# Input Parameters¶

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.

`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, some of the input parameters are automatically converted to the boosted frame. (See the corresponding documentation of each input parameters.)

Note

For now, only the laser parameters will be converted.

`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.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.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 two options:

`labframe`

: Poisson’s equation is solved in the lab frame with the charge density of all species combined. There will only be E fields.`relativistic`

: Poisson’s equation is solved for each species separately taking into account their averaged velocities. The field is mapped to the simulation frame and will produce both E and B fields.

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.

## 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.

Note: in development; currently,

`2`

is supported.

`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.Note: in development; currently allowed value:

`2 2 2`

.

`geometry.coord_sys`

(integer) optional (default 0)Coordinate system used by the simulation. 0 for Cartesian, 1 for cylindrical.

`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; 0 by default)When using mesh refinement: the particles that are located inside a refinement patch, but within

`n_field_gather_buffer`

cells of the edge of this patch, will 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 mesh-refinement section for more details. If this variable is not explicitly set in the input script,`n_field_gather_buffer`

is automatically set so that it is one cell larger than`n_current_deposition_buffer`

, on the fine grid.

`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.

`warpx.n_rz_azimuthal_modes`

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

## 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.do_particles_in_pml`

, 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. For the electromagnetic solve, at PEC, the tangential electric field and the normal magnetic field are set to 0. This boundary can be used to model a dielectric or metallic surface. In the guard-cell region, the tangential electric field is set equal and opposite to the respective field component in the mirror location across the PEC boundary, and the normal electric field is set equal to the field component in the mirror location in the domain across the PEC boundary. Similarly, the tangential (and normal) magnetic field components are set equal (and opposite) to the respective magnetic field components in the mirror locations across the PEC boundary. 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. If the electrostatic solver is used, a Neumann boundary condition (with gradient 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.

## Additional PML parameters¶

`warpx.pml_ncell`

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

`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.do_pml_dive_cleaning`

(bool; default: 1)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 PSATD solver.

`warpx.do_pml_divb_cleaning`

(bool; default: 1)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.

## 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.

## 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.

`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.

`warpx.do_dynamic_scheduling`

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

`warpx.safe_guard_cells`

(0 or 1) optional (default 0)For developers: run in safe mode, exchanging more guard cells, and more often in the PIC loop (for debugging).

## 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.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"`

,`"photon"`

,`"hydrogen"`

(or equivalently`"proton"`

),`"helium"`

(or equivalently`"alpha"`

),`"boron"`

,`"carbon"`

,`"oxygen"`

,`"nitrogen"`

,`"argon"`

,`"copper"`

and`"xenon"`

. Either this 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_vel`

(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_vel_x`

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

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

(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) optional (default is`q_tot=0`

),`<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_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 argument`<species_name>.do_symmetrize`

(whether to symmetrize the beam in the x and y directions).`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>.q_tot`

(double) optional (default is`q_tot=0`

and no re-scaling is done,`weight=q_p`

) when specified it is used to re-scale the weight of externally loaded`N`

physical particles, each of charge`q_p`

, to inject macroparticles of`weight=<species_name>.q_tot/q_p/N`

.`<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. The external file must include the species`openPMD::Record``s labeled ``position`

and`momentum`

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

and`setUnitSI`

. If the external file also contains`openPMD::Records``s 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. The density specified by the density profile is interpreted to have the units of #/m^2/s. This requires the additional parameters:`<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 or z for RZ)`<species_name>.flux_direction`

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

(double)`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>.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.

`predefined`

: use one of WarpX predefined plasma profiles. It requires additional arguments`<species_name>.predefined_profile_name`

and`<species_name>.predefined_profile_params`

(see below).

`<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.`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`

. Note that the average momenta normal to the plane is not used.`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 \(\theta = \frac{k_\mathrm{B} \cdot T}{m \cdot c^2}\), “math: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 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\[n = n_0 n(x,y) n(z)\]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, \(n(z)\) 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: \(L_{ramp,up}\) \(L_{plateau}\) \(L_{ramp,down}\) \(R_c\) \(n_0\)

`<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>.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 but is currently only accessible via the Python interface. The`pywarpx._libwarpx`

function`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

Currently the scraped particle buffer relies on the user to access the data in the buffer for processing and periodically clear the buffer. 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_back_transformed_diagnostics`

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

`warpx.do_back_transformed_diagnostics=1`

. When running in a boosted frame, whether or not to plot back-transformed diagnostics for this species.

`warpx.serialize_ics`

(0 or 1)Serialize the initial conditions for reproducible testing. Mainly whether or not to use OpenMP threading for particle initialization.

`<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`

. Elements up to atomic number Z=86 (Radon) are supported, let us know if you need higher Z.

`<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

`<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.`"Harris"`

: The transverse profile is Gaussian, but the longitudinal profile is given by the Harris function (see`<laser_name>.profile_duration`

for more details)`"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_txye_file"`

: the electric field of the laser is read from an external binary file whose format is explained below. It requires to provide the name of the binary file setting the additional parameter`<laser_name>.txye_file_name`

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

(int). This allows to read only time_chunk_size timesteps from the binary 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 binary 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. The external binary file should provide E(x,y,t) on a rectangular (but non 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 if the grid is uniform or not (1 byte, 0 means non-uniform, !=0 means uniform)

np, 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] if grid is uniform, double[np] otherwise)

x_coords (double[2] if grid is uniform, double[nx] otherwise)

y_coords (double[1] if 2D, double[2] if 3D & uniform grid, double[ny] if 3D & non uniform grid)

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

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

`Examples/Modules/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, defined as \(\tau\) below:

For the

`"gaussian"`

profile:

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

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

`"harris"`

profile:

\[E(\boldsymbol{x},t) \propto \frac{1}{32}\left[10 - 15 \cos\left(\frac{2\pi t}{\tau}\right) + 6 \cos\left(\frac{4\pi t}{\tau}\right) - \cos\left(\frac{6\pi t}{\tau}\right) \right]\Theta(\tau - t)\]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).

`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`

.

`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 in 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.

`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 in 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.

`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.

`particles.B_ext_particle_init_style`

(string) optional (default is “default”)This parameter determines the type of initialization for the external magnetic field that is applied directly to the particles at every timestep. The “default” style sets the external B-field (Bx,By,Bz) to (0.0,0.0,0.0). The string can be set to “constant” if a constant external B-field is applied every timestep. If this parameter is set to “constant”, then an additional parameter, namely,

`particles.B_external_particle`

must be specified in the input file. To parse a mathematical function for the external B-field, use the option`parse_B_ext_particle_function`

. This option requires additional parameters in the input file, namely,`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)`

to apply the external B-field on the particles. Constants required in the mathematical expression can be set using`my_constants`

. For a two-dimensional simulation, it is assumed that the first and second dimensions are x and z, respectively, and the value of the By component is set to zero. Note that the current implementation of the parser for B-field on particles is applied in cartesian co-ordinates as a function of (x,y,z) even for RZ. To apply a series of plasma lenses, use the option`repeated_plasma_lens`

. This option requires the following parameters, in the lab frame,`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_B`

, the focusing strength of each lens, an array of floats. The applied field is uniform longitudinally (along z) with a hard edge, where residence corrections are used for more accurate field calculation. The field is of the form \(B_x = \mathrm{strength} \cdot y\) and \(B_y = -\mathrm{strength} \cdot x\), :math`:B_z = 0`.

`particles.E_ext_particle_init_style`

(string) optional (default is “default”)This parameter determines the type of initialization for the external electric field that is applied directly to the particles at every timestep. The “default” style set the external E-field (Ex,Ey,Ez) to (0.0,0.0,0.0). The string can be set to “constant” if a constant external E-field is to be used in the simulation at every timestep. If this parameter is set to “constant”, then an additional parameter, namely,

`particles.E_external_particle`

must be specified in the input file. To parse a mathematical function for the external E-field, use the option`parse_E_ext_particle_function`

. This option requires additional parameters in the input file, namely,`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)`

to apply the external E-field on the particles. Constants required in the mathematical expression can be set using`my_constants`

. For a two-dimensional simulation, similar to the B-field, it is assumed that the first and second dimensions are x and z, respectively, and the value of the Ey component is set to zero. Note that the current implementation of the parser for E-field on particles is applied in cartesian co-ordinates as a function of (x,y,z) even for RZ. To apply a series of plasma lenses, use the option`repeated_plasma_lens`

. This option requires the following parameters, in the lab frame,`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 focusing strength of each lens, an array of floats. The applied field is uniform longitudinally (along z) with a hard edge, where residence corrections are used for more accurate field calculation. The field is of the form \(E_x = \mathrm{strength} \cdot x\) and \(E_y = \mathrm{strength} \cdot y\), \(Ez = 0\).

`particles.E_external_particle`

&`particles.B_external_particle`

(list of float) optional (default 0. 0. 0.)Two separate parameters which add an externally applied uniform E-field or B-field to each particle which is then added to the field values gathered from the grid in the PIC cycle.

## Collision initialization¶

WarpX provides a relativistic elastic Monte Carlo binary collision model, following the algorithm given by Perez et al. (Phys. Plasmas 19, 083104, 2012). A non-relativistic Monte Carlo treatment for particles colliding with a neutral, uniform background gas is also available. 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).

`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 collsion. The types implemented are

`pairwisecoulomb`

for pairwise Coulomb collisions and`background_mcc`

for collisions between particles and a neutral background. If not specified, it defaults to`pairwisecoulomb`

.

`<collision_name>.species`

(strings)If using

`pairwisecoulomb`

type this should be the names of two species, between which the collision will be considered. The number of provided`<collision_name>.species`

should match the number of collision names, i.e.`collisions.collision_names`

. If using`background_mcc`

type this should be the name of the species for which collisions will be included. Only one species name should be given.

`<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>.ndt`

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

`<collision_name>.background_density`

(float)Only for

`background_mcc`

. The density of the neutral background gas in \(m^{-3}\).

`<collision_name>.background_temperature`

(float)Only for

`background_mcc`

. The temperature of the neutral background gas in Kelvin.

`<collision_name>.background_mass`

(float) optionalOnly for

`background_mcc`

. The mass of the background gas in kg. 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.

`<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. 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¶

`warpx.cfl`

(float)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.)

`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.

`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 and`direct`

for standard or Galilean PSATD solver (that is, with`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 gridpoints depending on`warpx.do_nodal`

).`momentum-conserving`

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

If

`algo.field_gathering`

is not specified, the default is`energy-conserving`

. If`warpx.do_nodal`

is`true`

, then`energy-conserving`

and`momentum-conserving`

are equivalent.

`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.

`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), <https://ieeexplore.ieee.org/document/1551259>)

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.

`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.

`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. Defaults to 1 unless`warpx.do_nodal = 1`

and/or`algo.field_gathering = momentum-conserving`

.Warning

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

`interpolation.field_centering_nox`

,`interpolation.field_centering_noy`

,`interpolation.field_centering_noz`

(default:`2`

in all directions)The order of interpolation used with staggered grids (

`warpx.do_nodal = 0`

) 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. High-order interpolation (order 8 in each direction, at least) is necessary to ensure stability in typical LWFA boosted-frame simulations using the Galilean PSATD or comoving PSATD schemes. This finite-order interpolation is used only when the PSATD solver is used for Maxwell’s equations. With the FDTD solver, basic linear interpolation is used instead.

`interpolation.current_centering_nox`

,`interpolation.current_centering_noy`

,`interpolation.current_centering_noz`

(default:`2`

in all directions)The order of interpolation used to center the currents from nodal to staggered grids (if

`warpx.do_current_centering = 1`

), before pushing the Maxwell fields on staggered grids. This finite-order interpolation is used only when the PSATD solver is used for Maxwell’s equations. With the FDTD solver, basic linear interpolation is used instead.

`warpx.do_current_centering`

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

`warpx.do_nodal = 1`

, the Maxwell fields are pushed on a nodal grid, it is not necessary to center the currents to a staggered grid, and we set therefore`warpx.do_current_centering = 0`

automatically, overwriting the user-defined input.

`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_nodal`

(0 or 1 ; default: 0)Whether to use a nodal grid (i.e. all fields are defined at the same points in space) or a staggered grid (i.e. Yee grid ; different fields are defined at different points in space)

`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.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. 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.

`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 would be equal the order of the solver for nodal grid, and half the order of the solver for staggered.

`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: 0)If true, a current correction scheme in Fourier space is applied in order to guarantee charge conservation.

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 and Galilean PSATD schemes, while it is not yet available for the averaged Galilean PSATD scheme (activated by the input parameter

`psatd.do_time_averaging`

).This option guarantees charge conservation only when used in combination with

`psatd.periodic_single_box_fft=1`

, namely 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.

`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.This option is currently implemented only for the standard PSATD and Galilean PSATD schemes, while it is not yet available for the averaged Galilean PSATD scheme (activated by the input parameter

`psatd.do_time_averaging`

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

`pstad.v_galilean`

(3 floats, in units of the speed of light; default 0. 0. 0.)Defines the galilean velocity. Non-zero v_galilean activates Galilean algorithm, which suppresses the Numerical Cherenkov instability in boosted-frame simulation. This requires the code to be compiled with USE_PSATD=TRUE. (see the sub-section Numerical Stability and alternate formulation in a Galilean frame in the theory section). It also requires the use of the direct current deposition option algo.current_deposition = direct (does not work with Esirkepov algorithm).

`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.

`psatd.J_linear_in_time`

(0 or 1; default: 0)Whether to perform linear interpolation of two distinct currents deposited at the beginning and the end of the time step (

`psatd.J_linear_in_time = 1`

), instead of using one single current deposited at half time (`psatd.J_linear_in_time = 0`

), for the field update in Fourier space. Currently requires`psatd.update_with_rho = 1`

,`warpx.do_dive_cleaning = 1`

, and`warpx.do_divb_cleaning = 1`

.

`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, warpx.do_nodal must be set to 1 which is not its default value.

`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`

(int) optional (default 1)When running in an accelerated platform, whether to call a deviceSynchronize 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 by bin. If

`<=0`

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

`warpx.sort_bin_size`

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

)If

`sort_intervals`

is activated particles are sorted in bins of`sort_bin_size`

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

## Diagnostics and output¶

### In-situ visualization¶

WarpX has three 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, 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>.period`

.

`<diag_name>.diag_type`

(string)Type of diagnostics. So far, only

`Full`

is supported. example:`diag1.diag_type = Full`

.

`<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>.fields_to_plot`

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

`Ex`

`Ey`

`Ez`

`Bx`

`By`

`Bz`

`jx`

`jy`

`jz`

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

. Note that the fields are averaged on the cell centers before they are written to file.

`<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 parallelization 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 5)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 (the exact test is whether the return value is > 0.5). 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. E.g. If provided (x>0.0)*(uz<10.0) only those particles located at positions x greater than 0, and those having velocity 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.

### Back-Transformed Diagnostics¶

`BackTransformedDiagnostics`

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

`warpx.do_back_transformed_diagnostics`

(0 or 1)Whether to use the

**back-transformed diagnostics**(i.e. diagnostics that perform on-the-fly conversion to the laboratory frame, when running boosted-frame simulations)

`warpx.lab_data_directory`

(string)The directory in which to save the lab frame data when using the

**back-transformed diagnostics**. If not specified, the default is is lab_frame_data.

`warpx.num_snapshots_lab`

(integer)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

. The number of lab-frame snapshots that will be written.

`warpx.dt_snapshots_lab`

(float, in seconds)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

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

`warpx.dz_snapshots_lab`

(float, in meters)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

. 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.

`warpx.do_back_transformed_fields`

(0 or 1)Whether to use the

**back-transformed diagnostics**for the fields.

`warpx.back_transformed_diag_fields`

(space-separated list of string)Which fields to dumped in back-transformed diagnostics. Choices are ‘Ex’, ‘Ey’, Ez’, ‘Bx’, ‘By’, Bz’, ‘jx’, ‘jy’, jz’ and ‘rho’. Example:

`warpx.back_transformed_diag_fields = Ex Ez By`

. By default, all fields are dumped.

`warpx.buffer_size`

(integer)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.

`slice.num_slice_snapshots_lab`

(integer)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

. The number of back-transformed field and particle data that will be written for the reduced domain defined by`slice.dom_lo`

and`slice.dom_hi`

. Note that the ‘slice’ is a reduced diagnostic which could be 1D, 2D, or 3D, aligned with the co-ordinate axes. These slices can be visualized using read_raw_data.py and the HDF5 format can be visualized using the h5py library. Please see the documentation on visualization for further details.

`slice.dt_slice_snapshots_lab`

(float, in seconds)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

. The time interval between the back-transformed reduced diagnostics (where this time interval is expressed in the laboratory frame).

`slice.particle_slice_width_lab`

(float, in meters)Only used when

`warpx.do_back_transformed_diagnostics`

is`1`

and`slice.num_slice_snapshots_lab`

is non-zero. Particles are copied from the full back-transformed diagnostic to the reduced slice diagnostic if there are within the user-defined width from the slice region defined by`slice.dom_lo`

and`slice.dom_hi`

.

### 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 a point in the domain. 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`

.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 (\(x\), \(y\), \(z\)).

Note: the norms are always interpolated to the measurement point before they are written to file. The electromagnetic field components are interpolated to the measurement point by default, but can they be saved as non-averaged by setting

`<reduced_diags_name>.raw_fields = true`

, in which case the raw fields for the cell containing the measurement point are saved. The interpolation order can be set by specifying`<reduced_diags_name>.interp_order`

, otherwise it is set to`1`

. Integrated electric and magnetic field components can instead be obtained by specifying`<reduced_diags_name>.integrate == true`

.

`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 and the electromagnetic fields.

`<reduced_diags_name>.reduced_function(x,y,z,Ex,Ey,Ez,Bx,By,Bz)`

(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):

[1], [2], [3]: The mean values of beam positions (m) \(\langle x \rangle\), \(\langle y \rangle\), \(\langle z \rangle\).

[4], [5], [6]: The mean values of beam relativistic momenta (kg m/s) \(\langle p_x \rangle\), \(\langle p_y \rangle\), \(\langle p_z \rangle\).

[7]: The mean Lorentz factor \(\langle \gamma \rangle\).

[8], [9], [10]: The RMS values of beam positions (m) \(\delta_x = \sqrt{ \langle (x - \langle x \rangle)^2 \rangle }\), \(\delta_y = \sqrt{ \langle (y - \langle y \rangle)^2 \rangle }\), \(\delta_z = \sqrt{ \langle (z - \langle z \rangle)^2 \rangle }\).

[11], [12], [13]: The RMS values of beam relativistic momenta (kg m/s) \(\delta_{px} = \sqrt{ \langle (p_x - \langle p_x \rangle)^2 \rangle }\), \(\delta_{py} = \sqrt{ \langle (p_y - \langle p_y \rangle)^2 \rangle }\), \(\delta_{pz} = \sqrt{ \langle (p_z - \langle p_z \rangle)^2 \rangle }\).

[14]: The RMS value of the Lorentz factor \(\sqrt{ \langle (\gamma - \langle \gamma \rangle)^2 \rangle }\).

[15], [16], [17]: beam projected transverse RMS normalized emittance (m) \(\epsilon_x = \dfrac{1}{mc} \sqrt{\delta_x^2 \delta_{px}^2 - \Big\langle (x-\langle x \rangle) (p_x-\langle p_x \rangle) \Big\rangle^2}\), \(\epsilon_y = \dfrac{1}{mc} \sqrt{\delta_y^2 \delta_{py}^2 - \Big\langle (y-\langle y \rangle) (p_y-\langle p_y \rangle) \Big\rangle^2}\), \(\epsilon_z = \dfrac{1}{mc} \sqrt{\delta_z^2 \delta_{pz}^2 - \Big\langle (z-\langle z \rangle) (p_z-\langle p_z \rangle) \Big\rangle^2}\).

[18]: The charge of the beam (C).

For 2D-XZ, \(\langle y \rangle\), \(\delta_y\), and \(\epsilon_y\) will not be outputed.

`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 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. E.g.

`x`

produces the position (density) distribution in x.`ux`

produces the velocity 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 (the exact test is whether the return value is > 0.5). 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. E.g. If provided (x>0.0)*(uz<10.0) only those particles located at positions x greater than 0, and those having velocity 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/`

.

`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.

`<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.

## 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_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_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.do_nodal=1`

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`

.