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We derive a consistent set of moments equations for CR-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is…

High Energy Astrophysical Phenomena · Physics 2022-03-18 Philip F. Hopkins , Jonathan Squire , Iryna S. Butsky

Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC…

Computational Physics · Physics 2019-01-09 Gregory R. Werner , Thomas G. Jenkins , Andrew M. Chap , John R. Cary

We formulate a magnetohydrodynamic-particle-in-cell (MHD-PIC) method for describing the interaction between collisionless cosmic ray (CR) particles and a thermal plasma. The thermal plasma is treated as a fluid, obeying equations of ideal…

High Energy Astrophysical Phenomena · Physics 2015-08-19 Xue-Ning Bai , Damiano Caprioli , Lorenzo Sironi , Anatoly Spitkovsky

We describe an implementation of a particle physics module available for the PLUTO code, appropriate for the dynamical evolution of a plasma consisting of a thermal fluid and a non-thermal component represented by relativistic charged…

High Energy Astrophysical Phenomena · Physics 2018-05-23 A. Mignone , G. Bodo , B. Vaidya , G. Mattia

This paper introduces a novel formulation of the Particle-In-Cell (PIC) method for the modeling of relativistic plasmas, which leverages the ability of the Pseudo-Spectral Analytical Time-Domain solver (PSATD) to handle arbitrary time…

Plasma Physics · Physics 2023-12-29 Olga Shapoval , Edoardo Zoni , Remi Lehe , Maxence Thevenet , Jean-Luc Vay

The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To partially eliminate these…

Plasma Physics · Physics 2024-02-12 Arkady Gonoskov

Relativistic magnetic reconnection is a non-ideal plasma process that is a source of non-thermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection…

High Energy Astrophysical Phenomena · Physics 2023-07-19 Hannah Klion , Revathi Jambunathan , Michael E. Rowan , Eloise Yang , Donald Willcox , Jean-Luc Vay , Remi Lehe , Andrew Myers , Axel Huebl , Weiqun Zhang

The particle-in-cell (PIC) method is a well-established and widely used kinetic plasma modelling approach that provides a hybrid Lagrangian-Eulerian approach to solve the plasma kinetic equation. Despite its power in capturing details of…

Plasma Physics · Physics 2024-11-11 Maryam Reza , Farbod Faraji , Aaron Knoll

We present the formulation, algorithm and numerical tests of the magnetohydrodynamic-particle-in-cell (MHD-PIC) method with particles treated under the guiding center approximation, which we term the MHD-gPIC method, and it is implemented…

High Energy Astrophysical Phenomena · Physics 2025-10-20 Zitao Hu , Xue-Ning Bai , Xiaochen Sun

The reduced speed of light approximation (RSLA) has been employed to speed up radiative transfer simulations of reionization by a factor of $\gtrsim 5-10$. However, it has been shown to cause significant errors in the HI-ionizing background…

Cosmology and Nongalactic Astrophysics · Physics 2024-12-20 Christopher Cain

The gyro-resonant cosmic-ray (CR) streaming instability is believed to play a crucial role in CR transport, leading to growth of Alfv\'en waves at small scales that scatter CRs, and impacts the interaction of CRs with the ISM on large…

High Energy Astrophysical Phenomena · Physics 2019-05-15 Xue-Ning Bai , Eve C. Ostriker , Illya Plotnikov , James M. Stone

Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while…

Plasma Physics · Physics 2021-09-15 Yinsi Shou , Valeriy Tenishev , Yuxi Chen , Gabor Toth , Natalia Ganushkina

We extend the recently developed entropic and conservative variance reduction framework [M. Sadr, N. G. Hadjiconstantinou, A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of…

Computational Physics · Physics 2026-02-18 Victor Windhab , Andreas Adelmann , Mohsen Sadr

We present a novel Relativistic Semi-Implicit Method (RelSIM) for particle-in-cell (PIC) simulations of astrophysical plasmas, implemented in a code framework ready for production runs. While explicit PIC methods have gained widespread…

High Energy Astrophysical Phenomena · Physics 2023-08-29 Fabio Bacchini

Astrophysical observations suggest that magnetic reconnection in relativistic plasmas plays an important role in the acceleration of energetic particles. Modeling this accurately requires numerical schemes capable of addressing large scales…

Plasma Physics · Physics 2025-09-16 K. M. Schoeffler , F. Bacchini , K. Kormann , B. Eichmann , M. E. Innocenti

The acceleration of protons and electrons in a reconnecting current sheet (RCS) is simulated with a particle-in-cell (PIC) 2D3V code for the proton-to-electron mass ratio of 100. The electro-magnetic configuration forming the RCS…

Solar and Stellar Astrophysics · Physics 2015-05-13 Taras V. Siversky , Valentina V. Zharkova

We extend the recently-developed explicit, energy-conserving particle-in-cell (PIC) scheme of [1] to the relativistic Vlasov-Maxwell system. As in the non-relativistic case, the method is built on an optimization problem that is…

Plasma Physics · Physics 2026-05-19 Lee Ricketson , Jingwei Hu

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice…

Plasma Physics · Physics 2022-01-14 Gregory R. Werner , Scott Robertson , Thomas G. Jenkins , Andrew M. Chap , John R. Cary

Particle-in-cell with Monte Carlo collisions (PIC/MCC) is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form…

Plasma Physics · Physics 2022-06-15 Mate Vass , Peter Palla , Peter Hartmann

Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon…

Computational Physics · Physics 2022-07-20 Edoardo Zoni , Remi Lehe , Olga Shapoval , Daniel Belkin , Neil Zaïm , Luca Fedeli , Henri Vincenti , Jean-Luc Vay
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