On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

Abstract

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 acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles are generated and interact with plasmas. However, when relativistic particles stream across the grid both in vacuum and in plasma there are many numerical issues that may arise which can lead to incorrect physics. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented. Two types of errors to these expressions are identified. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. The second arises from errors to the denominator of the integrand and lead to Cerenkov like radiation in "vacuum". These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS. Results from the customized solver are also presented. This solution will be useful for a beam of particles that all move in one direction with a small angular divergence.

38 pages, 8 figures

References in corpus (13)

• Particle acceleration in relativistic outflows
• Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm
• Numerical instability due to relativistic plasma drift in EM-PIC simulations
• Suppressing the Numerical Cherenkov Instability in FDTD PIC Codes
• Numerical stability analysis of the Pseudo-Spectral Analytical Time-Domain PIC algorithm
• Controlling the Numerical Cerenkov Instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
• Elimination of Numerical Cherenkov Instability in flowing-plasma Particle-In-Cell simulations by using Galilean coordinates
• Stable discrete representation of relativistically drifting plasmas
• Improved Numerical Cherenkov Instability Suppression in the Generalized PSTD PIC Algorithm
• Elimination of the numerical Cerenkov instability for spectral EM-PIC codes
• Modeling of Laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver
• Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit
• Lorentz boosted frame simulation of Laser wakefield acceleration in quasi-3D geometry

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