Examples

This section allows you to download input files that correspond to different physical situations.

We provide two kinds of inputs:

For a complete list of all example input files, also have a look at our Examples/ directory. It contains folders and subfolders with self-describing names that you can try. All these input files are automatically tested, so they should always be up-to-date.

Plasma-Based Acceleration

Laser-Plasma Interaction

Particle Accelerator & Beam Physics

High Energy Astrophysical Plasma Physics

Microelectronics

ARTEMIS (Adaptive mesh Refinement Time-domain ElectrodynaMIcs Solver) is based on WarpX and couples the Maxwell’s equations implementation in WarpX with classical equations that describe quantum material behavior (such as, LLG equation for micromagnetics and London equation for superconducting materials) for quantifying the performance of next-generation microelectronics.

Nuclear Fusion

Note

TODO

Fundamental Plasma Physics

Kinetic-fluid Hybrid Models

WarpX includes a reduced plasma model in which electrons are treated as a massless fluid while ions are kinetically evolved, and Ohm’s law is used to calculate the electric field. This model is appropriate for problems in which ion kinetics dominate (ion cyclotron waves, for instance). See the theory section for more details. Several examples and benchmarks of this kinetic-fluid hybrid model are provided below. A few of the examples are replications of the verification tests described in Muñoz et al. [1]. The hybrid-PIC model was added to WarpX in PR #3665 - the figures in the examples below were generated at that time.

High-Performance Computing and Numerics

The following examples are commonly used to study the performance of WarpX, e.g., for computing efficiency, scalability, and I/O patterns. While all prior examples are used for such studies as well, the examples here need less explanation on the physics, less-detail tuning on load balancing, and often simply scale (weak or strong) by changing the number of cells, AMReX block size and number of compute units.

Manipulating fields via Python

Note

TODO: The section needs to be sorted into either science cases (above) or later sections (workflows and Python API details).

An example of using Python to access the simulation charge density, solve the Poisson equation (using superLU) and write the resulting electrostatic potential back to the simulation is given in the input file below. This example uses the fields.py module included in the pywarpx library.

An example of initializing the fields by accessing their data through Python, advancing the simulation for a chosen number of time steps, and plotting the fields again through Python. The simulation runs with 128 regular cells, 8 guard cells, and 10 PML cells, in each direction. Moreover, it uses div(E) and div(B) cleaning both in the regular grid and in the PML and initializes all available electromagnetic fields (E,B,F,G) identically.

Many Further Examples, Demos and Tests

WarpX runs over 200 integration tests on a variety of modeling cases, which validate and demonstrate its functionality. Please see the Examples/Tests/ directory for many more examples.

Example References

[1]

P. A. Muñoz, N. Jain, P. Kilian, and J. Büchner. A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation. Computer Physics Communications, 224:245–264, 2018. URL: https://www.sciencedirect.com/science/article/pii/S0010465517303521, doi:https://doi.org/10.1016/j.cpc.2017.10.012.

[2]

T. Tajima and J. M. Dawson. Laser accelerator by plasma waves. AIP Conference Proceedings, 91(1):69–93, Sep 1982. URL: https://doi.org/10.1063/1.33805, doi:10.1063/1.33805.

[3]

E. Esarey, P. Sprangle, J. Krall, and A. Ting. Overview of plasma-based accelerator concepts. IEEE Transactions on Plasma Science, 24(2):252–288, 1996. doi:10.1109/27.509991.

[4]

S. C. Wilks, A. B. Langdon, T. E. Cowan, M. Roth, M. Singh, S. Hatchett, M. H. Key, D. Pennington, A. MacKinnon, and R. A. Snavely. Energetic proton generation in ultra-intense laser–solid interactions. Physics of Plasmas, 8(2):542–549, Feb 2001. URL: https://doi.org/10.1063/1.1333697, arXiv:https://pubs.aip.org/aip/pop/article-pdf/8/2/542/12669088/542\_1\_online.pdf, doi:10.1063/1.1333697.

[5]

S. S. Bulanov, A. Brantov, V. Yu. Bychenkov, V. Chvykov, G. Kalinchenko, T. Matsuoka, P. Rousseau, S. Reed, V. Yanovsky, D. W. Litzenberg, K. Krushelnick, and A. Maksimchuk. Accelerating monoenergetic protons from ultrathin foils by flat-top laser pulses in the directed-Coulomb-explosion regime. Phys. Rev. E, 78:026412, Aug 2008. URL: https://link.aps.org/doi/10.1103/PhysRevE.78.026412, doi:10.1103/PhysRevE.78.026412.

[6]

A. Macchi, M. Borghesi, and M. Passoni. Ion acceleration by superintense laser-plasma interaction. Rev. Mod. Phys., 85:751–793, May 2013. URL: https://link.aps.org/doi/10.1103/RevModPhys.85.751, doi:10.1103/RevModPhys.85.751.

[7]

B. Dromey, S. Kar, M. Zepf, and P. Foster. The plasma mirror—A subpicosecond optical switch for ultrahigh power lasers. Review of Scientific Instruments, 75(3):645–649, Feb 2004. URL: https://doi.org/10.1063/1.1646737, arXiv:https://pubs.aip.org/aip/rsi/article-pdf/75/3/645/8814694/645\_1\_online.pdf, doi:10.1063/1.1646737.

[8]

C. Rödel, M. Heyer, M. Behmke, M. Kübel, O. Jäckel, W. Ziegler, D. Ehrt, M. C. Kaluza, and G. G. Paulus. High repetition rate plasma mirror for temporal contrast enhancement of terawatt femtosecond laser pulses by three orders of magnitude. Applied Physics B, 103(2):295–302, Nov 2010. URL: http://dx.doi.org/10.1007/s00340-010-4329-7, doi:10.1007/s00340-010-4329-7.

[9]

V. Yakimenko, S. Meuren, F. Del Gaudio, C. Baumann, A. Fedotov, F. Fiuza, T. Grismayer, M. J. Hogan, A. Pukhov, L. O. Silva, and G. White. Prospect of studying nonperturbative qed with beam-beam collisions. Phys. Rev. Lett., 122:190404, May 2019. doi:10.1103/PhysRevLett.122.190404.

[10]

A. Le, W. Daughton, H. Karimabadi, and J. Egedal. Hybrid simulations of magnetic reconnection with kinetic ions and fluid electron pressure anisotropy. Physics of Plasmas, Mar 2016. 032114. URL: https://doi.org/10.1063/1.4943893, doi:10.1063/1.4943893.

[11]

M. M. Turner, A. Derzsi, Z. Donkó, D. Eremin, S. J. Kelly, T. Lafleur, and T. Mussenbrock. Simulation benchmarks for low-pressure plasmas: Capacitive discharges. Physics of Plasmas, Jan 2013. 013507. URL: https://doi.org/10.1063/1.4775084, doi:10.1063/1.4775084.

[12]

T. H. Stix. Waves in Plasmas. American Inst. of Physics, 1992. ISBN 978-0-88318-859-0. URL: https://books.google.com/books?id=OsOWJ8iHpmMC.