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Many high power electronic devices operate in a regime where the current they draw is limited by the self-fields of the particles. This space-charge-limited current poses particular challenges for numerical modeling where common techniques…

Plasma Physics · Physics 2020-07-07 Peter H. Stoltz , John W. Luginsland , Andrew M. Chap , David N. Smithe , John R. Cary

The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or…

Computational Physics · Physics 2017-05-24 Giovanni Lapenta , Diego Gonzalez-Herrero , Elisabetta Boella

In this paper, we develop an asymptotic-preserving and energy-conserving (APEC) Particle-In-Cell (PIC) algorithm for the Vlasov-Maxwell system. This algorithm not only guarantees that the asymptotic limiting of the discrete scheme is a…

Plasma Physics · Physics 2023-06-14 Lijie Ji , Zhiguo Yang , Zhuoning Li , Dong Wu , Shi Jin , Zhenli Xu

Aging and stability of gaseous ionization detectors are intricately related to charging up, accumulation of space charge and formation of discharges. All these phenomena, in their turn, depend on the dynamics of charged particles within the…

Instrumentation and Detectors · Physics 2024-03-06 Purba Bhattacharya , Promita Roy , Tanay Dey , Jaydeep Datta , Prasant K. Rout , Nayana Majumdar , Supratik Mukhopadhyay

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

In this work, we present a novel family of explicit relaxation Particle-in-Cell (ER-PIC) methods for the Vlasov-Poisson equation with a strong magnetic field. These schemes achieve exact energy conservation by combining a splitting…

Numerical Analysis · Mathematics 2026-03-31 Lina Wang , Bin Wang

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

The Particle-In-Cell (PIC) method for plasma simulation tracks particle phase space information using particle and grid data structures. High computational costs in 2D and 3D device-scale PIC simulations necessitate parallelization, with…

Computational Physics · Physics 2025-06-27 Libn Varghese , Bhaskar Chaudhury , Miral Shah , Mainak Bandyopadhyay

Achieving large-scale kinetic modelling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications such as plasma etching, kinetic simulations are necessary to…

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

For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency.…

Computational Physics · Physics 2016-05-04 Guangye Chen , Luis Chacon

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

We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation…

Solar and Stellar Astrophysics · Physics 2015-06-12 Troels Haugboelle , Jacob Trier Frederiksen , Aake Nordlund

The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element (IFE) method is efficient for solving interface problems on…

Numerical Analysis · Mathematics 2019-10-18 Jinwei Bai , Yong Cao , Yuchuan Chu , Xu Zhang

We benchmark and analyze the error of energy conservation (EC) scheme for Particle in cell/Monte-Carlo Couple (PIC/MCC) algorithms by a radio frequency discharging simulation. The plasma heating behaviors and electron distributing functions…

Plasma Physics · Physics 2014-01-30 Wang Hong-Yu , Jiang Wei , Sun Peng , Kong Ling-Bao

This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach…

Computational Physics · Physics 2026-04-06 Tobias Ott , Stephen Copplestone , Marcel Pfeiffer

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

In simulations of partial differential equations using particle-in-cell (PIC) methods, it is often advantageous to resample the particle distribution function to increase simulation accuracy, reduce compute cost, and/or avoid numerical…

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

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