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We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining…

Numerical Analysis · Mathematics 2017-10-05 Michael Kraus , Katharina Kormann , Philip J. Morrison , Eric Sonnendrücker

In order to perform physically faithful particle-in-cell (PIC) simulations, the Gauss's law stands as a critical requirement, since its violation often leads to catastrophic errors in long-term plasma simulations. This work proposes a novel…

Plasma Physics · Physics 2025-06-04 Zhonghua Qiao , Zhenli Xu , Qian Yin , Shenggao Zhou

This paper presents a novel 3-D full electromagnetic particle-in-cell (PIC) code called JefiPIC, which uses Jefimenko's equations as the electromagnetic (EM) field solver through a full-space integration method. Leveraging the power of…

Computational Physics · Physics 2023-12-27 Jiannan Chen , Jun-Jie Zhang , Xueming Li , Hai-Liang Qiao , Yongtao Zhao

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

The state of the art in electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) has advanced significantly in the last few years. These have included understanding function spaces that must be used to represent sources and fields…

Computational Physics · Physics 2022-08-29 Omkar H. Ramachandran , Zane D. Crawford , Scott O'Connor , John Luginsland , B. Shanker

Phenomena taking place in capacitively coupled plasmas with large electrodes and driven at very high frequencies are studied numerically utilizing a novel energy- and charge-conserving implicit fully electromagnetic particle-in-cell / Monte…

Plasma Physics · Physics 2023-05-17 D. Eremin , E. Kemaneci , M. Matsukuma , T. Mussenbrock , R. P. Brinkmann

Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…

Computational Engineering, Finance, and Science · Computer Science 2026-01-13 Christian Faßbender , Tim Bürchner , Philipp Kopp , Ernst Rank , Stefan Kollmannsberger

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

Smoothing short-wavelength charge density variations can stabilize explicit electrostatic particle-in-cell (PIC) plasma simulations against grid heating and cold beam instabilities, which cause unphysical heating when the Debye length is…

Plasma Physics · Physics 2025-03-10 Gregory R. Werner , Luke C. Adams , John R. Cary

This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC methods are subject tostability constraints on the time and…

Numerical Analysis · Mathematics 2015-11-24 Francis Filbet , Luis Miguel Rodrigues

Optimizing iPIC3D, an implicit Particle-in-Cell (PIC) code, for large-scale 3D plasma simulations is crucial for space and astrophysical applications. This work focuses on characterizing iPIC3D's communication efficiency through strategic…

Plasma Physics · Physics 2024-08-06 Jeremy J. Williams , Daniel Medeiros , Ivy B. Peng , Stefano Markidis

We present a 2.5-dimensional charge-conservative electromagnetic particle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuum electronic devices (VED) with cylindrical symmetry (axisymmetry). We explore the axisymmetry present…

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty…

Plasma Physics · Physics 2013-12-19 E. Camporeale , G. L. Delzanno , B. K. Bergen , J. D. Moulton

An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to…

Numerical Analysis · Mathematics 2023-07-24 K. R. Arun , Rahuldev Ghorai , Mainak Kar

We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This…

Numerical Analysis · Mathematics 2016-05-04 Haksu Moon , Fernando L. Teixeira , Yuri A. Omelchenko

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 introduce a quasi-static particle-in-cell (PIC) code -- WAND-PIC -- which does not suffer from some of the common limitations of many quasi-static PICs, such as the need for a predictor-corrector method in solving electromagnetic fields.…

Plasma Physics · Physics 2022-04-22 Tianhong Wang , Vladimir Khudik , Jihoon Kim , Gennady Shvets

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

We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…

Numerical Analysis · Mathematics 2018-08-14 Fanhai Zeng , Ian Turner , Kevin Burrage , George Em Karniadakis

We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite…

Numerical Analysis · Mathematics 2023-04-05 Yingzhe Li , Martin Campos Pinto , Florian Holderied , Stefan Possanner , Eric Sonnendrücker