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Recent developments in high peak-power table-top laser systems reaching highly relativistic light intensities have led to significant advances in laser-driven particle acceleration schemes (mainly the laser wakefield acceleration, LWFA)…

Plasma Physics · Physics 2026-05-13 Szilárd Majorosi , Nasr A. M. Hafz , Zsolt Lécz

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based…

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

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code,…

Numerical Analysis · Mathematics 2024-05-16 Dong-Yeop Na , Fernando L. Teixeira , Yuri A. Omelchenko

Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…

Computational Physics · Physics 2025-06-16 Yuxi Chen , Hongyang Zhou , Gabor Toth

We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear geometry called Curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational…

We introduce a Galilean electromagnetic particle-in-cell (GEM-PIC) algorithm, which transforms the full set of Maxwell equations and the Vlasov equation into the boosted coordinates. This approach preserves the electromagnetic structure of…

Plasma Physics · Physics 2026-05-21 Alexander Pukhov , Nina Elkina , Tom Wilson

A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…

Plasma Physics · Physics 2020-08-26 Alexander Pukhov

In this article we describe a unifying framework for variational electromagnetic particle schemes of spectral type, and we propose a novel spectral Particle-In-Cell (PIC) scheme that preserves a discrete Hamiltonian structure. Our work is…

Computational Physics · Physics 2021-02-04 Martin Campos Pinto , Jakob Ameres , Katharina Kormann , Eric Sonnendrücker

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when…

Particle-in-Cell (PIC) methods have achieved widespread recognition as simple and flexible approaches to model collisionless plasma physics in fully kinetic simulations of astrophysical environments. However, in many situations the standard…

The Particle-in-Cell (PIC) simulation has been a widely used method for studying plasma physics. However, fully three-dimensional PIC simulations always require huge computational resources. For problems with near azimuthal symmetry, recent…

Plasma Physics · Physics 2024-02-09 Jianzhao Wang , Weiming An , Rong Tang , Weiyu Meng , Jiayong Zhong

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…

Numerical Analysis · Mathematics 2023-05-10 Omkar H. Ramachandran , Leo C. Kempel , John Luginsland , B. Shanker

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-20 Bei Wang , Stephane Ethier , William Tang , Khaled Ibrahim , Kamesh Madduri , Samuel Williams , Leonid Oliker

The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or…

Computational Physics · Physics 2021-02-03 Fei Li , Weiming An , Viktor K. Decyk , Xinlu Xu , Mark J. Hogan , Warren B. Mori

This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…

Plasma Physics · Physics 2024-01-18 Andrew J. Christlieb , William A. Sands , Stephen White

A new Particle-in-Cell (PIC) method, that conserves energy exactly, is presented. The particle equations of motion and the Maxwell's equations are differenced implicitly in time by the midpoint rule and solved concurrently by a…

Computational Physics · Physics 2015-05-30 Stefano Markidis , Giovanni Lapenta

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial…

High Energy Astrophysical Phenomena · Physics 2023-01-24 Rouven Lemmerz , Mohamad Shalaby , Timon Thomas , Christoph Pfrommer

Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in…

Computational Physics · Physics 2020-02-19 Guangye Chen , Luis Chacón , Lin Yin , Brian J. Albright , David J. Stark , Robert F. Bird

A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference…

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