Particle-in-cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms

Relativistic magnetic reconnection is a nonideal plasma process that is a source of nonthermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a nonstandard finite-difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that, for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than that of Yee, resulting in a ∼40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss’s law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4–3 times over the standard Yee step still yields accurate results, but it only translates to modest performance improvements over CKC, due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.

[1]  D. Uzdensky,et al.  High-energy synchrotron flares powered by strongly radiative relativistic magnetic reconnection: 2D and 3D PIC simulations , 2023, Monthly notices of the Royal Astronomical Society.

[2]  S. Y. Huang,et al.  A Scheme of Full Kinetic Particle-in-cell Algorithms for GPU Acceleration Using CUDA Fortran Programming , 2022, The Astrophysical Journal Supplement Series.

[3]  K. Toma,et al.  Interaction of a Relativistic Magnetized Collisionless Shock with a Dense Clump , 2022, The Astrophysical Journal Letters.

[4]  Xiaocan Li,et al.  First-principles theory of the rate of magnetic reconnection in magnetospheric and solar plasmas , 2022, Communications Physics.

[5]  H. Ji,et al.  Magnetic reconnection in the era of exascale computing and multiscale experiments , 2022, Nature Reviews Physics.

[6]  Henri Vincenti,et al.  Porting WarpX to GPU-accelerated platforms , 2021, Parallel Comput..

[7]  Y. Mizuno,et al.  PIC methods in astrophysics: simulations of relativistic jets and kinetic physics in astrophysical systems , 2020, Living reviews in computational astrophysics.

[8]  L. Sironi,et al.  Secondary Energization in Compressing Plasmoids during Magnetic Reconnection , 2020, The Astrophysical Journal.

[9]  Jaime Fern'andez del R'io,et al.  Array programming with NumPy , 2020, Nature.

[10]  A. Almgren,et al.  Toward the modeling of chains of plasma accelerator stages with WarpX , 2019, Journal of Physics: Conference Series.

[11]  Johannes L. Schönberger,et al.  SciPy 1.0: fundamental algorithms for scientific computing in Python , 2019, Nature Methods.

[12]  L. Sironi,et al.  Relativistic Magnetic Reconnection in Electron–Positron–Proton Plasmas: Implications for Jets of Active Galactic Nuclei , 2019, The Astrophysical Journal.

[13]  Marcus S. Day,et al.  AMReX: a framework for block-structured adaptive mesh refinement , 2019, J. Open Source Softw..

[14]  D. Uzdensky,et al.  Pulsar Radio Emission Mechanism: Radio Nanoshots as a Low-frequency Afterglow of Relativistic Magnetic Reconnection , 2019, The Astrophysical Journal.

[15]  Xiaocan Li,et al.  Determining the Dominant Acceleration Mechanism during Relativistic Magnetic Reconnection in Large-scale Systems , 2019, The Astrophysical Journal.

[16]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[17]  E. Rosolowsky,et al.  Extreme jet ejections from the black hole X-ray binary V404 Cygni , 2017, 1704.08726.

[18]  G. Werner,et al.  Non-thermal particle acceleration in collisionless relativistic electron-proton reconnection , 2016, 1612.04493.

[19]  G. Werner,et al.  Nonthermal Particle Acceleration in 3D Relativistic Magnetic Reconnection in Pair Plasma , 2016, 1705.05507.

[20]  Liang Wang,et al.  The Plasma Simulation Code: A modern particle-in-cell code with patch-based load-balancing , 2016, J. Comput. Phys..

[21]  Fei Li,et al.  Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction , 2016, Comput. Phys. Commun..

[22]  Henri Vincenti,et al.  Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver , 2015, Comput. Phys. Commun..

[23]  Seiji Zenitani,et al.  Loading relativistic Maxwell distributions in particle simulations , 2015, 1504.03910.

[24]  Y. Matsumoto,et al.  Stability Property of Numerical Cherenkov Radiation and its Application to Relativistic Shock Simulations , 2014, 1412.2480.

[25]  Bing Zhang,et al.  The physics of gamma-ray bursts & relativistic jets , 2014, 1410.0679.

[26]  D. Folini,et al.  Relativistic magnetic reconnection in collisionless ion-electron plasmas explored with particle-in-cell simulations , 2014, 1404.7366.

[27]  M. Hoshino,et al.  The Generation of Nonthermal Particles in the Relativistic Magnetic Reconnection of Pair Plasmas , 2014, 1402.7139.

[28]  Jean-Luc Vay,et al.  Suppressing the numerical Cherenkov instability in FDTD PIC codes , 2014, J. Comput. Phys..

[29]  Guido Juckeland,et al.  Radiative signature of the relativistic Kelvin-Helmholtz Instability , 2013, 2013 SC - International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[30]  P. Messmer,et al.  Apar-T: code, validation, and physical interpretation of particle-in-cell results , 2013, 1308.5892.

[31]  Jean-Luc Vay,et al.  PPPS-2013: Topic 1.2: A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas , 2013, 2013 Abstracts IEEE International Conference on Plasma Science (ICOPS).

[32]  Cameron G. R. Geddes,et al.  Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame , 2011, J. Comput. Phys..

[33]  F. Longo,et al.  Gamma-Ray Flares from the Crab Nebula , 2010, Science.

[34]  M. Trifoglio,et al.  Discovery of Powerful Gamma-Ray Flares from the Crab Nebula , 2011, Science.

[35]  M. Norman,et al.  yt: A MULTI-CODE ANALYSIS TOOLKIT FOR ASTROPHYSICAL SIMULATION DATA , 2010, 1011.3514.

[36]  Cosmology,et al.  A Reconnection Switch to Trigger gamma-Ray Burst Jet Dissipation , 2010, 1011.1904.

[37]  D. Giannios UHECRs from magnetic reconnection in relativistic jets , 2010, 1007.1522.

[38]  Wilfred Pinfold Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis , 2009, HiPC 2009.

[39]  M. Hoshino,et al.  Particle Acceleration and Magnetic Dissipation in Relativistic Current Sheet of Pair Plasmas , 2007, 0708.1000.

[40]  D. Uzdensky,et al.  Dynamics of Relativistic Reconnection , 2002, astro-ph/0210206.

[41]  J. B. Cole A high-accuracy realization of the Yee algorithm using non-standard finite differences , 1997 .

[42]  C. Birdsall,et al.  Plasma Physics Via Computer , 1985 .