balance_costs_update`

(heuristic or timers or gpuclock) optional (default timers)If this is heuristic: load balance costs are updated according to a measure of particles and cells assigned to each box of the domain. The cost \(c\) is computed as

\[c = n_{\text{particle}} \cdot w_{\text{particle}} + n_{\text{cell}} \cdot w_{\text{cell}},\]where \(n_{\text{particle}}\) is the number of particles on the box, \(w_{\text{particle}}\) is the particle cost weight factor (controlled by

`algo.costs_heuristic_particles_wt`

), \(n_{\text{cell}}\) is the number of cells on the box, and \(w_{\text{cell}}\) is the cell cost weight factor (controlled by`algo.costs_heuristic_cells_wt`

).If this is timers: costs are updated according to in-code timers.

If this is gpuclock: [

**requires to compile with option**`-DWarpX_GPUCLOCK=ON`

] costs are measured as (max-over-threads) time spent in current deposition routine (only applies when running on GPUs).

`algo.costs_heuristic_particles_wt`

(float) optionalParticle weight factor used in Heuristic strategy for costs update; if running on GPU, the particle weight is set to a value determined from single-GPU tests on Summit, depending on the choice of solver (FDTD or PSATD) and order of the particle shape. If running on CPU, the default value is 0.9. If running on GPU, the default value is

Particle shape factor

1

2

3

FDTD/CKC

0.599

0.732

0.855

PSATD

0.425

0.595

0.75

`algo.costs_heuristic_cells_wt`

(float) optionalCell weight factor used in Heuristic strategy for costs update; if running on GPU, the cell weight is set to a value determined from single-GPU tests on Summit, depending on the choice of solver (FDTD or PSATD) and order of the particle shape. If running on CPU, the default value is 0.1. If running on GPU, the default value is

Particle shape factor

1

2

3

FDTD/CKC

0.401

0.268

0.145

PSATD

0.575

0.405

0.25

`warpx.do_dynamic_scheduling`

(0 or 1) optional (default 1)Whether to activate OpenMP dynamic scheduling.

## Math parser and user-defined constants

WarpX uses AMReX’s math parser that reads expressions in the input file. It can be used in all input parameters that consist of one or more integers or floats. Integer input expecting boolean, 0 or 1, are not parsed. Note that when multiple values are expected, the expressions are space delimited. For integer input values, the expressions are evaluated as real numbers and the final result rounded to the nearest integer. See this section of the AMReX documentation for a complete list of functions supported by the math parser.

### WarpX constants

WarpX provides a few pre-defined constants, that can be used for any parameter that consists of one or more floats.

q_e |
elementary charge |

m_e |
electron mass |

m_p |
proton mass |

m_u |
unified atomic mass unit (Dalton) |

epsilon0 |
vacuum permittivity |

mu0 |
vacuum permeability |

clight |
speed of light |

kb |
Boltzmann’s constant (J/K) |

pi |
math constant pi |

See `Source/Utils/WarpXConst.H`

for the values.

### User-defined constants

Users can define their own constants in the input file.
These constants can be used for any parameter that consists of one or more integers or floats.
User-defined constant names can contain only letters, numbers and the character `_`

.
The name of each constant has to begin with a letter. The following names are used
by WarpX, and cannot be used as user-defined constants: `x`

, `y`

, `z`

, `X`

, `Y`

, `t`

.
The values of the constants can include the predefined WarpX constants listed above as well as other user-defined constants.
For example:

`my_constants.a0 = 3.0`

`my_constants.z_plateau = 150.e-6`

`my_constants.n0 = 1.e22`

`my_constants.wp = sqrt(n0*q_e**2/(epsilon0*m_e))`

### Coordinates

Besides, for profiles that depend on spatial coordinates (the plasma momentum distribution or the laser field, see below Particle initialization and Laser initialization), the parser will interpret some variables as spatial coordinates. These are specified in the input parameter, i.e., `density_function(x,y,z)`

and `field_function(X,Y,t)`

.

The parser reads python-style expressions between double quotes, for instance
`"a0*x**2 * (1-y*1.e2) * (x>0)"`

is a valid expression where `a0`

is a
user-defined constant (see above) and `x`

and `y`

are spatial coordinates. The names are case sensitive. The factor
`(x>0)`

is `1`

where `x>0`

and `0`

where `x<=0`

. It allows the user to
define functions by intervals.
Alternatively the expression above can be written as `if(x>0, a0*x**2 * (1-y*1.e2), 0)`

.

## Particle initialization

`particles.species_names`

(strings, separated by spaces)The name of each species. This is then used in the rest of the input deck ; in this documentation we use <species_name> as a placeholder.

`particles.photon_species`

(strings, separated by spaces)List of species that are photon species, if any.

**This is required when compiling with QED=TRUE.**

`particles.use_fdtd_nci_corr`

(0 or 1) optional (default 0)Whether to activate the FDTD Numerical Cherenkov Instability corrector. Not currently available in the RZ configuration.

`particles.rigid_injected_species`

(strings, separated by spaces)List of species injected using the rigid injection method. The rigid injection method is useful when injecting a relativistic particle beam, in boosted-frame simulation ; see the input-output section for more details. For species injected using this method, particles are translated along the +z axis with constant velocity as long as their

`z`

coordinate verifies`z<zinject_plane`

. When`z>zinject_plane`

, particles are pushed in a standard way, using the specified pusher. (see the parameter`<species_name>.zinject_plane`

below)

`particles.do_tiling`

(bool) optional (default false if WarpX is compiled for GPUs, true otherwise)Controls whether tiling (‘cache blocking’) transformation is used for particles. Tiling should be on when using OpenMP and off when using GPUs.

`<species_name>.species_type`

(string) optional (default unspecified)Type of physical species. Currently, the accepted species are

`"electron"`

,`"positron"`

,`"muon"`

,`"antimuon"`

,`"photon"`

,`"neutron"`

,`"proton"`

,`"alpha"`

,`"hydrogen1"`

(a.k.a.`"protium"`

),`"hydrogen2"`

(a.k.a.`"deuterium"`

),`"hydrogen3"`

(a.k.a.`"tritium"`

),`"helium"`

,`"helium3"`

,`"helium4"`

,`"lithium"`

,`"lithium6"`

,`"lithium7"`

,`"beryllium"`

,`"beryllium9"`

,`"boron"`

,`"boron10"`

,`"boron11"`

,`"carbon"`

,`"carbon12"`

,`"carbon13"`

,`"carbon14"`

,`"nitrogen"`

,`"nitrogen14"`

,`"nitrogen15"`

,`"oxygen"`

,`"oxygen16"`

,`"oxygen17"`

,`"oxygen18"`

,`"fluorine"`

,`"fluorine19"`

,`"neon"`

,`"neon20"`

,`"neon21"`

,`"neon22"`

,`"aluminium"`

,`"argon"`

,`"copper"`

,`"xenon"`

and`"gold"`

. The difference between`"proton"`

and`"hydrogen1"`

is that the mass of the latter includes also the mass of the bound electron (same for`"alpha"`

and`"helium4"`

). When only the name of an element is specified, the mass is a weighted average of the masses of the stable isotopes. For all the elements with`Z < 11`

we provide also the stable isotopes as an option for`species_type`

(e.g.,`"helium3"`

and`"helium4"`

). Either`species_type`

or both`mass`

and`charge`

have to be specified.

`<species_name>.charge`

(float) optional (default NaN)The charge of one physical particle of this species. If

`species_type`

is specified, the charge will be set to the physical value and`charge`

is optional. When`<species>.do_field_ionization = 1`

, the physical particle charge is equal to`ionization_initial_level * charge`

, so latter parameter should be equal to q_e (which is defined in WarpX as the elementary charge in coulombs).

`<species_name>.mass`

(float) optional (default NaN)The mass of one physical particle of this species. If

`species_type`

is specified, the mass will be set to the physical value and`mass`

is optional.

`<species_name>.xmin,ymin,zmin`

and`<species_name>.xmax,ymax,zmax`

(float) optional (default unlimited)When

`<species_name>.xmin`

and`<species_name>.xmax`

are set, they delimit the region within which particles are injected. If periodic boundary conditions are used in direction`i`

, then the default (i.e. if the range is not specified) range will be the simulation box,`[geometry.prob_hi[i], geometry.prob_lo[i]]`

.

`<species_name>.injection_style`

(string; default:`none`

)Determines how the (macro-)particles will be injected in the simulation. The number of particles per cell is always given with respect to the coarsest level (level 0/mother grid), even if particles are immediately assigned to a refined patch.

The options are:

`NUniformPerCell`

: injection with a fixed number of evenly-spaced particles per cell. This requires the additional parameter`<species_name>.num_particles_per_cell_each_dim`

.`NRandomPerCell`

: injection with a fixed number of randomly-distributed particles per cell. This requires the additional parameter`<species_name>.num_particles_per_cell`

.`SingleParticle`

: Inject a single macroparticle. This requires the additional parameters:`<species_name>.single_particle_pos`

(3 doubles, particle 3D position [meter])`<species_name>.single_particle_u`

(3 doubles, particle 3D normalized momentum, i.e. \(\gamma \beta\))`<species_name>.single_particle_weight`

( double, macroparticle weight, i.e. number of physical particles it represents)`MultipleParticles`

: Inject multiple macroparticles. This requires the additional parameters:`<species_name>.multiple_particles_pos_x`

(list of doubles, X positions of the particles [meter])`<species_name>.multiple_particles_pos_y`

(list of doubles, Y positions of the particles [meter])`<species_name>.multiple_particles_pos_z`

(list of doubles, Z positions of the particles [meter])`<species_name>.multiple_particles_ux`

(list of doubles, X normalized momenta of the particles, i.e. \(\gamma \beta_x\))`<species_name>.multiple_particles_uy`

(list of doubles, Y normalized momenta of the particles, i.e. \(\gamma \beta_y\))`<species_name>.multiple_particles_uz`

(list of doubles, Z normalized momenta of the particles, i.e. \(\gamma \beta_z\))`<species_name>.multiple_particles_weight`

(list of doubles, macroparticle weights, i.e. number of physical particles each represents)`gaussian_beam`

: Inject particle beam with gaussian distribution in space in all directions. This requires additional parameters:`<species_name>.q_tot`

(beam charge),`<species_name>.npart`

(number of particles in the beam),`<species_name>.x/y/z_m`

(average position in x/y/z),`<species_name>.x/y/z_rms`

(standard deviation in x/y/z),`<species_name>.x/y/z_cut`

(optional, particles with`abs(x-x_m) > x_cut*x_rms`

are not injected, same for y and z.`<species_name>.q_tot`

is the charge of the un-cut beam, so that cutting the distribution is likely to result in a lower total charge), and optional arguments`<species_name>.do_symmetrize`

(whether to symmetrize the beam) and`<species_name>.symmetrization_order`

(order of symmetrization, default is 4, can be 4 or 8). If`<species_name>.do_symmetrize`

is 0, no symmetrization occurs. If`<species_name>.do_symmetrize`

is 1, then the beam is symmetrized according to the value of`<species_name>.symmetrization_order`

. If set to 4, symmetrization is in the x and y direction, (x,y) (-x,y) (x,-y) (-x,-y). If set to 8, symmetrization is also done with x and y exchanged, (y,x), (-y,x), (y,-x), (-y,-x)).`external_file`

: Inject macroparticles with properties (mass, charge, position, and momentum - \(\gamma \beta m c\)) read from an external openPMD file. With it users can specify the additional arguments:`<species_name>.injection_file`

(string) openPMD file name and`<species_name>.charge`

(double) optional (default is read from openPMD file) when set this will be the charge of the physical particle represented by the injected macroparticles.`<species_name>.mass`

(double) optional (default is read from openPMD file) when set this will be the charge of the physical particle represented by the injected macroparticles.`<species_name>.z_shift`

(double) optional (default is no shift) when set this value will be added to the longitudinal,`z`

, position of the particles. Warning:`q_tot!=0`

is not supported with the`external_file`

injection style. If a value is provided, it is ignored and no re-scaling is done. The external file must include the species`openPMD::Record`

labeled`position`

and`momentum`

(double arrays), with dimensionality and units set via`openPMD::setUnitDimension`

and`setUnitSI`

. If the external file also contains`openPMD::Records`

for`mass`

and`charge`

(constant double scalars) then the species will use these, unless overwritten in the input file (see`<species_name>.mass`

,`<species_name>.charge`

or`<species_name>.species_type`

). The`external_file`

option is currently implemented for 2D, 3D and RZ geometries, with record components in the cartesian coordinates`(x,y,z)`

for 3D and RZ, and`(x,z)`

for 2D. For more information on the openPMD format and how to build WarpX with it, please visit the install section.`NFluxPerCell`

: Continuously inject a flux of macroparticles from a planar surface. This requires the additional parameters:`<species_name>.flux_profile`

(see the description of this parameter further below)`<species_name>.surface_flux_pos`

(double, location of the injection plane [meter])`<species_name>.flux_normal_axis`

(x, y, or z for 3D, x or z for 2D, or r, t, or z for RZ. When flux_normal_axis is r or t, the x and y components of the user-specified momentum distribution are interpreted as the r and t components respectively)`<species_name>.flux_direction`

(-1 or +1, direction of flux relative to the plane)`<species_name>.num_particles_per_cell`

(double)`<species_name>.flux_tmin`

(double, Optional time at which the flux will be turned on. Ignored when negative.)`<species_name>.flux_tmax`

(double, Optional time at which the flux will be turned off. Ignored when negative.)`none`

: Do not inject macro-particles (for example, in a simulation that starts with neutral, ionizable atoms, one may want to create the electrons species – where ionized electrons can be stored later on – without injecting electron macro-particles).

`<species_name>.num_particles_per_cell_each_dim`

(3 integers in 3D and RZ, 2 integers in 2D)With the NUniformPerCell injection style, this specifies the number of particles along each axis within a cell. Note that for RZ, the three axis are radius, theta, and z and that the recommended number of particles per theta is at least two times the number of azimuthal modes requested. (It is recommended to do a convergence scan of the number of particles per theta)

`<species_name>.random_theta`

(bool) optional (default 1)When using RZ geometry, whether to randomize the azimuthal position of particles. This is used when

`<species_name>.injection_style = NUniformPerCell`

.

`<species_name>.do_splitting`

(bool) optional (default 0)Split particles of the species when crossing the boundary from a lower resolution domain to a higher resolution domain.

Currently implemented on CPU only.

`<species_name>.do_continuous_injection`

(0 or 1)Whether to inject particles during the simulation, and not only at initialization. This can be required with a moving window and/or when running in a boosted frame.

`<species_name>.initialize_self_fields`

(0 or 1)Whether to calculate the space-charge fields associated with this species at the beginning of the simulation. The fields are calculated for the mean gamma of the species.

`<species_name>.self_fields_required_precision`

(float, default: 1.e-11)The relative precision with which the initial space-charge fields should be calculated. More specifically, the initial space-charge fields are computed with an iterative Multi-Level Multi-Grid (MLMG) solver. For highly-relativistic beams, this solver can fail to reach the default precision within a reasonable time ; in that case, users can set a relaxed precision requirement through

`self_fields_required_precision`

.

`<species_name>.self_fields_absolute_tolerance`

(float, default: 0.0)The absolute tolerance with which the space-charge fields should be calculated in units of \(\mathrm{V/m}^2\). More specifically, the acceptable residual with which the solution can be considered converged. In general this should be left as the default, but in cases where the simulation state changes very little between steps it can occur that the initial guess for the MLMG solver is so close to the converged value that it fails to improve that solution sufficiently to reach the

`self_fields_required_precision`

value.

`<species_name>.self_fields_max_iters`

(integer, default: 200)Maximum number of iterations used for MLMG solver for initial space-charge fields calculation. In case if MLMG converges but fails to reach the desired

`self_fields_required_precision`

, this parameter may be increased.

`<species_name>.profile`

(string)Density profile for this species. The options are:

`constant`

: Constant density profile within the box, or between`<species_name>.xmin`

and`<species_name>.xmax`

(and same in all directions). This requires additional parameter`<species_name>.density`

. i.e., the plasma density in \(m^{-3}\).`predefined`

: Predefined density profile. This requires additional parameters`<species_name>.predefined_profile_name`

and`<species_name>.predefined_profile_params`

. Currently, only a parabolic channel density profile is implemented.`parse_density_function`

: the density is given by a function in the input file. It requires additional argument`<species_name>.density_function(x,y,z)`

, which is a mathematical expression for the density of the species, e.g.`electrons.density_function(x,y,z) = "n0+n0*x**2*1.e12"`

where`n0`

is a user-defined constant, see above. WARNING: where`density_function(x,y,z)`

is close to zero, particles will still be injected between`xmin`

and`xmax`

etc., with a null weight. This is undesirable because it results in useless computing. To avoid this, see option`density_min`

below.

`<species_name>.flux_profile`

(string)Defines the expression of the flux, when using

`<species_name>.injection_style=NFluxPerCell`

`constant`

: Constant flux. This requires the additional parameter`<species_name>.flux`

. i.e., the injection flux in \(m^{-2}.s^{-1}\).`parse_flux_function`

: the flux is given by a function in the input file. It requires the additional argument`<species_name>.flux_function(x,y,z,t)`

, which is a mathematical expression for the flux of the species.

`<species_name>.density_min`

(float) optional (default 0.)Minimum plasma density. No particle is injected where the density is below this value.

`<species_name>.density_max`

(float) optional (default infinity)Maximum plasma density. The density at each point is the minimum between the value given in the profile, and density_max.

`<species_name>.radially_weighted`

(bool) optional (default true)Whether particle’s weight is varied with their radius. This only applies to cylindrical geometry. The only valid value is true.

`<species_name>.momentum_distribution_type`

(string)Distribution of the normalized momentum (u=p/mc) for this species. The options are:

`at_rest`

: Particles are initialized with zero momentum.`constant`

: constant momentum profile. This can be controlled with the additional parameters`<species_name>.ux`

,`<species_name>.uy`

and`<species_name>.uz`

, the normalized momenta in the x, y and z direction respectively, which are all`0.`

by default.`uniform`

: uniform probability distribution between a minumum and a maximum value. The x, y and z directions are sampled independently and the final momentum space is a cuboid. The parameters that control the minimum and maximum domain of the distribution are`<species_name>.u<x,y,z>_min`

and`<species_name>.u<x,y,z>_max`

in each direction respectively (e.g.,`<species_name>.uz_min = 0.2`

and`<species_name>.uz_max = 0.4`

to control the generation along the`z`

direction). All the parameters default to`0`

.`gaussian`

: gaussian momentum distribution in all 3 directions. This can be controlled with the additional arguments for the average momenta along each direction`<species_name>.ux_m`

,`<species_name>.uy_m`

and`<species_name>.uz_m`

as well as standard deviations along each direction`<species_name>.ux_th`

,`<species_name>.uy_th`

and`<species_name>.uz_th`

. These 6 parameters are all`0.`

by default.`gaussianflux`

: Gaussian momentum flux distribution, which is Gaussian in the plane and v*Gaussian normal to the plane. It can only be used when`injection_style = NFluxPerCell`

. This can be controlled with the additional arguments to specify the plane’s orientation,`<species_name>.flux_normal_axis`

and`<species_name>.flux_direction`

, for the average momenta along each direction`<species_name>.ux_m`

,`<species_name>.uy_m`

and`<species_name>.uz_m`

, as well as standard deviations along each direction`<species_name>.ux_th`

,`<species_name>.uy_th`

and`<species_name>.uz_th`

.`ux_m`

,`uy_m`

,`uz_m`

,`ux_th`

,`uy_th`

and`uz_th`

are all`0.`

by default.`maxwell_boltzmann`

: Maxwell-Boltzmann distribution that takes a dimensionless temperature parameter \(\theta\) as an input, where \(\theta = \frac{k_\mathrm{B} \cdot T}{m \cdot c^2}\), \(T\) is the temperature in Kelvin, \(k_\mathrm{B}\) is the Boltzmann constant, \(c\) is the speed of light, and \(m\) is the mass of the species. Theta is specified by a combination of`<species_name>.theta_distribution_type`

,`<species_name>.theta`

, and`<species_name>.theta_function(x,y,z)`

(see below). For values of \(\theta > 0.01\), errors due to ignored relativistic terms exceed 1%. Temperatures less than zero are not allowed. The plasma can be initialized to move at a bulk velocity \(\beta = v/c\). The speed is specified by the parameters`<species_name>.beta_distribution_type`

,`<species_name>.beta`

, and`<species_name>.beta_function(x,y,z)`

(see below). \(\beta\) can be positive or negative and is limited to the range \(-1 < \beta < 1\). The direction of the velocity field is given by`<species_name>.bulk_vel_dir = (+/-) 'x', 'y', 'z'`

, and must be the same across the domain. Please leave no whitespace between the sign and the character on input. A direction without a sign will be treated as positive. The MB distribution is initialized in the drifting frame by sampling three Gaussian distributions in each dimension using, the Box Mueller method, and then the distribution is transformed to the simulation frame using the flipping method. The flipping method can be found in Zenitani 2015 section III. B. (Phys. Plasmas 22, 042116). By default,`beta`

is equal to`0.`

and`bulk_vel_dir`

is`+x`

.Note that though the particles may move at relativistic speeds in the simulation frame, they are not relativistic in the drift frame. This is as opposed to the Maxwell Juttner setting, which initializes particles with relativistic momentums in their drifting frame.

`maxwell_juttner`

: Maxwell-Juttner distribution for high temperature plasma that takes a dimensionless temperature parameter \(\theta\) as an input, where \(\theta = \frac{k_\mathrm{B} \cdot T}{m \cdot c^2}\), \(T\) is the temperature in Kelvin, \(k_\mathrm{B}\) is the Boltzmann constant, and \(m\) is the mass of the species. Theta is specified by a combination of`<species_name>.theta_distribution_type`

,`<species_name>.theta`

, and`<species_name>.theta_function(x,y,z)`

(see below). The Sobol method used to generate the distribution will not terminate for \(\theta \lesssim 0.1\), and the code will abort if it encounters a temperature below that threshold. The Maxwell-Boltzmann distribution is recommended for temperatures in the range \(0.01 < \theta < 0.1\). Errors due to relativistic effects can be expected to approximately between 1% and 10%. The plasma can be initialized to move at a bulk velocity \(\beta = v/c\). The speed is specified by the parameters`<species_name>.beta_distribution_type`

,`<species_name>.beta`

, and`<species_name>.beta_function(x,y,z)`

(see below). \(\beta\) can be positive or negative and is limited to the range \(-1 < \beta < 1\). The direction of the velocity field is given by`<species_name>.bulk_vel_dir = (+/-) 'x', 'y', 'z'`

, and must be the same across the domain. Please leave no whitespace between the sign and the character on input. A direction without a sign will be treated as positive. The MJ distribution will be initialized in the moving frame using the Sobol method, and then the distribution will be transformed to the simulation frame using the flipping method. Both the Sobol and the flipping method can be found in Zenitani 2015 (Phys. Plasmas 22, 042116). By default,`beta`

is equal to`0.`

and`bulk_vel_dir`

is`+x`

.Please take notice that particles initialized with this setting can be relativistic in two ways. In the simulation frame, they can drift with a relativistic speed beta. Then, in the drifting frame they are still moving with relativistic speeds due to high temperature. This is as opposed to the Maxwell Boltzmann setting, which initializes non-relativistic plasma in their relativistic drifting frame.

`radial_expansion`

: momentum depends on the radial coordinate linearly. This can be controlled with additional parameter`u_over_r`

which is the slope (`0.`

by default).`parse_momentum_function`

: the momentum \(u = (u_{x},u_{y},u_{z})=(\gamma v_{x}/c,\gamma v_{y}/c,\gamma v_{z}/c)\) is given by a function in the input file. It requires additional arguments`<species_name>.momentum_function_ux(x,y,z)`

,`<species_name>.momentum_function_uy(x,y,z)`

and`<species_name>.momentum_function_uz(x,y,z)`

, which gives the distribution of each component of the momentum as a function of space.

`<species_name>.theta_distribution_type`

(string) optional (default`constant`

)Only read if

`<species_name>.momentum_distribution_type`

is`maxwell_boltzmann`

or`maxwell_juttner`

. See documentation for these distributions (above) for constraints on values of theta. Temperatures less than zero are not allowed.If

`constant`

, use a constant temperature, given by the required float parameter`<species_name>.theta`

.If

`parser`

, use a spatially-dependent analytic parser function, given by the required parameter`<species_name>.theta_function(x,y,z)`

.

`<species_name>.beta_distribution_type`

(string) optional (default`constant`

)Only read if

`<species_name>.momentum_distribution_type`

is`maxwell_boltzmann`

or`maxwell_juttner`

. See documentation for these distributions (above) for constraints on values of beta.If

`constant`

, use a constant speed, given by the required float parameter`<species_name>.beta`

.If

`parser`

, use a spatially-dependent analytic parser function, given by the required parameter`<species_name>.beta_function(x,y,z)`

.

`<species_name>.zinject_plane`

(float)Only read if

`<species_name>`

is in`particles.rigid_injected_species`

. Injection plane when using the rigid injection method. See`particles.rigid_injected_species`

above.

`<species_name>.rigid_advance`

(bool)Only read if

`<species_name>`

is in`particles.rigid_injected_species`

.If

`false`

, each particle is advanced with its own velocity`vz`

until it reaches`zinject_plane`

.If

`true`

, each particle is advanced with the average speed of the species`vzbar`

until it reaches`zinject_plane`

.

`species_name.predefined_profile_name`

(string)Only read if

`<species_name>.profile`

is`predefined`

.If

`parabolic_channel`

, the plasma profile is a parabolic profile with cosine-like ramps at the beginning and the end of the profile. The density is given by\[n = n_0 n(x,y) n(z-z_0)\]with

\[n(x,y) = 1 + 4\frac{x^2+y^2}{k_p^2 R_c^4}\]where \(k_p\) is the plasma wavenumber associated with density \(n_0\). Here, with \(z_0\) as the start of the plasma, \(n(z-z_0)\) is a cosine-like up-ramp from \(0\) to \(L_{ramp,up}\), constant to \(1\) from \(L_{ramp,up}\) to \(L_{ramp,up} + L_{plateau}\) and a cosine-like down-ramp from \(L_{ramp,up} + L_{plateau}\) to \(L_{ramp,up} + L_{plateau}+L_{ramp,down}\). All parameters are given in

`predefined_profile_params`

.

`<species_name>.predefined_profile_params`

(list of float)Parameters for the predefined profiles.

If

`species_name.predefined_profile_name`

is`parabolic_channel`

,`predefined_profile_params`

contains a space-separated list of the following parameters, in this order: \(z_0\) \(L_{ramp,up}\) \(L_{plateau}\) \(L_{ramp,down}\) \(R_c\) \(n_0\)

`<species_name>.do_backward_propagation`

(bool)Inject a backward-propagating beam to reduce the effect of charge-separation fields when running in the boosted frame. See examples.

`<species_name>.split_type`

(int) optional (default 0)Splitting technique. When 0, particles are split along the simulation axes (4 particles in 2D, 6 particles in 3D). When 1, particles are split along the diagonals (4 particles in 2D, 8 particles in 3D).

`<species_name>.do_not_deposit`

(0 or 1 optional; default 0)If 1 is given, both charge deposition and current deposition will not be done, thus that species does not contribute to the fields.

`<species_name>.do_not_gather`

(0 or 1 optional; default 0)If 1 is given, field gather from grids will not be done, thus that species will not be affected by the field on grids.

`<species_name>.do_not_push`

(0 or 1 optional; default 0)If 1 is given, this species will not be pushed by any pusher during the simulation.

`<species_name>.addIntegerAttributes`

(list of string)User-defined integer particle attribute for species,

`species_name`

. These integer attributes will be initialized with user-defined functions when the particles are generated. If the user-defined integer attribute is`<int_attrib_name>`

then the following required parameter must be specified to initialize the attribute. *`<species_name>.attribute.<int_attrib_name>(x,y,z,ux,uy,uz,t)`

(string)`t`

represents the physical time in seconds during the simulation.`x`

,`y`

,`z`

represent particle positions in the unit of meter.`ux`

,`uy`

,`uz`

represent the particle momenta in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. E.g. If`electrons.addIntegerAttributes = upstream`

and`electrons.upstream(x,y,z,ux,uy,uz,t) = (x>0.0)*1`

is provided then, an integer attribute`upstream`

is added to all electron particles and when these particles are generated, the particles with position less than`0`

are assigned a value of`1`

.

`<species_name>.addRealAttributes`

(list of string)User-defined real particle attribute for species,

`species_name`

. These real attributes will be initialized with user-defined functions when the particles are generated. If the user-defined real attribute is`<real_attrib_name>`

then the following required parameter must be specified to initialize the attribute.`<species_name>.attribute.<real_attrib_name>(x,y,z,ux,uy,uz,t)`

(string)`t`

represents the physical time in seconds during the simulation.`x`

,`y`

,`z`

represent particle positions in the unit of meter.`ux`

,`uy`

,`uz`

represent the particle momenta in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light.

`<species>.save_particles_at_xlo/ylo/zlo`

,`<species>.save_particles_at_xhi/yhi/zhi`

and`<species>.save_particles_at_eb`

(0 or 1 optional, default 0)If 1 particles of this species will be copied to the scraped particle buffer for the specified boundary if they leave the simulation domain in the specified direction.

**If USE_EB=TRUE**the`save_particles_at_eb`

flag can be set to 1 to also save particle data for the particles of this species that impact the embedded boundary. The scraped particle buffer can be used to track particle fluxes out of the simulation. The particle data can be written out by setting up a`BoundaryScrapingDiagnostic`

. It is also accessible via the Python interface. The function`get_particle_boundary_buffer`

, found in the`picmi.Simulation`

class as`sim.extension.get_particle_boundary_buffer()`

, can be used to access the scraped particle buffer. An entry is included for every particle in the buffer of the timestep at which the particle was scraped. This can be accessed by passing the argument`comp_name="step_scraped"`

to the above mentioned function.Note

When accessing the data via Python, the scraped particle buffer relies on the user to clear the buffer after processing the data. The buffer will grow unbounded as particles are scraped and therefore could lead to memory issues if not periodically cleared. To clear the buffer call

`warpx_clearParticleBoundaryBuffer()`

.

`<species>.do_field_ionization`

(0 or 1) optional (default 0)Do field ionization for this species (using the ADK theory).

`<species>.physical_element`

(string)Only read if do_field_ionization = 1. Symbol of chemical element for this species. Example: for Helium, use

`physical_element = He`

. All the elements up to atomic number Z=100 (Fermium) are supported.

`<species>.ionization_product_species`

(string)Only read if do_field_ionization = 1. Name of species in which ionized electrons are stored. This species must be created as a regular species in the input file (in particular, it must be in particles.species_names).

`<species>.ionization_initial_level`

(int) optional (default 0)Only read if do_field_ionization = 1. Initial ionization level of the species (must be smaller than the atomic number of chemical element given in physical_element).

`<species>.do_classical_radiation_reaction`

(int) optional (default 0)Enables Radiation Reaction (or Radiation Friction) for the species. Species must be either electrons or positrons. Boris pusher must be used for the simulation. If both

`<species>.do_classical_radiation_reaction`

and`<species>.do_qed_quantum_sync`

are enabled, then the classical module will be used when the particle’s chi parameter is below`qed_qs.chi_min`

, the discrete quantum module otherwise.

`<species>.do_qed_quantum_sync`

(int) optional (default 0)Enables Quantum synchrotron emission for this species. Quantum synchrotron lookup table should be either generated or loaded from disk to enable this process (see “Lookup tables for QED modules” section below). <species> must be either an electron or a positron species.

**This feature requires to compile with QED=TRUE**

`<species>.do_qed_breit_wheeler`

(int) optional (default 0)Enables non-linear Breit-Wheeler process for this species. Breit-Wheeler lookup table should be either generated or loaded from disk to enable this process (see “Lookup tables for QED modules” section below). <species> must be a photon species.

**This feature requires to compile with QED=TRUE**

`<species>.qed_quantum_sync_phot_product_species`

(string)If an electron or a positron species has the Quantum synchrotron process, a photon product species must be specified (the name of an existing photon species must be provided)

**This feature requires to compile with QED=TRUE**

`<species>.qed_breit_wheeler_ele_product_species`

(string)If a photon species has the Breit-Wheeler process, an electron product species must be specified (the name of an existing electron species must be provided)

**This feature requires to compile with QED=TRUE**

`<species>.qed_breit_wheeler_pos_product_species`

(string)If a photon species has the Breit-Wheeler process, a positron product species must be specified (the name of an existing positron species must be provided).

**This feature requires to compile with QED=TRUE**

`<species>.do_resampling`

(0 or 1) optional (default 0)If 1 resampling is performed for this species. This means that the number of macroparticles will be reduced at specific timesteps while preserving the distribution function as much as possible (in particular the weight of the remaining particles will be increased on average). This can be useful in situations with continuous creation of particles (e.g. with ionization or with QED effects). At least one resampling trigger (see below) must be specified to actually perform resampling.

`<species>.resampling_algorithm`

(string) optional (default leveling_thinning)The algorithm used for resampling. Currently there is only one option, which is already set by default:

`leveling_thinning`

This algorithm is defined in Muraviev et al., arXiv:2006.08593 (2020). It has two parameters:`<species>.resampling_algorithm_target_ratio`

(float) optional (default 1.5)This

**roughly**corresponds to the ratio between the number of particles before and after resampling.

`<species>.resampling_algorithm_min_ppc`

(int) optional (default 1)Resampling is not performed in cells with a number of macroparticles strictly smaller than this parameter.

`<species>.resampling_trigger_intervals`

(string) optional (default 0)Using the Intervals parser syntax, this string defines timesteps at which resampling is performed.

`<species>.resampling_trigger_max_avg_ppc`

(float) optional (default infinity)Resampling is performed everytime the number of macroparticles per cell of the species averaged over the whole simulation domain exceeds this parameter.

## Laser initialization

`lasers.names`

(list of string)Name of each laser. This is then used in the rest of the input deck ; in this documentation we use <laser_name> as a placeholder. The parameters below must be provided for each laser pulse.

`<laser_name>.position`

(3 floats in 3D and 2D ; in meters)The coordinates of one of the point of the antenna that will emit the laser. The plane of the antenna is entirely defined by

`<laser_name>.position`

and`<laser_name>.direction`

.`<laser_name>.position`

also corresponds to the origin of the coordinates system for the laser tranverse profile. For instance, for a Gaussian laser profile, the peak of intensity will be at the position given by`<laser_name>.position`

. This variable can thus be used to shift the position of the laser pulse transversally.Note

In 2D,

`<laser_name>.position`

is still given by 3 numbers, but the second number is ignored.When running a

**boosted-frame simulation**, provide the value of`<laser_name>.position`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame. Note that, in this case, the laser antenna will be moving, in the boosted frame.

`<laser_name>.polarization`

(3 floats in 3D and 2D)The coordinates of a vector that points in the direction of polarization of the laser. The norm of this vector is unimportant, only its direction matters.

Note

Even in 2D, all the 3 components of this vectors are important (i.e. the polarization can be orthogonal to the plane of the simulation).

`<laser_name>.direction`

(3 floats in 3D)The coordinates of a vector that points in the propagation direction of the laser. The norm of this vector is unimportant, only its direction matters.

The plane of the antenna that will emit the laser is orthogonal to this vector.

Warning

When running

**boosted-frame simulations**,`<laser_name>.direction`

should be parallel to`warpx.boost_direction`

, for now.

`<laser_name>.e_max`

(float ; in V/m)Peak amplitude of the laser field.

For a laser with a wavelength \(\lambda = 0.8\,\mu m\), the peak amplitude is related to \(a_0\) by:

\[E_{max} = a_0 \frac{2 \pi m_e c^2}{e\lambda} = a_0 \times (4.0 \cdot 10^{12} \;V.m^{-1})\]When running a

**boosted-frame simulation**, provide the value of`<laser_name>.e_max`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame.

`<laser_name>.a0`

(float ; dimensionless)Peak normalized amplitude of the laser field (given in the lab frame, just as

`e_max`

above). See the description of`<laser_name>.e_max`

for the conversion between`a0`

and`e_max`

. Exactly one of`a0`

and`e_max`

must be specified.

`<laser_name>.wavelength`

(float; in meters)The wavelength of the laser in vacuum.

When running a

**boosted-frame simulation**, provide the value of`<laser_name>.wavelength`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame.

`<laser_name>.profile`

(string)The spatio-temporal shape of the laser. The options that are currently implemented are:

`"Gaussian"`

: The transverse and longitudinal profiles are Gaussian.`"parse_field_function"`

: the laser electric field is given by a function in the input file. It requires additional argument`<laser_name>.field_function(X,Y,t)`

, which is a mathematical expression , e.g.`<laser_name>.field_function(X,Y,t) = "a0*X**2 * (X>0) * cos(omega0*t)"`

where`a0`

and`omega0`

are a user-defined constant, see above. The profile passed here is the full profile, not only the laser envelope.`t`

is time and`X`

and`Y`

are coordinates orthogonal to`<laser_name>.direction`

(not necessarily the x and y coordinates of the simulation). All parameters above are required, but none of the parameters below are used when`<laser_name>.parse_field_function=1`

. Even though`<laser_name>.wavelength`

and`<laser_name>.e_max`

should be included in the laser function, they still have to be specified as they are used for numerical purposes.`"from_file"`

: the electric field of the laser is read from an external file. Currently both the lasy format as well as a custom binary format are supported. It requires to provide the name of the file to load setting the additional parameter`<laser_name>.binary_file_name`

or`<laser_name>.lasy_file_name`

(string). It accepts an optional parameter`<laser_name>.time_chunk_size`

(int), supported for both lasy and binary files; this allows to read only time_chunk_size timesteps from the file. New timesteps are read as soon as they are needed.The default value is automatically set to the number of timesteps contained in the file (i.e. only one read is performed at the beginning of the simulation). It also accepts the optional parameter

`<laser_name>.delay`

(float; in seconds), which allows delaying (`delay > 0`

) or anticipating (`delay < 0`

) the laser by the specified amount of time.Details about the usage of the lasy format: lasy can produce either 3D Cartesian files or RZ files. WarpX can read both types of files independently of the geometry in which it was compiled (e.g. WarpX compiled with

`WarpX_DIMS=RZ`

can read 3D Cartesian lasy files). In the case where WarpX is compiled in 2D (or 1D) Cartesian, the laser antenna will emit the field values that correspond to the slice`y=0`

in the lasy file (and`x=0`

in the 1D case). One can generate a lasy file from Python, see an example at`Examples/Tests/laser_injection_from_file`

.Details about the usage of the binary format: The external binary file should provide E(x,y,t) on a rectangular (necessarily uniform) grid. The code performs a bi-linear (in 2D) or tri-linear (in 3D) interpolation to set the field values. x,y,t are meant to be in S.I. units, while the field value is meant to be multiplied by

`<laser_name>.e_max`

(i.e. in most cases the maximum of abs(E(x,y,t)) should be 1, so that the maximum field intensity can be set straightforwardly with`<laser_name>.e_max`

). The binary file has to respect the following format:flag to indicate the grid is uniform(1 byte, 0 means non-uniform, !=0 means uniform) - only uniform is supported

nt, number of timesteps (uint32_t, must be >=2)

nx, number of points along x (uint32_t, must be >=2)

ny, number of points along y (uint32_t, must be 1 for 2D simulations and >=2 for 3D simulations)

timesteps (double[2]=[t_min,t_max])

x_coords (double[2]=[x_min,x_max])

y_coords (double[1] in 2D, double[2]=[y_min,y_max] in 3D)

field_data (double[nt * nx * ny], with nt being the slowest coordinate).

A binary file can be generated from Python, see an example at

`Examples/Tests/laser_injection_from_file`

`<laser_name>.profile_t_peak`

(float; in seconds)The time at which the laser reaches its peak intensity, at the position given by

`<laser_name>.position`

(only used for the`"gaussian"`

profile)When running a

**boosted-frame simulation**, provide the value of`<laser_name>.profile_t_peak`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame.

`<laser_name>.profile_duration`

(float ; in seconds)The duration of the laser pulse for the

`"gaussian"`

profile, defined as \(\tau\) below:\[E(\boldsymbol{x},t) \propto \exp\left( -\frac{(t-t_{peak})^2}{\tau^2} \right)\]Note that \(\tau\) relates to the full width at half maximum (FWHM) of

*intensity*, which is closer to pulse length measurements in experiments, as \(\tau = \mathrm{FWHM}_I / \sqrt{2\ln(2)}\) \(\approx \mathrm{FWHM}_I / 1.174\).When running a

**boosted-frame simulation**, provide the value of`<laser_name>.profile_duration`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame.

`<laser_name>.profile_waist`

(float ; in meters)The waist of the transverse Gaussian laser profile, defined as \(w_0\) :

\[E(\boldsymbol{x},t) \propto \exp\left( -\frac{\boldsymbol{x}_\perp^2}{w_0^2} \right)\]

`<laser_name>.profile_focal_distance`

(float; in meters)The distance from

`laser_position`

to the focal plane. (where the distance is defined along the direction given by`<laser_name>.direction`

.)Use a negative number for a defocussing laser instead of a focussing laser.

When running a

**boosted-frame simulation**, provide the value of`<laser_name>.profile_focal_distance`

in the laboratory frame, and use`warpx.gamma_boost`

to automatically perform the conversion to the boosted frame.

`<laser_name>.phi0`

(float; in radians) optional (default 0.)The Carrier Envelope Phase, i.e. the phase of the laser oscillation, at the position where the laser envelope is maximum (only used for the

`"gaussian"`

profile)

`<laser_name>.stc_direction`

(3 floats) optional (default 1. 0. 0.)Direction of laser spatio-temporal couplings. See definition in Akturk et al., Opt Express, vol 12, no 19 (2004).

`<laser_name>.zeta`

(float; in meters.seconds) optional (default 0.)Spatial chirp at focus in direction

`<laser_name>.stc_direction`

. See definition in Akturk et al., Opt Express, vol 12, no 19 (2004).

`<laser_name>.beta`

(float; in seconds) optional (default 0.)Angular dispersion (or angular chirp) at focus in direction

`<laser_name>.stc_direction`

. See definition in Akturk et al., Opt Express, vol 12, no 19 (2004).

`<laser_name>.phi2`

(float; in seconds**2) optional (default 0.)Temporal chirp at focus. See definition in Akturk et al., Opt Express, vol 12, no 19 (2004).

`<laser_name>.do_continuous_injection`

(0 or 1) optional (default 0).Whether or not to use continuous injection. If the antenna starts outside of the simulation domain but enters it at some point (due to moving window or moving antenna in the boosted frame), use this so that the laser antenna is injected when it reaches the box boundary. If running in a boosted frame, this requires the boost direction, moving window direction and laser propagation direction to be along z. If not running in a boosted frame, this requires the moving window and laser propagation directions to be the same (x, y or z)

`<laser_name>.min_particles_per_mode`

(int) optional (default 4)When using the RZ version, this specifies the minimum number of particles per angular mode. The laser particles are loaded into radial spokes, with the number of spokes given by min_particles_per_mode*(warpx.n_rz_azimuthal_modes-1).

`lasers.deposit_on_main_grid`

(int) optional (default 0)When using mesh refinement, whether the antenna that emits the laser deposits charge/current only on the main grid (i.e. level 0), or also on the higher mesh-refinement levels.

`warpx.num_mirrors`

(int) optional (default 0)Users can input perfect mirror condition inside the simulation domain. The number of mirrors is given by

`warpx.num_mirrors`

. The mirrors are orthogonal to the z direction. The following parameters are required when`warpx.num_mirrors`

is >0.

`warpx.mirror_z`

(list of float) required if`warpx.num_mirrors>0`

`z`

location of the front of the mirrors.

`warpx.mirror_z_width`

(list of float) required if`warpx.num_mirrors>0`

`z`

width of the mirrors.

`warpx.mirror_z_npoints`

(list of int) required if`warpx.num_mirrors>0`

In the boosted frame, depending on gamma_boost,

`warpx.mirror_z_width`

can be smaller than the cell size, so that the mirror would not work. This parameter is the minimum number of points for the mirror. If`mirror_z_width < dz/cell_size`

, the upper bound of the mirror is increased so that it contains at least`mirror_z_npoints`

.

## External fields

### Grid initialization

`warpx.B_ext_grid_init_style`

(string) optional (default is “default”)This parameter determines the type of initialization for the external magnetic field. The “default” style initializes the external magnetic field (Bx,By,Bz) to (0.0, 0.0, 0.0). The string can be set to “constant” if a constant magnetic field is required to be set at initialization. If set to “constant”, then an additional parameter, namely,

`warpx.B_external_grid`

must be specified. If set to`parse_B_ext_grid_function`

, then a mathematical expression can be used to initialize the external magnetic field on the grid. It requires additional parameters in the input file, namely,`warpx.Bx_external_grid_function(x,y,z)`

,`warpx.By_external_grid_function(x,y,z)`

,`warpx.Bz_external_grid_function(x,y,z)`

to initialize the external magnetic field for each of the three components on the grid. Constants required in the expression can be set using`my_constants`

. For example, if`warpx.Bx_external_grid_function(x,y,z)=Bo*x + delta*(y + z)`

then the constants Bo and delta required in the above equation can be set using`my_constants.Bo=`

and`my_constants.delta=`

in the input file. For a two-dimensional simulation, it is assumed that the first dimension is x and the second dimension is z, and the value of y is set to zero. Note that the current implementation of the parser for external B-field does not work with RZ and the code will abort with an error message.If

`B_ext_grid_init_style`

is set to be`read_from_file`

, an additional parameter, indicating the path of an openPMD data file,`warpx.read_fields_from_path`

must be specified, from which external B field data can be loaded into WarpX. One can refer to input files in`Examples/Tests/LoadExternalField`

for more information. Regarding how to prepare the openPMD data file, one can refer to the openPMD-example-datasets.

`warpx.E_ext_grid_init_style`

(string) optional (default is “default”)This parameter determines the type of initialization for the external electric field. The “default” style initializes the external electric field (Ex,Ey,Ez) to (0.0, 0.0, 0.0). The string can be set to “constant” if a constant electric field is required to be set at initialization. If set to “constant”, then an additional parameter, namely,

`warpx.E_external_grid`

must be specified in the input file. If set to`parse_E_ext_grid_function`

, then a mathematical expression can be used to initialize the external electric field on the grid. It required additional parameters in the input file, namely,`warpx.Ex_external_grid_function(x,y,z)`

,`warpx.Ey_external_grid_function(x,y,z)`

,`warpx.Ez_external_grid_function(x,y,z)`

to initialize the external electric field for each of the three components on the grid. Constants required in the expression can be set using`my_constants`

. For example, if`warpx.Ex_external_grid_function(x,y,z)=Eo*x + delta*(y + z)`

then the constants Bo and delta required in the above equation can be set using`my_constants.Eo=`

and`my_constants.delta=`

in the input file. For a two-dimensional simulation, it is assumed that the first dimension is x and the second dimension is z, and the value of y is set to zero. Note that the current implementation of the parser for external E-field does not work with RZ and the code will abort with an error message.If

`E_ext_grid_init_style`

is set to be`read_from_file`

, an additional parameter, indicating the path of an openPMD data file,`warpx.read_fields_from_path`

must be specified, from which external E field data can be loaded into WarpX. One can refer to input files in`Examples/Tests/LoadExternalField`

for more information. Regarding how to prepare the openPMD data file, one can refer to the openPMD-example-datasets. Note that if both B_ext_grid_init_style and E_ext_grid_init_style are set to read_from_file, the openPMD file specified by warpx.read_fields_from_path should contain both B and E external fields data.

`warpx.E_external_grid`

&`warpx.B_external_grid`

(list of 3 floats)required when

`warpx.E_ext_grid_init_style="constant"`

and when`warpx.B_ext_grid_init_style="constant"`

, respectively. External uniform and constant electrostatic and magnetostatic field added to the grid at initialization. Use with caution as these fields are used for the field solver. In particular, do not use any other boundary condition than periodic.

### Applied to Particles

`particles.E_ext_particle_init_style`

&`particles.B_ext_particle_init_style`

(string) optional (default “none”)These parameters determine the type of the external electric and magnetic fields respectively that are applied directly to the particles at every timestep. The field values are specified in the lab frame. With the default

`none`

style, no field is applied. Possible values are`constant`

,`parse_E_ext_particle_function`

or`parse_B_ext_particle_function`

, or`repeated_plasma_lens`

.`constant`

: a constant field is applied, given by the input parameters`particles.E_external_particle`

or`particles.B_external_particle`

, which are lists of the field components.`parse_E_ext_particle_function`

or`parse_B_ext_particle_function`

: the field is specified as an analytic expression that is a function of space (x,y,z) and time (t), relative to the lab frame. The E-field is specified by the input parameters:`particles.Ex_external_particle_function(x,y,z,t)`

`particles.Ey_external_particle_function(x,y,z,t)`

`particles.Ez_external_particle_function(x,y,z,t)`

The B-field is specified by the input parameters:

`particles.Bx_external_particle_function(x,y,z,t)`

`particles.By_external_particle_function(x,y,z,t)`

`particles.Bz_external_particle_function(x,y,z,t)`

Note that the position is defined in Cartesian coordinates, as a function of (x,y,z), even for RZ.

`repeated_plasma_lens`

: apply a series of plasma lenses. The properties of the lenses are defined in the lab frame by the input parameters:`repeated_plasma_lens_period`

, the period length of the repeat, a single float number,`repeated_plasma_lens_starts`

, the start of each lens relative to the period, an array of floats,`repeated_plasma_lens_lengths`

, the length of each lens, an array of floats,`repeated_plasma_lens_strengths_E`

, the electric focusing strength of each lens, an array of floats, when`particles.E_ext_particle_init_style`

is set to`repeated_plasma_lens`

.`repeated_plasma_lens_strengths_B`

, the magnetic focusing strength of each lens, an array of floats, when`particles.B_ext_particle_init_style`

is set to`repeated_plasma_lens`

.

The applied field is uniform longitudinally (along z) with a hard edge, where residence corrections are used for more accurate field calculation. On the time step when a particle enters or leaves each lens, the field applied is scaled by the fraction of the time step spent within the lens. The fields are of the form \(E_x = \mathrm{strength} \cdot x\), \(E_y = \mathrm{strength} \cdot y\), and \(E_z = 0\), and \(B_x = \mathrm{strength} \cdot y\), \(B_y = -\mathrm{strength} \cdot x\), and \(B_z = 0\).

### Accelerator Lattice

Several accelerator lattice elements can be defined as described below. The elements are defined relative to the z axis and in the lab frame, starting at z = 0. They are described using a simplified MAD like syntax. Note that elements of the same type cannot overlap each other.

`lattice.elements`

(`list of strings`

) optional (default: no elements)A list of names (one name per lattice element), in the order that they appear in the lattice.

`lattice.reverse`

(`boolean`

) optional (default:`false`

)Reverse the list of elements in the lattice.

`<element_name>.type`

(`string`

)Indicates the element type for this lattice element. This should be one of:

`drift`

for free drift. This requires this additional parameter:`<element_name>.ds`

(`float`

, in meters) the segment length

`quad`

for a hard edged quadrupole. This applies a quadrupole field that is uniform within the z extent of the element with a sharp cut off at the ends. This uses residence corrections, with the field scaled by the amount of time within the element for particles entering or leaving it, to increase the accuracy. This requires these additional parameters:`<element_name>.ds`

(`float`

, in meters) the segment length`<element_name>.dEdx`

(`float`

, in volts/meter^2) optional (default: 0.) the electric quadrupole field gradient The field applied to the particles will be Ex = dEdx*x and Ey = -dEdx*y.`<element_name>.dBdx`

(`float`

, in Tesla/meter) optional (default: 0.) the magnetic quadrupole field gradient The field applied to the particles will be Bx = dBdx*y and By = dBdx*x.

`plasmalens`

for a field modeling a plasma lens This applies a radially directed plasma lens field that is uniform within the z extent of the element with a sharp cut off at the ends. This uses residence corrections, with the field scaled by the amount of time within the element for particles entering or leaving it, to increase the accuracy. This requires these additional parameters:`<element_name>.ds`

(`float`

, in meters) the segment length`<element_name>.dEdx`

(`float`

, in volts/meter^2) optional (default: 0.) the electric field gradient The field applied to the particles will be Ex = dEdx*x and Ey = dEdx*y.`<element_name>.dBdx`

(`float`

, in Tesla/meter) optional (default: 0.) the magnetic field gradient The field applied to the particles will be Bx = dBdx*y and By = -dBdx*x.

`line`

a sub-lattice (line) of elements to append to the lattice.`<element_name>.elements`

(`list of strings`

) optional (default: no elements) A list of names (one name per lattice element), in the order that they appear in the lattice.`<element_name>.reverse`

(`boolean`

) optional (default:`false`

) Reverse the list of elements in the line before appending to the lattice.

## Collision models

WarpX provides several particle collision models, using varying degrees of approximation.

`collisions.collision_names`

(strings, separated by spaces)The name of each collision type. This is then used in the rest of the input deck; in this documentation we use

`<collision_name>`

as a placeholder.

`<collision_name>.type`

(string) optionalThe type of collision. The types implemented are:

`pairwisecoulomb`

for pairwise Coulomb collisions, the default if unspecified. This provides a pair-wise relativistic elastic Monte Carlo binary Coulomb collision model, following the algorithm given by Perez et al. (Phys. Plasmas 19, 083104, 2012). When the RZ mode is used, warpx.n_rz_azimuthal_modes must be set to 1 at the moment, since the current implementation of the collision module assumes axisymmetry.`nuclearfusion`

for fusion reactions. This implements the pair-wise fusion model by Higginson et al. (JCP 388, 439-453, 2019). Currently, WarpX supports deuterium-deuterium, deuterium-tritium, deuterium-helium and proton-boron fusion. When initializing the reactant and product species, you need to use`species_type`

(see the documentation for this parameter), so that WarpX can identify the type of reaction to use. (e.g.`<species_name>.species_type = 'deuterium'`

)`background_mcc`

for collisions between particles and a neutral background. This is a relativistic Monte Carlo treatment for particles colliding with a neutral background gas. The implementation follows the so-called null collision strategy discussed for example in Birdsall (IEEE Transactions on Plasma Science, vol. 19, no. 2, pp. 65-85, 1991). See also collisions section.`background_stopping`

for slowing of ions due to collisions with electrons or ions. This implements the approximate formulae as derived in Introduction to Plasma Physics, from Goldston and Rutherford, section 14.2.

`<collision_name>.species`

(strings)If using

`pairwisecoulomb`

or`nuclearfusion`

, this should be the name(s) of the species, between which the collision will be considered. (Provide only one name for intra-species collisions.) If using`background_mcc`

or`background_stopping`

type this should be the name of the species for which collisions with a background will be included. In this case, only one species name should be given.

`<collision_name>.product_species`

(strings)Only for

`nuclearfusion`

. The name(s) of the species in which to add the new macroparticles created by the reaction.

`<collision_name>.ndt`

(int) optionalExecute collision every # time steps. The default value is 1.

`<collision_name>.CoulombLog`

(float) optionalOnly for

`pairwisecoulomb`

. A provided fixed Coulomb logarithm of the collision type`<collision_name>`

. For example, a typical Coulomb logarithm has a form of \(\ln(\lambda_D/R)\), where \(\lambda_D\) is the Debye length, \(R\approx1.4A^{1/3}\) is the effective Coulombic radius of the nucleus, \(A\) is the mass number. If this is not provided, or if a non-positive value is provided, a Coulomb logarithm will be computed automatically according to the algorithm in Perez et al. (Phys. Plasmas 19, 083104, 2012).

`<collision_name>.fusion_multiplier`

(float) optional.Only for

`nuclearfusion`

. Increasing`fusion_multiplier`

creates more macroparticles of fusion products, but with lower weight (in such a way that the corresponding total number of physical particle remains the same). This can improve the statistics of the simulation, in the case where fusion reactions are very rare. More specifically, in a fusion reaction between two macroparticles with weight`w_1`

and`w_2`

, the weight of the product macroparticles will be`min(w_1,w_2)/fusion_multipler`

. (And the weights of the reactant macroparticles are reduced correspondingly after the reaction.) See Higginson et al. (JCP 388, 439-453, 2019) for more details. The default value of`fusion_multiplier`

is 1.

- ``<collision_name>.fusion_probability_threshold``(float) optional.
Only for

`nuclearfusion`

. If the fusion multiplier is too high and results in a fusion probability that approaches 1 (for a given collision between two macroparticles), then there is a risk of underestimating the total fusion yield. In these cases, WarpX reduces the fusion multiplier used in that given collision.`m_probability_threshold`

is the fusion probability threshold above which WarpX reduces the fusion multiplier.

`<collision_name>.fusion_probability_target_value`

(float) optional.Only for

`nuclearfusion`

. When the probability of fusion for a given collision exceeds`fusion_probability_threshold`

, WarpX reduces the fusion multiplier for that collisions such that the fusion probability approches`fusion_probability_target_value`

.

`<collision_name>.background_density`

(float)Only for

`background_mcc`

and`background_stopping`

. The density of the background in \(m^{-3}\). Can also provide`<collision_name>.background_density(x,y,z,t)`

using the parser initialization style for spatially and temporally varying density. With`background_mcc`

, if a function is used for the background density, the input parameter`<collision_name>.max_background_density`

must also be provided to calculate the maximum collision probability.

`<collision_name>.background_temperature`

(float)Only for

`background_mcc`

and`background_stopping`

. The temperature of the background in Kelvin. Can also provide`<collision_name>.background_temperature(x,y,z,t)`

using the parser initialization style for spatially and temporally varying temperature.

`<collision_name>.background_mass`

(float) optionalOnly for

`background_mcc`

and`background_stopping`

. The mass of the background gas in kg. With`background_mcc`

, if not given the mass of the colliding species will be used unless ionization is included in which case the mass of the product species will be used. With`background_stopping`

, and`background_type`

set to`electrons`

, if not given defaults to the electron mass. With`background_type`

set to`ions`

, the mass must be given.

`<collision_name>.background_charge_state`

(float)Only for

`background_stopping`

, where it is required when`background_type`

is set to`ions`

. This specifies the charge state of the background ions.

`<collision_name>.background_type`

(string)Only for

`background_stopping`

, where it is required, the type of the background. The possible values are`electrons`

and`ions`

. When`electrons`

, equation 14.12 from Goldston and Rutherford is used. This formula is based on Coulomb collisions with the approximations that \(M_b >> m_e\) and \(V << v_{thermal\_e}\), and the assumption that the electrons have a Maxwellian distribution with temperature \(T_e\).\[\frac{dV}{dt} = - \frac{2^{1/2}n_eZ_b^2e^4m_e^{1/2}\log\Lambda}{12\pi^{3/2}\epsilon_0M_bT_e^{3/2}}V\]where \(V\) is each velocity component, \(n_e\) is the background density, \(Z_b\) is the ion charge state, \(e\) is the electron charge, \(m_e\) is the background mass, \(\log\Lambda=\log((12\pi/Z_b)(n_e\lambda_{de}^3))\), \(\lambda_{de}\) is the DeBye length, and \(M_b\) is the ion mass. The equation is integrated over a time step, giving \(V(t+dt) = V(t)*\exp(-\alpha*{dt})\) where \(\alpha\) is the factor multiplying \(V\).

When

`ions`

, equation 14.20 is used. This formula is based on Coulomb collisions with the approximations that \(M_b >> M\) and \(V >> v_{thermal\_i}\). The background ion temperature only appears in the \(\log\Lambda\) term.\[\frac{dW_b}{dt} = - \frac{2^{1/2}n_iZ^2Z_b^2e^4M_b^{1/2}\log\Lambda}{8\pi\epsilon_0MW_b^{1/2}}\]where \(W_b\) is the ion energy, \(n_i\) is the background density, \(Z\) is the charge state of the background ions, \(Z_b\) is the ion charge state, \(e\) is the electron charge, \(M_b\) is the ion mass, \(\log\Lambda=\log((12\pi/Z_b)(n_i\lambda_{di}^3))\), \(\lambda_{di}\) is the DeBye length, and \(M\) is the background ion mass. The equation is integrated over a time step, giving \(W_b(t+dt) = ((W_b(t)^{3/2}) - 3/2\beta{dt})^{2/3}\) where \(\beta\) is the term on the r.h.s except \(W_b\).

`<collision_name>.scattering_processes`

(strings separated by spaces)Only for

`background_mcc`

. The MCC scattering processes that should be included. Available options are`elastic`

,`back`

&`charge_exchange`

for ions and`elastic`

,`excitationX`

&`ionization`

for electrons. The`elastic`

option uses hard-sphere scattering, with a differential cross section that is independent of angle. With`charge_exchange`

, the ion velocity is replaced with the neutral velocity, chosen from a Maxwellian based on the value of`<collision_name>.background_temperature`

. Multiple excitation events can be included for electrons corresponding to excitation to different levels, the`X`

above can be changed to a unique identifier for each excitation process. For each scattering process specified a path to a cross-section data file must also be given. We use`<scattering_process>`

as a placeholder going forward.

`<collision_name>.<scattering_process>_cross_section`

(string)Only for

`background_mcc`

. Path to the file containing cross-section data for the given scattering processes. The cross-section file must have exactly 2 columns of data, the first containing equally spaced energies in eV and the second the corresponding cross-section in \(m^2\).

`<collision_name>.<scattering_process>_energy`

(float)Only for

`background_mcc`

. If the scattering process is either`excitationX`

or`ionization`

the energy cost of that process must be given in eV.

`<collision_name>.ionization_species`

(float)Only for

`background_mcc`

. If the scattering process is`ionization`

the produced species must also be given. For example if argon properties is used for the background gas, a species of argon ions should be specified here.

## Numerics and algorithms

This section describes the input parameters used to select numerical methods and algorithms for your simulation setup.

### Time step

`warpx.cfl`

(float) optional (default 0.999)The ratio between the actual timestep that is used in the simulation and the Courant-Friedrichs-Lewy (CFL) limit. (e.g. for warpx.cfl=1, the timestep will be exactly equal to the CFL limit.) This parameter will only be used with the electromagnetic solver.

`warpx.const_dt`

(float)Allows direct specification of the time step size, in units of seconds. When the electrostatic solver is being used, this must be supplied. This can be used with the electromagnetic solver, overriding

`warpx.cfl`

, but it is up to the user to ensure that the CFL condition is met.

### Filtering

`warpx.use_filter`

(0 or 1; default: 1, except for RZ FDTD)Whether to smooth the charge and currents on the mesh, after depositing them from the macro-particles. This uses a bilinear filter (see the filtering section). The default is 1 in all cases, except for simulations in RZ geometry using the FDTD solver. With the RZ PSATD solver, the filtering is done in \(k\)-space.

Warning

Known bug: filter currently not working with FDTD solver in RZ geometry (see https://github.com/ECP-WarpX/WarpX/issues/1943).

`warpx.filter_npass_each_dir`

(3 int) optional (default 1 1 1)Number of passes along each direction for the bilinear filter. In 2D simulations, only the first two values are read.

`warpx.use_filter_compensation`

(0 or 1; default: 0)Whether to add compensation when applying filtering. This is only supported with the RZ spectral solver.

### Particle push, charge and current deposition, field gathering

`algo.current_deposition`

(string, optional)This parameter selects the algorithm for the deposition of the current density. Available options are:

`direct`

,`esirkepov`

, and`vay`

. The default choice is`esirkepov`

for FDTD maxwell solvers but`direct`

for standard or Galilean PSATD solver (i.e. with`algo.maxwell_solver = psatd`

) and for the hybrid-PIC solver (i.e. with`algo.maxwell_solver = hybrid`

). Note that`vay`

is only available for`algo.maxwell_solver = psatd`

.`direct`

The current density is deposited as described in the section Current deposition. This deposition scheme does not conserve charge.

`esirkepov`

The current density is deposited as described in (Esirkepov, CPC, 2001). This deposition scheme guarantees charge conservation for shape factors of arbitrary order.

`vay`

The current density is deposited as described in (Vay et al, 2013) (see section Current deposition for more details). This option guarantees charge conservation only when used in combination with

`psatd.periodic_single_box_fft=1`

, that is, only for periodic single-box simulations with global FFTs without guard cells. The implementation for domain decomposition with local FFTs over guard cells is planned but not yet completed.

`algo.charge_deposition`

(string, optional)The algorithm for the charge density deposition. Available options are:

`standard`

: standard charge deposition algorithm, described in the particle-in-cell theory section.

`algo.field_gathering`

(string, optional)The algorithm for field gathering. Available options are:

`energy-conserving`

: gathers directly from the grid points (either staggered or nodal grid points depending on`warpx.grid_type`

).`momentum-conserving`

: first average the fields from the grid points to the nodes, and then gather from the nodes.

Default:

`algo.field_gathering = energy-conserving`

with collocated or staggered grids (note that`energy-conserving`

and`momentum-conserving`

are equivalent with collocated grids),`algo.field_gathering = momentum-conserving`

with hybrid grids.

`algo.particle_pusher`

(string, optional)The algorithm for the particle pusher. Available options are:

`boris`

: Boris pusher.`vay`

: Vay pusher (see Vay, Phys. Plasmas (2008))`higuera`

: Higuera-Cary pusher (see Higuera and Cary, Phys. Plasmas (2017))

If

`algo.particle_pusher`

is not specified,`boris`

is the default.

`algo.particle_shape`

(integer; 1, 2, or 3)The order of the shape factors (splines) for the macro-particles along all spatial directions: 1 for linear, 2 for quadratic, 3 for cubic. Low-order shape factors result in faster simulations, but may lead to more noisy results. High-order shape factors are computationally more expensive, but may increase the overall accuracy of the results. For production runs it is generally safer to use high-order shape factors, such as cubic order.

Note that this input parameter is not optional and must always be set in all input files provided that there is at least one particle species (set in input as

`particles.species_names`

) or one laser species (set in input as`lasers.names`

) in the simulation. No default value is provided automatically.

### Maxwell solver

Two families of Maxwell solvers are implemented in WarpX, based on the Finite-Difference Time-Domain method (FDTD) or the Pseudo-Spectral Analytical Time-Domain method (PSATD), respectively.

`algo.maxwell_solver`

(string, optional)The algorithm for the Maxwell field solver. Available options are:

`yee`

: Yee FDTD solver.`ckc`

: (not available in`RZ`

geometry) Cole-Karkkainen solver with Cowan coefficients (see Cowan, PRSTAB 16 (2013)).`psatd`

: Pseudo-spectral solver (see theory).`ect`

: Enlarged cell technique (conformal finite difference solver. See Xiao and Liu, IEEE Antennas and Propagation Society International Symposium (2005)).`hybrid`

: The E-field will be solved using Ohm’s law and a kinetic-fluid hybrid model (see theory).`none`

: No field solve will be performed.

If

`algo.maxwell_solver`

is not specified,`yee`

is the default.

`algo.em_solver_medium`

(string, optional)The medium for evaluating the Maxwell solver. Available options are :

`vacuum`

: vacuum properties are used in the Maxwell solver.`macroscopic`

: macroscopic Maxwell equation is evaluated. If this option is selected, then the corresponding properties of the medium must be provided using`macroscopic.sigma`

,`macroscopic.epsilon`

, and`macroscopic.mu`

for each case where the initialization style is`constant`

. Otherwise if the initialization style uses the parser,`macroscopic.sigma_function(x,y,z)`

,`macroscopic.epsilon_function(x,y,z)`

and/or`macroscopic.mu_function(x,y,z)`

must be provided using the parser initialization style for spatially varying macroscopic properties.

If

`algo.em_solver_medium`

is not specified,`vacuum`

is the default.

### Maxwell solver: PSATD method

`psatd.nox`

,`psatd.noy`

,`pstad.noz`

(integer) optional (default 16 for all)The order of accuracy of the spatial derivatives, when using the code compiled with a PSATD solver. If

`psatd.periodic_single_box_fft`

is used, these can be set to`inf`

for infinite-order PSATD.

`psatd.nx_guard`

,`psatd.ny_guard`

,`psatd.nz_guard`

(integer) optionalThe number of guard cells to use with PSATD solver. If not set by users, these values are calculated automatically and determined

*empirically*and equal the order of the solver for collocated grids and half the order of the solver for staggered grids.

`psatd.periodic_single_box_fft`

(0 or 1; default: 0)If true, this will

*not*incorporate the guard cells into the box over which FFTs are performed. This is only valid when WarpX is run with periodic boundaries and a single box. In this case, using psatd.periodic_single_box_fft is equivalent to using a global FFT over the whole domain. Therefore, all the approximations that are usually made when using local FFTs with guard cells (for problems with multiple boxes) become exact in the case of the periodic, single-box FFT without guard cells.

`psatd.current_correction`

(0 or 1; default: 1, with the exceptions mentioned below)If true, a current correction scheme in Fourier space is applied in order to guarantee charge conservation. The default value is

`psatd.current_correction=1`

, unless a charge-conserving current deposition scheme is used (by setting`algo.current_deposition=esirkepov`

or`algo.current_deposition=vay`

) or unless the`div(E)`

cleaning scheme is used (by setting`warpx.do_dive_cleaning=1`

).If

`psatd.v_galilean`

is zero, the spectral solver used is the standard PSATD scheme described in (Vay et al, JCP 243, 2013) and the current correction reads\[\widehat{\boldsymbol{J}}^{\,n+1/2}_{\mathrm{correct}} = \widehat{\boldsymbol{J}}^{\,n+1/2} - \bigg(\boldsymbol{k}\cdot\widehat{\boldsymbol{J}}^{\,n+1/2} - i \frac{\widehat{\rho}^{n+1} - \widehat{\rho}^{n}}{\Delta{t}}\bigg) \frac{\boldsymbol{k}}{k^2}\]If

`psatd.v_galilean`

is non-zero, the spectral solver used is the Galilean PSATD scheme described in (Lehe et al, PRE 94, 2016) and the current correction reads\[\widehat{\boldsymbol{J}}^{\,n+1/2}_{\mathrm{correct}} = \widehat{\boldsymbol{J}}^{\,n+1/2} - \bigg(\boldsymbol{k}\cdot\widehat{\boldsymbol{J}}^{\,n+1/2} - (\boldsymbol{k}\cdot\boldsymbol{v}_G) \,\frac{\widehat\rho^{n+1} - \widehat\rho^{n}\theta^2}{1 - \theta^2}\bigg) \frac{\boldsymbol{k}}{k^2}\]where \(\theta=\exp(i\,\boldsymbol{k}\cdot\boldsymbol{v}_G\,\Delta{t}/2)\).

This option is currently implemented only for the standard PSATD, Galilean PSATD, and averaged Galilean PSATD schemes, while it is not yet available for the multi-J algorithm.

`psatd.update_with_rho`

(0 or 1)If true, the update equation for the electric field is expressed in terms of both the current density and the charge density, namely \(\widehat{\boldsymbol{J}}^{\,n+1/2}\), \(\widehat\rho^{n}\), and \(\widehat\rho^{n+1}\). If false, instead, the update equation for the electric field is expressed in terms of the current density \(\widehat{\boldsymbol{J}}^{\,n+1/2}\) only. If charge is expected to be conserved (by setting, for example,

`psatd.current_correction=1`

), then the two formulations are expected to be equivalent.If

`psatd.v_galilean`

is zero, the spectral solver used is the standard PSATD scheme described in (Vay et al, JCP 243, 2013):if

`psatd.update_with_rho=0`

, the update equation for the electric field reads

\[\begin{split}\begin{split} \widehat{\boldsymbol{E}}^{\,n+1}= & \: C \widehat{\boldsymbol{E}}^{\,n} + i \, \frac{S c}{k} \boldsymbol{k}\times\widehat{\boldsymbol{B}}^{\,n} - \frac{S}{\epsilon_0 c \, k} \widehat{\boldsymbol{J}}^{\,n+1/2} \\[0.2cm] & +\frac{1-C}{k^2} (\boldsymbol{k}\cdot\widehat{\boldsymbol{E}}^{\,n}) \boldsymbol{k} + \frac{1}{\epsilon_0 k^2} \left(\frac{S}{c \, k}-\Delta{t}\right) (\boldsymbol{k}\cdot\widehat{\boldsymbol{J}}^{\,n+1/2}) \boldsymbol{k} \end{split}\end{split}\]if

`psatd.update_with_rho=1`

, the update equation for the electric field reads

\[\begin{split}\begin{split} \widehat{\boldsymbol{E}}^{\,n+1}= & \: C\widehat{\boldsymbol{E}}^{\,n} + i \, \frac{S c}{k} \boldsymbol{k}\times\widehat{\boldsymbol{B}}^{\,n} - \frac{S}{\epsilon_0 c \, k} \widehat{\boldsymbol{J}}^{\,n+1/2} \\[0.2cm] & + \frac{i}{\epsilon_0 k^2} \left(C-\frac{S}{c\,k}\frac{1}{\Delta{t}}\right) \widehat{\rho}^{n} \boldsymbol{k} - \frac{i}{\epsilon_0 k^2} \left(1-\frac{S}{c \, k} \frac{1}{\Delta{t}}\right)\widehat{\rho}^{n+1} \boldsymbol{k} \end{split}\end{split}\]The coefficients \(C\) and \(S\) are defined in (Vay et al, JCP 243, 2013).

If

`psatd.v_galilean`

is non-zero, the spectral solver used is the Galilean PSATD scheme described in (Lehe et al, PRE 94, 2016):if

`psatd.update_with_rho=0`

, the update equation for the electric field reads

\[\begin{split}\begin{split} \widehat{\boldsymbol{E}}^{\,n+1} = & \: \theta^{2} C \widehat{\boldsymbol{E}}^{\,n} + i \, \theta^{2} \frac{S c}{k} \boldsymbol{k}\times\widehat{\boldsymbol{B}}^{\,n} + \frac{i \, \nu \, \theta \, \chi_1 - \theta^{2} S}{\epsilon_0 c \, k} \widehat{\boldsymbol{J}}^{\,n+1/2} \\[0.2cm] & + \theta^{2} \frac{\chi_2-\chi_3}{k^{2}} (\boldsymbol{k}\cdot\widehat{\boldsymbol{E}}^{\,n}) \boldsymbol{k} + i \, \frac{\chi_2\left(\theta^{2}-1\right)}{\epsilon_0 c \, k^{3} \nu} (\boldsymbol{k}\cdot\widehat{\boldsymbol{J}}^{\,n+1/2}) \boldsymbol{k} \end{split}\end{split}\]if

`psatd.update_with_rho=1`

, the update equation for the electric field reads

\[\begin{split}\begin{split} \widehat{\boldsymbol{E}}^{\,n+1} = & \: \theta^{2} C \widehat{\boldsymbol{E}}^{\,n} + i \, \theta^{2} \frac{S c}{k} \boldsymbol{k}\times\widehat{\boldsymbol{B}}^{\,n} + \frac{i \, \nu \, \theta \, \chi_1 - \theta^{2} S}{\epsilon_0 c \, k} \widehat{\boldsymbol{J}}^{\,n+1/2} \\[0.2cm] & + i \, \frac{\theta^{2} \chi_3}{\epsilon_0 k^{2}} \widehat{\rho}^{\,n} \boldsymbol{k} - i \, \frac{\chi_2}{\epsilon_0 k^{2}} \widehat{\rho}^{\,n+1} \boldsymbol{k} \end{split}\end{split}\]The coefficients \(C\), \(S\), \(\theta\), \(\nu\), \(\chi_1\), \(\chi_2\), and \(\chi_3\) are defined in (Lehe et al, PRE 94, 2016).

The default value for

`psatd.update_with_rho`

is`1`

if`psatd.v_galilean`

is non-zero and`0`

otherwise. The option`psatd.update_with_rho=0`

is not implemented with the following algorithms: comoving PSATD (`psatd.v_comoving`

), time averaging (`psatd.do_time_averaging=1`

), div(E) cleaning (`warpx.do_dive_cleaning=1`

), and multi-J (`warpx.do_multi_J=1`

).Note that the update with and without rho is also supported in RZ geometry.

`psatd.J_in_time`

(`constant`

or`linear`

; default`constant`

)This determines whether the current density is assumed to be constant or linear in time, within the time step over which the electromagnetic fields are evolved.

`psatd.rho_in_time`

(`linear`

; default`linear`

)This determines whether the charge density is assumed to be linear in time, within the time step over which the electromagnetic fields are evolved.

`psatd.v_galilean`

(3 floats, in units of the speed of light; default`0. 0. 0.`

)Defines the Galilean velocity. A non-zero velocity activates the Galilean algorithm, which suppresses numerical Cherenkov instabilities (NCI) in boosted-frame simulations (see the section Numerical Stability and alternate formulation in a Galilean frame for more information). This requires the code to be compiled with the spectral solver. It also requires the use of the direct current deposition algorithm (by setting

`algo.current_deposition = direct`

).

`psatd.use_default_v_galilean`

(0 or 1; default: 0)This can be used in boosted-frame simulations only and sets the Galilean velocity along the \(z\) direction automatically as \(v_{G} = -\sqrt{1-1/\gamma^2}\), where \(\gamma\) is the Lorentz factor of the boosted frame (set by

`warpx.gamma_boost`

). See the section Numerical Stability and alternate formulation in a Galilean frame for more information on the Galilean algorithm for boosted-frame simulations.

`psatd.v_comoving`

(3 floating-point values, in units of the speed of light; default`0. 0. 0.`

)Defines the comoving velocity in the comoving PSATD scheme. A non-zero comoving velocity selects the comoving PSATD algorithm, which suppresses the numerical Cherenkov instability (NCI) in boosted-frame simulations, under certain assumptions. This option requires that WarpX is compiled with

`USE_PSATD = TRUE`

. It also requires the use of direct current deposition (`algo.current_deposition = direct`

) and has not been neither implemented nor tested with other current deposition schemes.

`psatd.do_time_averaging`

(0 or 1; default: 0)Whether to use an averaged Galilean PSATD algorithm or standard Galilean PSATD.

`warpx.do_multi_J`

(0 or 1; default: 0)Whether to use the multi-J algorithm, where current deposition and field update are performed multiple times within each time step. The number of sub-steps is determined by the input parameter

`warpx.do_multi_J_n_depositions`

. Unlike sub-cycling, field gathering is performed only once per time step, as in regular PIC cycles. When`warpx.do_multi_J = 1`

, we perform linear interpolation of two distinct currents deposited at the beginning and the end of the time step, instead of using one single current deposited at half time. For simulations with strong numerical Cherenkov instability (NCI), it is recommended to use the multi-J algorithm in combination with`psatd.do_time_averaging = 1`

.

`warpx.do_multi_J_n_depositions`

(integer)Number of sub-steps to use with the multi-J algorithm, when

`warpx.do_multi_J = 1`

. Note that this input parameter is not optional and must always be set in all input files where`warpx.do_multi_J = 1`

. No default value is provided automatically.

### Maxwell solver: macroscopic media

`algo.macroscopic_sigma_method`

(string, optional)The algorithm for updating electric field when

`algo.em_solver_medium`

is macroscopic. Available options are:`backwardeuler`

is a fully-implicit, first-order in time scheme for E-update (default).`laxwendroff`

is the semi-implicit, second order in time scheme for E-update.

Comparing the two methods, Lax-Wendroff is more prone to developing oscillations and requires a smaller timestep for stability. On the other hand, Backward Euler is more robust but it is first-order accurate in time compared to the second-order Lax-Wendroff method.

`macroscopic.sigma_function(x,y,z)`

,`macroscopic.epsilon_function(x,y,z)`

,`macroscopic.mu_function(x,y,z)`

(string)To initialize spatially varying conductivity, permittivity, and permeability, respectively, using a mathematical function in the input. Constants required in the mathematical expression can be set using

`my_constants`

. These parameters are parsed if`algo.em_solver_medium=macroscopic`

.

`macroscopic.sigma`

,`macroscopic.epsilon`

,`macroscopic.mu`

(double)To initialize a constant conductivity, permittivity, and permeability of the computational medium, respectively. The default values are the corresponding values in vacuum.

### Maxwell solver: kinetic-fluid hybrid

`hybrid_pic_model.elec_temp`

(float)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the electron temperature, in eV, used to calculate the electron pressure (see here).

`hybrid_pic_model.n0_ref`

(float)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the reference density, in \(m^{-3}\), used to calculate the electron pressure (see here).

`hybrid_pic_model.gamma`

(float) optional (default`5/3`

)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the exponent used to calculate the electron pressure (see here).

`hybrid_pic_model.plasma_resistivity(rho)`

(float or str) optional (default`0`

)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the plasma resistivity in \(\Omega m\).

`hybrid_pic_model.n_floor`

(float) optional (default`1`

)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the plasma density floor, in \(m^{-3}\), which is useful since the generalized Ohm’s law used to calculate the E-field includes a \(1/n\) term.

`hybrid_pic_model.substeps`

(int) optional (default`100`

)If

`algo.maxwell_solver`

is set to`hybrid`

, this sets the number of sub-steps to take during the B-field update.

Note

Based on results from Stanier *et al.* [1] it is recommended to use
linear particles when using the hybrid-PIC model.

### Grid types (collocated, staggered, hybrid)

`warpx.grid_type`

(string,`collocated`

,`staggered`

or`hybrid`

)Whether to use a collocated grid (all fields defined at the cell nodes), a staggered grid (fields defined on a Yee grid), or a hybrid grid (fields and currents are interpolated back and forth between a staggered grid and a nodal grid, must be used with momentum-conserving field gathering algorithm,

`algo.field_gathering = momentum-conserving`

).Default:

`warpx.grid_type = staggered`

.

`interpolation.galerkin_scheme`

(0 or 1)Whether to use a Galerkin scheme when gathering fields to particles. When set to

`1`

, the interpolation orders used for field-gathering are reduced for certain field components along certain directions. For example, \(E_z\) is gathered using`algo.particle_shape`

along \((x,y)\) and`algo.particle_shape - 1`

along \(z\). See equations (21)-(23) of (Godfrey and Vay, 2013) and associated references for details.Default:

`interpolation.galerkin_scheme = 0`

with collocated grids and/or momentum-conserving field gathering,`interpolation.galerkin_scheme = 1`

otherwise.Warning

The default behavior should not normally be changed. At present, this parameter is intended mainly for testing and development purposes.

`warpx.field_centering_nox`

,`warpx.field_centering_noy`

,`warpx.field_centering_noz`

(integer, optional)The order of interpolation used with staggered or hybrid grids (

`warpx.grid_type = staggered`

or`warpx.grid_type = hybrid`

) and momentum-conserving field gathering (`algo.field_gathering = momentum-conserving`

) to interpolate the electric and magnetic fields from the cell centers to the cell nodes, before gathering the fields from the cell nodes to the particle positions.Default:

`warpx.field_centering_no<x,y,z> = 2`

with staggered grids,`warpx.field_centering_no<x,y,z> = 8`

with hybrid grids (typically necessary to ensure stability in boosted-frame simulations of relativistic plasmas and beams).

`warpx.current_centering_nox`

,`warpx.current_centering_noy`

,`warpx.current_centering_noz`

(integer, optional)The order of interpolation used with hybrid grids (

`warpx.grid_type = hybrid`

) to interpolate the currents from the cell nodes to the cell centers when`warpx.do_current_centering = 1`

, before pushing the Maxwell fields on staggered grids.Default:

`warpx.current_centering_no<x,y,z> = 8`

with hybrid grids (typically necessary to ensure stability in boosted-frame simulations of relativistic plasmas and beams).

`warpx.do_current_centering`

(bool, 0 or 1)If true, the current is deposited on a nodal grid and then centered to a staggered grid (Yee grid), using finite-order interpolation.

Default:

`warpx.do_current_centering = 0`

with collocated or staggered grids,`warpx.do_current_centering = 1`

with hybrid grids.

### Additional parameters

`warpx.do_dive_cleaning`

(0 or 1 ; default: 0)Whether to use modified Maxwell equations that progressively eliminate the error in \(div(E)-\rho\). This can be useful when using a current deposition algorithm which is not strictly charge-conserving, or when using mesh refinement. These modified Maxwell equation will cause the error to propagate (at the speed of light) to the boundaries of the simulation domain, where it can be absorbed.

`warpx.do_subcycling`

(0 or 1; default: 0)Whether or not to use sub-cycling. Different refinement levels have a different cell size, which results in different Courant–Friedrichs–Lewy (CFL) limits for the time step. By default, when using mesh refinement, the same time step is used for all levels. This time step is taken as the CFL limit of the finest level. Hence, for coarser levels, the timestep is only a fraction of the CFL limit for this level, which may lead to numerical artifacts. With sub-cycling, each level evolves with its own time step, set to its own CFL limit. In practice, it means that when level 0 performs one iteration, level 1 performs two iterations. Currently, this option is only supported when

`amr.max_level = 1`

. More information can be found at https://ieeexplore.ieee.org/document/8659392.

`warpx.override_sync_intervals`

(string) optional (default 1)Using the Intervals parser syntax, this string defines the timesteps at which synchronization of sources (rho and J) and fields (E and B) on grid nodes at box boundaries is performed. Since the grid nodes at the interface between two neighbor boxes are duplicated in both boxes, an instability can occur if they have too different values. This option makes sure that they are synchronized periodically. Note that if Perfectly Matched Layers (PML) are used, synchronization of the E and B fields is performed at every timestep regardless of this parameter.

`warpx.use_hybrid_QED`

(bool; default: 0)Will use the Hybird QED Maxwell solver when pushing fields: a QED correction is added to the field solver to solve non-linear Maxwell’s equations, according to [Quantum Electrodynamics vacuum polarization solver, P. Carneiro et al., ArXiv 2016]. Note that this option can only be used with the PSATD build. Furthermore, one must set

`warpx.grid_type = collocated`

(which otherwise would be`staggered`

by default).

`warpx.quantum_xi`

(float; default: 1.3050122.e-52)Overwrites the actual quantum parameter used in Maxwell’s QED equations. Assigning a value here will make the simulation unphysical, but will allow QED effects to become more apparent. Note that this option will only have an effect if the

`warpx.use_Hybrid_QED`

flag is also triggered.

`warpx.do_device_synchronize`

(bool) optional (default 1)When running in an accelerated platform, whether to call a

`amrex::Gpu::synchronize()`

around profiling regions. This allows the profiler to give meaningful timers, but (hardly) slows down the simulation.

`warpx.sort_intervals`

(string) optional (defaults:`-1`

on CPU;`4`

on GPU)Using the Intervals parser syntax, this string defines the timesteps at which particles are sorted. If

`<=0`

, do not sort particles. It is turned on on GPUs for performance reasons (to improve memory locality).

`warpx.sort_particles_for_deposition`

(bool) optional (default:`true`

for the CUDA backend, otherwise`false`

)This option controls the type of sorting used if particle sorting is turned on, i.e. if

`sort_intervals`

is not`<=0`

. If`true`

, particles will be sorted by cell to optimize deposition with many particles per cell, in the order x -> y -> z -> ppc. If`false`

, particles will be sorted by bin, using the`sort_bin_size`

parameter below, in the order ppc -> x -> y -> z.`true`

is recommend for best performance on NVIDIA GPUs, especially if there are many particles per cell.

`warpx.sort_idx_type`

(list of int) optional (default:`0 0 0`

)This controls the type of grid used to sort the particles when

`sort_particles_for_deposition`

is`true`

. Possible values are:`idx_type = {0, 0, 0}`

: Sort particles to a cell centered grid`idx_type = {1, 1, 1}`

: Sort particles to a node centered grid`idx_type = {2, 2, 2}`

: Compromise between a cell and node centered grid.In 2D (XZ and RZ), only the first two elements are read. In 1D, only the first element is read.

`warpx.sort_bin_size`

(list of int) optional (default`1 1 1`

)If

`sort_intervals`

is activated and`sort_particles_for_deposition`

is`false`

, particles are sorted in bins of`sort_bin_size`

cells. In 2D, only the first two elements are read.

`warpx.do_shared_mem_charge_deposition`

(bool) optional (default false)If activated, charge deposition will allocate and use small temporary buffers on which to accumulate deposited charge values from particles. On GPUs these buffers will reside in

`__shared__`

memory, which is faster than the usual`__global__`

memory. Performance impact will depend on the relative overhead of assigning the particles to bins small enough to fit in the space available for the temporary buffers.

`warpx.do_shared_mem_current_deposition`

(bool) optional (default false)If activated, current deposition will allocate and use small temporary buffers on which to accumulate deposited current values from particles. On GPUs these buffers will reside in

`__shared__`

memory, which is faster than the usual`__global__`

memory. Performance impact will depend on the relative overhead of assigning the particles to bins small enough to fit in the space available for the temporary buffers. Performance is mostly improved when there is lots of contention between particles writing to the same cell (e.g. for high particles per cell). This feature is only available for CUDA and HIP, and is only recommended for 3D or 2D.

`warpx.shared_tilesize`

(list of int) optional (default 6 6 8 in 3D; 14 14 in 2D; 1s otherwise)Used to tune performance when

`do_shared_mem_current_deposition`

or`do_shared_mem_charge_depostion`

is enabled.`shared_tilesize`

is the size of the temporary buffer allocated in shared memory for a threadblock. A larger tilesize requires more shared memory, but gives more work to each threadblock, which can lead to higher occupancy, and allows for more buffered writes to`__shared__`

instead of`__global__`

. The defaults in 2D and 3D are chosen from experimentation, but can be improved upon for specific problems. The other defaults are not optimized and should always be fine tuned for the problem.

`warpx.shared_mem_current_tpb`

(int) optional (default 128)Used to tune performance when

`do_shared_mem_current_deposition`

is enabled.`shared_mem_current_tpb`

controls the number of threads per block (tpb), i.e. the number of threads operating on a shared buffer.

## Diagnostics and output

### In-situ visualization

WarpX has four types of diagnostics:
`FullDiagnostics`

consist in dumps of fields and particles at given iterations,
`BackTransformedDiagnostics`

are used when running a simulation in a boosted frame, to reconstruct output data to the lab frame,
`BoundaryScrapingDiagnostics`

are used to collect the particles that are absorbed at the boundary, throughout the simulation, and
`ReducedDiags`

allow the user to compute some reduced quantity (particle temperature, max of a field) and write a small amount of data to text files.
Similar to what is done for physical species, WarpX has a class Diagnostics that allows users to initialize different diagnostics, each of them with different fields, resolution and period.
This currently applies to standard diagnostics, but should be extended to back-transformed diagnostics and reduced diagnostics (and others) in a near future.

### Full Diagnostics

`FullDiagnostics`

consist in dumps of fields and particles at given iterations.
Similar to what is done for physical species, WarpX has a class Diagnostics that allows users to initialize different diagnostics, each of them with different fields, resolution and period.
The user specifies the number of diagnostics and the name of each of them, and then specifies options for each of them separately.
Note that some parameter (those that do not start with a `<diag_name>.`

prefix) apply to all diagnostics.
This should be changed in the future.
In-situ capabilities can be used by turning on Sensei or Ascent (provided they are installed) through the output format, see below.

`diagnostics.enable`

(0 or 1, optional, default 1)Whether to enable or disable diagnostics. This flag overwrites all other diagnostics input parameters.

`diagnostics.diags_names`

(list of string optional, default empty)Name of each diagnostics. example:

`diagnostics.diags_names = diag1 my_second_diag`

.

`<diag_name>.intervals`

(string)Using the Intervals parser syntax, this string defines the timesteps at which data is dumped. Use a negative number or 0 to disable data dumping. example:

`diag1.intervals = 10,20:25:1`

. Note that by default the last timestep is dumped regardless of this parameter. This can be changed using the parameter`<diag_name>.dump_last_timestep`

described below.

`<diag_name>.dump_last_timestep`

(bool optional, default 1)If this is 1, the last timestep is dumped regardless of

`<diag_name>.intervals`

.

`<diag_name>.diag_type`

(string)Type of diagnostics.

`Full`

,`BackTransformed`

, and`BoundaryScraping`

example:`diag1.diag_type = Full`

or`diag1.diag_type = BackTransformed`

`<diag_name>.format`

(string optional, default`plotfile`

)Flush format. Possible values are:

`plotfile`

for native AMReX format.`checkpoint`

for a checkpoint file, only works with`<diag_name>.diag_type = Full`

.`openpmd`

for OpenPMD format openPMD. Requires to build WarpX with`USE_OPENPMD=TRUE`

(see instructions).`ascent`

for in-situ visualization using Ascent.`sensei`

for in-situ visualization using Sensei.

example:

`diag1.format = openpmd`

.

`<diag_name>.sensei_config`

(string)Only read if

`<diag_name>.format = sensei`

. Points to the SENSEI XML file which selects and configures the desired back end.

`<diag_name>.sensei_pin_mesh`

(integer; 0 by default)Only read if

`<diag_name>.format = sensei`

. When 1 lower left corner of the mesh is pinned to 0.,0.,0.

`<diag_name>.openpmd_backend`

(`bp`

,`h5`

or`json`

) optional, only used if`<diag_name>.format = openpmd`

I/O backend for openPMD data dumps.

`bp`

is the ADIOS I/O library,`h5`

is the HDF5 format, and`json`

is a simple text format.`json`

only works with serial/single-rank jobs. When WarpX is compiled with openPMD support, the first available backend in the order given above is taken.

`<diag_name>.openpmd_encoding`

(optional,`v`

(variable based),`f`

(file based) or`g`

(group based) ) only read if`<diag_name>.format = openpmd`

.openPMD file output encoding. File based: one file per timestep (slower), group/variable based: one file for all steps (faster)).

`variable based`

is an experimental feature with ADIOS2 and not supported for back-transformed diagnostics. Default:`f`

(full diagnostics)

`<diag_name>.adios2_operator.type`

(`zfp`

,`blosc`

) optional,ADIOS2 I/O operator type for openPMD data dumps.

`<diag_name>.adios2_operator.parameters.*`

optional,ADIOS2 I/O operator parameters for openPMD data dumps.

A typical example for ADIOS2 output using lossless compression with

`blosc`

using the`zstd`

compressor and 6 CPU treads per MPI Rank (e.g. for a GPU run with spare CPU resources):<diag_name>.adios2_operator.type = blosc <diag_name>.adios2_operator.parameters.compressor = zstd <diag_name>.adios2_operator.parameters.clevel = 1 <diag_name>.adios2_operator.parameters.doshuffle = BLOSC_BITSHUFFLE <diag_name>.adios2_operator.parameters.threshold = 2048 <diag_name>.adios2_operator.parameters.nthreads = 6 # per MPI rank (and thus per GPU)

or for the lossy ZFP compressor using very strong compression per scalar:

<diag_name>.adios2_operator.type = zfp <diag_name>.adios2_operator.parameters.precision = 3

`<diag_name>.adios2_engine.type`

(`bp4`

,`sst`

,`ssc`

,`dataman`

) optional,ADIOS2 Engine type for openPMD data dumps. See full list of engines at ADIOS2 readthedocs

`<diag_name>.adios2_engine.parameters.*`

optional,ADIOS2 Engine parameters for openPMD data dumps.

An example for parameters for the BP engine are setting the number of writers (

`NumAggregators`

), transparently redirecting data to burst buffers etc. A detailed list of engine-specific parameters are available at the official ADIOS2 documentation<diag_name>.adios2_engine.parameters.NumAggregators = 2048 <diag_name>.adios2_engine.parameters.BurstBufferPath="/mnt/bb/username"

`<diag_name>.fields_to_plot`

(list of strings, optional)Fields written to output. Possible scalar fields:

`part_per_cell`

`rho`

`phi`

`F`

`part_per_grid`

`divE`

`divB`

and`rho_<species_name>`

, where`<species_name>`

must match the name of one of the available particle species. Note that`phi`

will only be written out when do_electrostatic==labframe. Also, note that for`<diag_name>.diag_type = BackTransformed`

, the only scalar field currently supported is`rho`

. Possible vector field components in Cartesian geometry:`Ex`

`Ey`

`Ez`

`Bx`

`By`

`Bz`

`jx`

`jy`

`jz`

. Possible vector field components in RZ geometry:`Er`

`Et`

`Ez`

`Br`

`Bt`

`Bz`

`jr`

`jt`

`jz`

. The default is`<diag_name>.fields_to_plot = Ex Ey Ez Bx By Bz jx jy jz`

in Cartesian geometry and`<diag_name>.fields_to_plot = Er Et Ez Br Bt Bz jr jt jz`

in RZ geometry. When the special value`none`

is specified, no fields are written out. Note that the fields are averaged on the cell centers before they are written to file. Otherwise, we reconstruct a 2D Cartesian slice of the fields for output at \(\theta=0\).

`<diag_name>.dump_rz_modes`

(0 or 1) optional (default 0)Whether to save all modes when in RZ. When

`openpmd_backend = openpmd`

, this parameter is ignored and all modes are saved.

`<diag_name>.particle_fields_to_plot`

(list of strings, optional)Names of per-cell diagnostics of particle properties to calculate and output as additional fields. Note that the deposition onto the grid does not respect the particle shape factor, but instead uses nearest-grid point interpolation. Default is none. Parser functions for these field names are specified by

`<diag_name>.particle_fields.<field_name>(x,y,z,ux,uy,uz)`

. Also, note that this option is only available for`<diag_name>.diag_type = Full`

`<diag_name>.particle_fields_species`

(list of strings, optional)Species for which to calculate

`particle_fields_to_plot`

. Fields will be calculated separately for each specified species. The default is a list of all of the available particle species.

`<diag_name>.particle_fields.<field_name>.do_average`

(0 or 1) optional (default 1)Whether the diagnostic is an average or a sum. With an average, the sum over the specified function is divided by the sum of the particle weights in each cell.

`<diag_name>.particle_fields.<field_name>(x,y,z,ux,uy,uz)`

(parser string)Parser function to be calculated for each particle per cell. The averaged field written is

\[\texttt{<field_name>_<species>} = \frac{\sum_{i=1}^N w_i \, f(x_i,y_i,z_i,u_{x,i},u_{y,i},u_{z,i})}{\sum_{i=1}^N w_i}\]where \(w_i\) is the particle weight, \(f()\) is the parser function, and \((x_i,y_i,z_i)\) are particle positions in units of a meter. The sums are over all particles of type

`<species>`

in a cell (ignoring the particle shape factor) that satisfy`<diag_name>.particle_fields.<field_name>.filter(x,y,z,ux,uy,uz)`

. When`<diag_name>.particle_fields.<field_name>.do_average`

is 0, the division by the sum over particle weights is not done. In 1D or 2D, the particle coordinates will follow the WarpX convention. \((u_{x,i},u_{y,i},u_{z,i})\) are components of the particle four-momentum. \(u = \gamma v/c\), \(\gamma\) is the Lorentz factor, \(v\) is the particle velocity and \(c\) is the speed of light. For photons, we use the standardized momentum \(u = p/(m_{e}c)\), where \(p\) is the momentum of the photon and \(m_{e}\) the mass of an electron.

`<diag_name>.particle_fields.<field_name>.filter(x,y,z,ux,uy,uz)`

(parser string, optional)Parser function returning a boolean for whether to include a particle in the diagnostic. If not specified, all particles will be included (see above). The function arguments are the same as above.

`<diag_name>.plot_raw_fields`

(0 or 1) optional (default 0)By default, the fields written in the plot files are averaged on the cell centers. When

`<diag_name>.plot_raw_fields = 1`

, then the raw (i.e. non-averaged) fields are also saved in the output files. Only works with`<diag_name>.format = plotfile`

. See this section in the yt documentation for more details on how to view raw fields.

`<diag_name>.plot_raw_fields_guards`

(0 or 1) optional (default 0)Only used when

`<diag_name>.plot_raw_fields = 1`

. Whether to include the guard cells in the output of the raw fields. Only works with`<diag_name>.format = plotfile`

.

`<diag_name>.coarsening_ratio`

(list of int) optional (default 1 1 1)Reduce size of the field output by this ratio in each dimension. (This is done by averaging the field over 1 or 2 points along each direction, depending on the staggering). If

`blocking_factor`

and`max_grid_size`

are used for the domain decomposition, as detailed in the domain decomposition section,`coarsening_ratio`

should be an integer divisor of`blocking_factor`

. If`warpx.numprocs`

is used instead, the total number of cells in a given dimension must be a multiple of the`coarsening_ratio`

multiplied by`numprocs`

in that dimension.

`<diag_name>.file_prefix`

(string) optional (default diags/<diag_name>)Root for output file names. Supports sub-directories.

`<diag_name>.file_min_digits`

(int) optional (default 6)The minimum number of digits used for the iteration number appended to the diagnostic file names.

`<diag_name>.diag_lo`

(list float, 1 per dimension) optional (default -infinity -infinity -infinity)Lower corner of the output fields (if smaller than

`warpx.dom_lo`

, then set to`warpx.dom_lo`

). Currently, when the`diag_lo`

is different from`warpx.dom_lo`

, particle output is disabled.

`<diag_name>.diag_hi`

(list float, 1 per dimension) optional (default +infinity +infinity +infinity)Higher corner of the output fields (if larger than

`warpx.dom_hi`

, then set to`warpx.dom_hi`

). Currently, when the`diag_hi`

is different from`warpx.dom_hi`

, particle output is disabled.

`<diag_name>.write_species`

(0 or 1) optional (default 1)Whether to write species output or not. For checkpoint format, always set this parameter to 1.

`<diag_name>.species`

(list of string, default all physical species in the simulation)Which species dumped in this diagnostics.

`<diag_name>.<species_name>.variables`

(list of strings separated by spaces, optional)List of particle quantities to write to output. Choices are

`w`

for the particle weight and`ux`

`uy`

`uz`

for the particle momenta. By default, all particle quantities are written. If`<diag_name>.<species_name>.variables = none`

, no particle data are written, except for particle positions, which are always included.

`<diag_name>.<species_name>.random_fraction`

(float) optionalIf provided

`<diag_name>.<species_name>.random_fraction = a`

, only a fraction of the particle data of this species will be dumped randomly in diag`<diag_name>`

, i.e. if rand() < a, this particle will be dumped, where rand() denotes a random number generator. The value a provided should be between 0 and 1.

`<diag_name>.<species_name>.uniform_stride`

(int) optionalIf provided

`<diag_name>.<species_name>.uniform_stride = n`

, every n particle of this species will be dumped, selected uniformly. The value provided should be an integer greater than or equal to 0.

`<diag_name>.<species_name>.plot_filter_function(t,x,y,z,ux,uy,uz)`

(string) optionalUsers can provide an expression returning a boolean for whether a particle is dumped. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent particle momenta in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. E.g. If provided (x>0.0)*(uz<10.0) only those particles located at positions x greater than 0, and those having momentum uz less than 10, will be dumped.

`amrex.async_out`

(0 or 1) optional (default 0)Whether to use asynchronous IO when writing plotfiles. This only has an effect when using the AMReX plotfile format. Please see the data analysis section for more information.

`amrex.async_out_nfiles`

(int) optional (default 64)The maximum number of files to write to when using asynchronous IO. To use asynchronous IO with more than

`amrex.async_out_nfiles`

MPI ranks, WarpX must be configured with`-DWarpX_MPI_THREAD_MULTIPLE=ON`

. Please see the data analysis section for more information.

`warpx.field_io_nfiles`

and`warpx.particle_io_nfiles`

(int) optional (default 1024)The maximum number of files to use when writing field and particle data to plotfile directories.

`warpx.mffile_nstreams`

(int) optional (default 4)Limit the number of concurrent readers per file.

### BackTransformed Diagnostics

`BackTransformed`

diag type are used when running a simulation in a boosted frame, to reconstruct output data to the lab frame. This option can be set using `<diag_name>.diag_type = BackTransformed`

. Additional options for this diagnostic include:

`<diag_name>.num_snapshots_lab`

(integer)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

. The number of lab-frame snapshots that will be written. Only this option or`intervals`

should be specified; a run-time error occurs if the user attempts to set both`num_snapshots_lab`

and`intervals`

.

`<diag_name>.intervals`

(string)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

. Using the Intervals parser syntax, this string defines the lab frame times at which data is dumped, given as multiples of the step size`dt_snapshots_lab`

or`dz_snapshots_lab`

described below. Example:`btdiag1.intervals = 10:11,20:24:2`

and`btdiag1.dt_snapshots_lab = 1.e-12`

indicate to dump at lab times`1e-11`

,`1.1e-11`

,`2e-11`

,`2.2e-11`

, and`2.4e-11`

seconds. Note that the stop interval, the second number in the slice, must always be specified. Only this option or`num_snapshots_lab`

should be specified; a run-time error occurs if the user attempts to set both`num_snapshots_lab`

and`intervals`

.

`<diag_name>.dt_snapshots_lab`

(float, in seconds)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

. The time interval in between the lab-frame snapshots (where this time interval is expressed in the laboratory frame).

`<diag_name>.dz_snapshots_lab`

(float, in meters)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

. Distance between the lab-frame snapshots (expressed in the laboratory frame).`dt_snapshots_lab`

is then computed by`dt_snapshots_lab = dz_snapshots_lab/c`

. Either dt_snapshots_lab or dz_snapshot_lab is required.

`<diag_name>.buffer_size`

(integer)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

. The default size of the back transformed diagnostic buffers used to generate lab-frame data is 256. That is, when the multifab with lab-frame data has 256 z-slices, the data will be flushed out. However, if many lab-frame snapshots are required for diagnostics and visualization, the GPU may run out of memory with many large boxes with a size of 256 in the z-direction. This input parameter can then be used to set a smaller buffer-size, preferably multiples of 8, such that, a large number of lab-frame snapshot data can be generated without running out of gpu memory. The downside to using a small buffer size, is that the I/O time may increase due to frequent flushes of the lab-frame data. The other option is to keep the default value for buffer size and use slices to reduce the memory footprint and maintain optimum I/O performance.

`<diag_name>.do_back_transformed_fields`

(0 or 1) optional (default 1)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

Whether to back transform the fields or not. Note that for`BackTransformed`

diagnostics, at least one of the options`<diag_name>.do_back_transformed_fields`

or`<diag_name>.do_back_transformed_particles`

must be 1.

`<diag_name>.do_back_transformed_particles`

(0 or 1) optional (default 1)Only used when

`<diag_name>.diag_type`

is`BackTransformed`

Whether to back transform the particle data or not. Note that for`BackTransformed`

diagnostics, at least one of the options`<diag_name>.do_back_transformed_fields`

or`<diag_name>.do_back_transformed_particles`

must be 1. If`diag_name.write_species = 0`

, then`<diag_name>.do_back_transformed_particles`

will be set to 0 in the simulation and particles will not be backtransformed.

### Boundary Scraping Diagnostics

`BoundaryScrapingDiagnostics`

are used to collect the particles that are absorbed at the boundaries, throughout the simulation.
This diagnostic type is specified by setting `<diag_name>.diag_type`

= `BoundaryScraping`

.
Currently, the only supported output format is openPMD, so the user also needs to set `<diag>.format=openpmd`

and WarpX must be compiled with openPMD turned on.
The data that is to be collected and recorded is controlled per species and per boundary by setting one or more of the flags to `1`

,
`<species>.save_particles_at_xlo/ylo/zlo`

, `<species>.save_particles_at_xhi/yhi/zhi`

, and `<species>.save_particles_at_eb`

.
(Note that this diagnostics does not save any field ; it only saves particles.)

The data collected at each boundary is written out to a subdirectory of the diagnostics directory with the name of the boundary, for example, `particles_at_xlo`

, `particles_at_zhi`

, or `particles_at_eb`

.
By default, all of the collected particle data is written out at the end of the simulation. Optionally, the `<diag_name>.intervals`

parameter can be given to specify writing out the data more often.
This can be important if a large number of particles are lost, avoiding filling up memory with the accumulated lost particle data.

In addition to their usual attributes, the saved particles have an integer attribute `timestamp`

, which
indicates the PIC iteration at which each particle was absorbed at the boundary.

### Reduced Diagnostics

`ReducedDiags`

allow the user to compute some reduced quantity (particle temperature, max of a field) and write a small amount of data to text files.

`warpx.reduced_diags_names`

(strings, separated by spaces)The names given by the user of simple reduced diagnostics. Also the names of the output .txt files. This reduced diagnostics aims to produce simple outputs of the time history of some physical quantities. If

`warpx.reduced_diags_names`

is not provided in the input file, no reduced diagnostics will be done. This is then used in the rest of the input deck; in this documentation we use`<reduced_diags_name>`

as a placeholder.

`<reduced_diags_name>.type`

(string)The type of reduced diagnostics associated with this

`<reduced_diags_name>`

. For example,`ParticleEnergy`

,`FieldEnergy`

, etc. All available types are described below in detail. For all reduced diagnostics, the first and the second columns in the output file are the time step and the corresponding physical time in seconds, respectively.`ParticleEnergy`

This type computes the total and mean relativistic particle kinetic energy among all species:

\[E_p = \sum_{i=1}^N w_i \, \left( \sqrt{|\boldsymbol{p}_i|^2 c^2 + m_0^2 c^4} - m_0 c^2 \right)\]where \(\boldsymbol{p}_i\) is the relativistic momentum of the \(i\)-th particle, \(c\) is the speed of light, \(m_0\) is the rest mass, \(N\) is the number of particles, and \(w_i\) is the weight of the \(i\)-th particle.

The output columns are the total energy of all species, the total energy per species, the total mean energy \(E_p / \sum_i w_i\) of all species, and the total mean energy per species.

`ParticleMomentum`

This type computes the total and mean relativistic particle momentum among all species:

\[\boldsymbol{P}_p = \sum_{i=1}^N w_i \, \boldsymbol{p}_i\]where \(\boldsymbol{p}_i\) is the relativistic momentum of the \(i\)-th particle, \(N\) is the number of particles, and \(w_i\) is the weight of the \(i\)-th particle.

The output columns are the components of the total momentum of all species, the total momentum per species, the total mean momentum \(\boldsymbol{P}_p / \sum_i w_i\) of all species, and the total mean momentum per species.

`FieldEnergy`

This type computes the electromagnetic field energy

\[E_f = \frac{1}{2} \sum_{\text{cells}} \left( \varepsilon_0 |\boldsymbol{E}|^2 + \frac{|\boldsymbol{B}|^2}{\mu_0} \right) \Delta V\]where \(\boldsymbol{E}\) is the electric field, \(\boldsymbol{B}\) is the magnetic field, \(\varepsilon_0\) is the vacuum permittivity, \(\mu_0\) is the vacuum permeability, \(\Delta V\) is the cell volume (or cell area in 2D), and the sum is over all cells.

The output columns are the total field energy \(E_f\), the \(\boldsymbol{E}\) field energy, and the \(\boldsymbol{B}\) field energy, at each mesh refinement level.

`FieldMomentum`

This type computes the electromagnetic field momentum

\[\boldsymbol{P}_f = \varepsilon_0 \sum_{\text{cells}} \left( \boldsymbol{E} \times \boldsymbol{B} \right) \Delta V\]where \(\boldsymbol{E}\) is the electric field, \(\boldsymbol{B}\) is the magnetic field, \(\varepsilon_0\) is the vacuum permittivity, \(\Delta V\) is the cell volume (or cell area in 2D), and the sum is over all cells.

The output columns are the components of the total field momentum \(\boldsymbol{P}_f\) at each mesh refinement level.

Note that the fields are

*not*averaged on the cell centers before their energy is computed.

`FieldMaximum`

This type computes the maximum value of each component of the electric and magnetic fields and of the norm of the electric and magnetic field vectors. Measuring maximum fields in a plasma might be very noisy in PIC, use this instead for analysis of scenarios such as an electromagnetic wave propagating in vacuum.

The output columns are the maximum value of the \(E_x\) field, the maximum value of the \(E_y\) field, the maximum value of the \(E_z\) field, the maximum value of the norm \(|E|\) of the electric field, the maximum value of the \(B_x\) field, the maximum value of the \(B_y\) field, the maximum value of the \(B_z\) field and the maximum value of the norm \(|B|\) of the magnetic field, at mesh refinement levels from 0 to \(n\).

Note that the fields are averaged on the cell centers before their maximum values are computed.

`FieldProbe`

This type computes the value of each component of the electric and magnetic fields and of the Poynting vector (a measure of electromagnetic flux) at points in the domain.

Multiple geometries for point probes can be specified via

`<reduced_diags_name>.probe_geometry = ...`

:`Point`

(default): a single point`Line`

: a line of points with equal spacing`Plane`

: a plane of points with equal spacing

**Point**: The point where the fields are measured is specified through the input parameters`<reduced_diags_name>.x_probe`

,`<reduced_diags_name>.y_probe`

and`<reduced_diags_name>.z_probe`

.**Line**: probe a 1 dimensional line of points to create a line detector. Initial input parameters`x_probe`

,`y_probe`

, and`z_probe`

designate one end of the line detector, while the far end is specified via`<reduced_diags_name>.x1_probe`

,`<reduced_diags_name>.y1_probe`

,`<reduced_diags_name>.z1_probe`

. Additionally,`<reduced_diags_name>.resolution`

must be defined to give the number of detector points along the line (equally spaced) to probe.**Plane**: probe a 2 dimensional plane of points to create a square plane detector. Initial input parameters`x_probe`

,`y_probe`

, and`z_probe`

designate the center of the detector. The detector plane is normal to a vector specified by`<reduced_diags_name>.target_normal_x`

,`<reduced_diags_name>.target_normal_y`

, and`<reduced_diags_name>.target_normal_z`

. Note that it is not necessary to specify the`target_normal`

vector in a 2D simulation (the only supported normal is in`y`

). The top of the plane is perpendicular to an “up” vector denoted by`<reduced_diags_name>.target_up_x`

,`<reduced_diags_name>.target_up_y`

, and`<reduced_diags_name>.target_up_z`

. The detector has a square radius to be determined by`<reduced_diags_name>.detector_radius`

. Similarly to the line detector, the plane detector requires a resolution`<reduced_diags_name>.resolution`

, which denotes the number of detector particles along each side of the square detector.The output columns are the value of the \(E_x\) field, the value of the \(E_y\) field, the value of the \(E_z\) field, the value of the \(B_x\) field, the value of the \(B_y\) field, the value of the \(B_z\) field and the value of the Poynting Vector \(|S|\) of the electromagnetic fields, at mesh refinement levels from 0 to \(n\), at point (\(x\), \(y\), \(z\)).

The fields are always interpolated to the measurement point. The interpolation order can be set by specifying

`<reduced_diags_name>.interp_order`

, defaulting to`1`

. In RZ geometry, this only saves the 0’th azimuthal mode component of the fields. Integrated electric and magnetic field components can instead be obtained by specifying`<reduced_diags_name>.integrate == true`

. In a*moving window*simulation, the FieldProbe can be set to follow the moving frame by specifying`<reduced_diags_name>.do_moving_window_FP = 1`

(default 0).Warning

The FieldProbe reduced diagnostic does not yet add a Lorentz back transformation for boosted frame simulations. Thus, it records field data in the boosted frame, not (yet) in the lab frame.

`RhoMaximum`

This type computes the maximum and minimum values of the total charge density as well as the maximum absolute value of the charge density of each charged species. Please be aware that measuring maximum charge densities might be very noisy in PIC simulations.

The output columns are the maximum value of the \(rho\) field, the minimum value of the \(rho\) field, the maximum value of the absolute \(|rho|\) field of each charged species.

Note that the charge densities are averaged on the cell centers before their maximum values are computed.

`FieldReduction`

This type computes an arbitrary reduction of the positions, the current density, and the electromagnetic fields.

`<reduced_diags_name>.reduced_function(x,y,z,Ex,Ey,Ez,Bx,By,Bz,jx,jy,jz)`

(string)An analytic function to be reduced must be provided, using the math parser.

`<reduced_diags_name>.reduction_type`

(string)The type of reduction to be performed. It must be either

`Maximum`

,`Minimum`

or`Integral`

.`Integral`

computes the spatial integral of the function defined in the parser by summing its value on all grid points and multiplying the result by the volume of a cell. Please be also aware that measuring maximum quantities might be very noisy in PIC simulations.

The only output column is the reduced value.

Note that the fields are averaged on the cell centers before the reduction is performed.

`ParticleNumber`

This type computes the total number of macroparticles and of physical particles (i.e. the sum of their weights) in the whole simulation domain (for each species and summed over all species). It can be useful in particular for simulations with creation (ionization, QED processes) or removal (resampling) of particles.

The output columns are total number of macroparticles summed over all species, total number of macroparticles of each species, sum of the particles’ weight summed over all species, sum of the particles’ weight of each species.

`BeamRelevant`

This type computes properties of a particle beam relevant for particle accelerators, like position, momentum, emittance, etc.

`<reduced_diags_name>.species`

must be provided, such that the diagnostics are done for this (beam-like) species only.The output columns (for 3D-XYZ) are the following, where the average is done over the whole species (typical usage: the particle beam is in a separate species):

[0]: simulation step (iteration).

[1]: time (s).

[2], [3], [4]: The mean values of beam positions (m) \(\langle x \rangle\), \(\langle y \rangle\), \(\langle z \rangle\).

[5], [6], [7]: The mean values of beam relativistic momenta (kg m/s) \(\langle p_x \rangle\), \(\langle p_y \rangle\), \(\langle p_z \rangle\).

[8]: The mean Lorentz factor \(\langle \gamma \rangle\).

[9], [10], [11]: The RMS values of beam positions (m) \(\delta_x = \sqrt{ \langle (x - \langle x \rangle)^2 \rangle }\), \(\delta_y = \sqrt{ \langle (y - \langle y \rangle)^2 \rangle }\), \(\delta_z = \sqrt{ \langle (z - \langle z \rangle)^2 \rangle }\).

[12], [13], [14]: The RMS values of beam relativistic momenta (kg m/s) \(\delta_{px} = \sqrt{ \langle (p_x - \langle p_x \rangle)^2 \rangle }\), \(\delta_{py} = \sqrt{ \langle (p_y - \langle p_y \rangle)^2 \rangle }\), \(\delta_{pz} = \sqrt{ \langle (p_z - \langle p_z \rangle)^2 \rangle }\).

[15]: The RMS value of the Lorentz factor \(\sqrt{ \langle (\gamma - \langle \gamma \rangle)^2 \rangle }\).

[16], [17], [18]: beam projected transverse RMS normalized emittance (m) \(\epsilon_x = \dfrac{1}{mc} \sqrt{\delta_x^2 \delta_{px}^2 - \Big\langle (x-\langle x \rangle) (p_x-\langle p_x \rangle) \Big\rangle^2}\), \(\epsilon_y = \dfrac{1}{mc} \sqrt{\delta_y^2 \delta_{py}^2 - \Big\langle (y-\langle y \rangle) (p_y-\langle p_y \rangle) \Big\rangle^2}\), \(\epsilon_z = \dfrac{1}{mc} \sqrt{\delta_z^2 \delta_{pz}^2 - \Big\langle (z-\langle z \rangle) (p_z-\langle p_z \rangle) \Big\rangle^2}\).

[19], [20]: Twiss alpha for the transverse directions \(\alpha_x = - \Big\langle (x-\langle x \rangle) (p_x-\langle p_x \rangle) \Big\rangle \Big/ \epsilon_x\), \(\alpha_y = - \Big\langle (y-\langle y \rangle) (p_y-\langle p_y \rangle) \Big\rangle \Big/ \epsilon_y\).

[21], [22]: beta function for the transverse directions (m) \(\beta_x = \dfrac{{\delta_x}^2}{\epsilon_x}\), \(\beta_y = \dfrac{{\delta_y}^2}{\epsilon_y}\).

[23]: The charge of the beam (C).

For 2D-XZ, \(\langle y \rangle\), \(\delta_y\), and \(\epsilon_y\) will not be outputted.

`LoadBalanceCosts`

This type computes the cost, used in load balancing, for each box on the domain. The cost \(c\) is computed as

\[c = n_{\text{particle}} \cdot w_{\text{particle}} + n_{\text{cell}} \cdot w_{\text{cell}},\]where \(n_{\text{particle}}\) is the number of particles on the box, \(w_{\text{particle}}\) is the particle cost weight factor (controlled by

`algo.costs_heuristic_particles_wt`

), \(n_{\text{cell}}\) is the number of cells on the box, and \(w_{\text{cell}}\) is the cell cost weight factor (controlled by`algo.costs_heuristic_cells_wt`

).

`LoadBalanceEfficiency`

This type computes the load balance efficiency, given the present costs and distribution mapping. Load balance efficiency is computed as the mean cost over all ranks, divided by the maximum cost over all ranks. Until costs are recorded, load balance efficiency is output as -1; at earliest, the load balance efficiency can be output starting at step 2, since costs are not recorded until step 1.

`ParticleHistogram`

This type computes a user defined particle histogram.

`<reduced_diags_name>.species`

(string)A species name must be provided, such that the diagnostics are done for this species.

`<reduced_diags_name>.histogram_function(t,x,y,z,ux,uy,uz)`

(string)A histogram function must be provided. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent the particle momenta in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. E.g.

`x`

produces the position (density) distribution in x.`ux`

produces the momentum distribution in x,`sqrt(ux*ux+uy*uy+uz*uz)`

produces the speed distribution. The default value of the histogram without normalization is \(f = \sum\limits_{i=1}^N w_i\), where \(\sum\limits_{i=1}^N\) is the sum over \(N\) particles in that bin, \(w_i\) denotes the weight of the ith particle.

`<reduced_diags_name>.bin_number`

(int > 0)This is the number of bins used for the histogram.

`<reduced_diags_name>.bin_max`

(float)This is the maximum value of the bins.

`<reduced_diags_name>.bin_min`

(float)This is the minimum value of the bins.

`<reduced_diags_name>.normalization`

(optional)This provides options to normalize the histogram:

`unity_particle_weight`

uses unity particle weight to compute the histogram, such that the values of the histogram are the number of counted macroparticles in that bin, i.e. \(f = \sum\limits_{i=1}^N 1\), \(N\) is the number of particles in that bin.`max_to_unity`

will normalize the histogram such that its maximum value is one.`area_to_unity`

will normalize the histogram such that the area under the histogram is one, so the histogram is also the probability density function.If nothing is provided, the macroparticle weight will be used to compute the histogram, and no normalization will be done.

`<reduced_diags_name>.filter_function(t,x,y,z,ux,uy,uz)`

(string) optionalUsers can provide an expression returning a boolean for whether a particle is taken into account when calculating the histogram. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent particle momenta in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. E.g. If provided (x>0.0)*(uz<10.0) only those particles located at positions x greater than 0, and those having momentum uz less than 10, will be taken into account when calculating the histogram.

The output columns are values of the 1st bin, the 2nd bin, …, the nth bin. An example input file and a loading python script of using the histogram reduced diagnostics are given in

`Examples/Tests/initial_distribution/`

.

`ParticleHistogram2D`

This type computes a user defined, 2D particle histogram.

`<reduced_diags_name>.species`

(string)A species name must be provided, such that the diagnostics are done for this species.

`<reduced_diags_name>.histogram_function_abs(t,x,y,z,ux,uy,uz,w)`

(string)A histogram function must be provided for the abscissa axis. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent the particle velocities in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. w represents the weight.

`<reduced_diags_name>.histogram_function_ord(t,x,y,z,ux,uy,uz,w)`

(string)A histogram function must be provided for the ordinate axis.

`<reduced_diags_name>.bin_number_abs`

(int > 0) and`<reduced_diags_name>.bin_number_ord`

(int > 0)These are the number of bins used for the histogram for the abscissa and ordinate axis respectively.

`<reduced_diags_name>.bin_max_abs`

(float) and`<reduced_diags_name>.bin_max_ord`

(float)These are the maximum value of the bins for the abscissa and ordinate axis respectively. Particles with values outside of these ranges are discarded.

`<reduced_diags_name>.bin_min_abs`

(float) and`<reduced_diags_name>.bin_min_ord`

(float)These are the minimum value of the bins for the abscissa and ordinate axis respectively. Particles with values outside of these ranges are discarded.

`<reduced_diags_name>.filter_function(t,x,y,z,ux,uy,uz,w)`

(string) optionalUsers can provide an expression returning a boolean for whether a particle is taken into account when calculating the histogram. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent particle velocities in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. w represents the weight.

`<reduced_diags_name>.value_function(t,x,y,z,ux,uy,uz,w)`

(string) optionalUsers can provide an expression for the weight used to calculate the number of particles per cell associated with the selected abscissa and ordinate functions and/or the filter function. t represents the physical time in seconds during the simulation. x, y, z represent particle positions in the unit of meter. ux, uy, uz represent particle velocities in the unit of \(\gamma v/c\), where \(\gamma\) is the Lorentz factor, \(v/c\) is the particle velocity normalized by the speed of light. w represents the weight.

The output is a

`<reduced_diags_name>`

folder containing a set of openPMD files. An example input file and a loading python script of using the histogram2D reduced diagnostics are given in`Examples/Tests/histogram2D/`

.

`ParticleExtrema`

This type computes the minimum and maximum values of particle position, momentum, gamma, weight, and the \(\chi\) parameter for QED species.

`<reduced_diags_name>.species`

must be provided, such that the diagnostics are done for this species only.The output columns are minimum and maximum position \(x\), \(y\), \(z\); minimum and maximum momentum \(p_x\), \(p_y\), \(p_z\); minimum and maximum gamma \(\gamma\); minimum and maximum weight \(w\); minimum and maximum \(\chi\).

Note that when the QED parameter \(\chi\) is computed, field gather is carried out at every output, so the time of the diagnostic may be long depending on the simulation size.

`ChargeOnEB`

This type computes the total surface charge on the embedded boundary (in Coulombs), by using the formula

\[Q_{tot} = \epsilon_0 \iint dS \cdot E\]where the integral is performed over the surface of the embedded boundary.

When providing

`<reduced_diags_name>.weighting_function(x,y,z)`

, the computed integral is weighted:\[Q = \epsilon_0 \iint dS \cdot E \times weighting(x, y, z)\]In particular, by choosing a weighting function which returns either 1 or 0, it is possible to compute the charge on only some part of the embedded boundary.

`<reduced_diags_name>.intervals`

(string)Using the Intervals Parser syntax, this string defines the timesteps at which reduced diagnostics are written to file.

`<reduced_diags_name>.path`

(string) optional (default ./diags/reducedfiles/)The path that the output file will be stored.

`<reduced_diags_name>.extension`

(string) optional (default txt)The extension of the output file.

`<reduced_diags_name>.separator`

(string) optional (default a whitespace)The separator between row values in the output file. The default separator is a whitespace.

`<reduced_diags_name>.precision`

(integer) optional (default 14)The precision used when writing out the data to the text files.

## Lookup tables and other settings for QED modules

Lookup tables store pre-computed values for functions used by the QED modules.
**This feature requires to compile with QED=TRUE (and also with QED_TABLE_GEN=TRUE for table generation)**

`qed_bw.lookup_table_mode`

(string)There are three options to prepare the lookup table required by the Breit-Wheeler module:

`builtin`

: a built-in table is used (Warning: the table gives reasonable results but its resolution is quite low).`generate`

: a new table is generated. This option requires Boost math library (version >= 1.66) and to compile with`QED_TABLE_GEN=TRUE`

. All the following parameters must be specified (table 1 is used to evolve the optical depth of the photons, while table 2 is used for pair generation):`qed_bw.tab_dndt_chi_min`

(float): minimum chi parameter for lookup table 1 ( used for the evolution of the optical depth of the photons)`qed_bw.tab_dndt_chi_max`

(float): maximum chi parameter for lookup table 1`qed_bw.tab_dndt_how_many`

(int): number of points to be used for lookup table 1`qed_bw.tab_pair_chi_min`

(float): minimum chi parameter for lookup table 2 ( used for pair generation)`qed_bw.tab_pair_chi_max`

(float): maximum chi parameter for lookup table 2`qed_bw.tab_pair_chi_how_many`

(int): number of points to be used for chi axis in lookup table 2`qed_bw.tab_pair_frac_how_many`

(int): number of points to be used for the second axis in lookup table 2 (the second axis is the ratio between the quantum parameter of the less energetic particle of the pair and the quantum parameter of the photon).`qed_bw.save_table_in`

(string): where to save the lookup table

`load`

: a lookup table is loaded from a pre-generated binary file. The following parameter must be specified:`qed_bw.load_table_from`

(string): name of the lookup table file to read from.

`qed_qs.lookup_table_mode`

(string)There are three options to prepare the lookup table required by the Quantum Synchrotron module:

`builtin`

: a built-in table is used (Warning: the table gives reasonable results but its resolution is quite low).`generate`

: a new table is generated. This option requires Boost math library (version >= 1.66) and to compile with`QED_TABLE_GEN=TRUE`

. All the following parameters must be specified (table 1 is used to evolve the optical depth of the particles, while table 2 is used for photon emission):`qed_qs.tab_dndt_chi_min`

(float): minimum chi parameter for lookup table 1 ( used for the evolution of the optical depth of electrons and positrons)`qed_qs.tab_dndt_chi_max`

(float): maximum chi parameter for lookup table 1`qed_qs.tab_dndt_how_many`

(int): number of points to be used for lookup table 1`qed_qs.tab_em_chi_min`

(float): minimum chi parameter for lookup table 2 ( used for photon emission)`qed_qs.tab_em_chi_max`

(float): maximum chi parameter for lookup table 2`qed_qs.tab_em_chi_how_many`

(int): number of points to be used for chi axis in lookup table 2`qed_qs.tab_em_frac_how_many`

(int): number of points to be used for the second axis in lookup table 2 (the second axis is the ratio between the quantum parameter of the photon and the quantum parameter of the charged particle).`qed_qs.tab_em_frac_min`

(float): minimum value to be considered for the second axis of lookup table 2`qed_qs.save_table_in`

(string): where to save the lookup table

`load`

: a lookup table is loaded from a pre-generated binary file. The following parameter must be specified:`qed_qs.load_table_from`

(string): name of the lookup table file to read from.

`qed_bw.chi_min`

(float): minimum chi parameter to be considered by the Breit-Wheeler engine(suggested value : 0.01)

`qed_qs.chi_min`

(float): minimum chi parameter to be considered by the Quantum Synchrotron engine(suggested value : 0.001)

`qed_qs.photon_creation_energy_threshold`

(float) optional (default 2)Energy threshold for photon particle creation in *me*c^2 units.

`warpx.do_qed_schwinger`

(bool) optional (default 0)If this is 1, Schwinger electron-positron pairs can be generated in vacuum in the cells where the EM field is high enough. Activating the Schwinger process requires the code to be compiled with

`QED=TRUE`

and`PICSAR`

. If`warpx.do_qed_schwinger = 1`

, Schwinger product species must be specified with`qed_schwinger.ele_product_species`

and`qed_schwinger.pos_product_species`

. Schwinger process requires either`warpx.grid_type = collocated`

or`algo.field_gathering=momentum-conserving`

(so that different field components are computed at the same location in the grid) and does not currently support mesh refinement, cylindrical coordinates or single precision.

`qed_schwinger.ele_product_species`

(string)If Schwinger process is activated, an electron product species must be specified (the name of an existing electron species must be provided).

`qed_schwinger.pos_product_species`

(string)If Schwinger process is activated, a positron product species must be specified (the name of an existing positron species must be provided).

`qed_schwinger.y_size`

(float; in meters)If Schwinger process is activated with

`DIM=2D`

, a transverse size must be specified. It is used to convert the pair production rate per unit volume into an actual number of created particles. This value should correspond to the typical transverse extent for which the EM field has a very high value (e.g. the beam waist for a focused laser beam).

`qed_schwinger.xmin,ymin,zmin`

and`qed_schwinger.xmax,ymax,zmax`

(float) optional (default unlimited)When

`qed_schwinger.xmin`

and`qed_schwinger.xmax`

are set, they delimit the region within which Schwinger pairs can be created. The same is applicable in the other directions.

`qed_schwinger.threshold_poisson_gaussian`

(integer) optional (default 25)If the expected number of physical pairs created in a cell at a given timestep is smaller than this threshold, a Poisson distribution is used to draw the actual number of physical pairs created. Otherwise a Gaussian distribution is used. Note that, regardless of this parameter, the number of macroparticles created is at most one per cell per timestep per species (with a weight corresponding to the number of physical pairs created).

## Checkpoints and restart

WarpX supports checkpoints/restart via AMReX.
The checkpoint capability can be turned with regular diagnostics: `<diag_name>.format = checkpoint`

.

`amr.restart`

(string)Name of the checkpoint file to restart from. Returns an error if the folder does not exist or if it is not properly formatted.

## Intervals parser

WarpX can parse time step interval expressions of the form `start:stop:period`

, e.g.
`1:2:3, 4::, 5:6, :, ::10`

.
A comma is used as a separator between groups of intervals, which we call slices.
The resulting time steps are the union set of all given slices.
White spaces are ignored.
A single slice can have 0, 1 or 2 colons `:`

, just as numpy slices, but with inclusive upper bound for `stop`

.

For 0 colon the given value is the period

For 1 colon the given string is of the type

`start:stop`

For 2 colons the given string is of the type

`start:stop:period`

Any value that is not given is set to default.
Default is `0`

for the start, `std::numeric_limits<int>::max()`

for the stop and `1`

for the
period.
For the 1 and 2 colon syntax, actually having values in the string is optional
(this means that `::5`

, `100 ::10`

and `100 :`

are all valid syntaxes).

All values can be expressions that will be parsed in the same way as other integer input parameters.

**Examples**

`something_intervals = 50`

-> do something at timesteps 0, 50, 100, 150, etc. (equivalent to`something_intervals = ::50`

)`something_intervals = 300:600:100`

-> do something at timesteps 300, 400, 500 and 600.`something_intervals = 300::50`

-> do something at timesteps 300, 350, 400, 450, etc.`something_intervals = 105:108,205:208`

-> do something at timesteps 105, 106, 107, 108, 205, 206, 207 and 208. (equivalent to`something_intervals = 105 : 108 : , 205 : 208 :`

)`something_intervals = :`

or`something_intervals = ::`

-> do something at every timestep.`something_intervals = 167:167,253:253,275:425:50`

do something at timesteps 167, 253, 275, 325, 375 and 425.

This is essentially the python slicing syntax except that the stop is inclusive
(`0:100`

contains 100) and that no colon means that the given value is the period.

Note that if a given period is zero or negative, the corresponding slice is disregarded.
For example, `something_intervals = -1`

deactivates `something`

and
`something_intervals = ::-1,100:1000:25`

is equivalent to `something_intervals = 100:1000:25`

.

## Testing and Debugging

When developing, testing and debugging WarpX, the following options can be considered.

`warpx.verbose`

(`0`

or`1`

; default is`1`

for true)Controls how much information is printed to the terminal, when running WarpX.

`warpx.always_warn_immediately`

(`0`

or`1`

; default is`0`

for false)If set to

`1`

, WarpX immediately prints every warning message as soon as it is generated. It is mainly intended for debug purposes, in case a simulation crashes before a global warning report can be printed.

`warpx.abort_on_warning_threshold`

(string:`low`

,`medium`

or`high`

) optionalOptional threshold to abort as soon as a warning is raised. If the threshold is set, warning messages with priority greater than or equal to the threshold trigger an immediate abort. It is mainly intended for debug purposes, and is best used with

`warpx.always_warn_immediately=1`

.

`amrex.abort_on_unused_inputs`

(`0`

or`1`

; default is`0`

for false)When set to

`1`

, this option causes simulation to fail*after*its completion if there were unused parameters. It is mainly intended for continuous integration and automated testing to check that all tests and inputs are adapted to API changes.

`amrex.use_profiler_syncs`

(`0`

or`1`

; default is`0`

for false)Adds a synchronization at the start of communication, so any load balance will be caught there (the timer is called

`SyncBeforeComms`

), then the comm operation will run. This will slow down the run.

`warpx.serialize_initial_conditions`

(0 or 1) optional (default 0)Serialize the initial conditions for reproducible testing, e.g, in our continuous integration tests. Mainly whether or not to use OpenMP threading for particle initialization.

`warpx.safe_guard_cells`

(0 or 1) optional (default 0)Run in safe mode, exchanging more guard cells, and more often in the PIC loop (for debugging).

`ablastr.fillboundary_always_sync`

(0 or 1) optional (default 0)Run all

`FillBoundary`

operations on`MultiFab`

to force-synchronize shared nodal points. This slightly increases communication cost and can help to spot missing`nodal_sync`

flags in these operations.

A. Stanier, L. Chacón, and A. Le. A cancellation problem in hybrid particle-in-cell schemes due to finite particle size. *Journal of Computational Physics*, 420:109705, 2020. URL: https://www.sciencedirect.com/science/article/pii/S0021999120304794, doi:https://doi.org/10.1016/j.jcp.2020.109705.