Ion Weibel Instability in the hybrid framework: the optimal resolution

Abstract

The study of collisionless shocks and their role in cosmic-ray acceleration has gained increasing importance through both observations and simulations. Accurately modeling the shock transition region, where particle injection occurs, requires a proper description of the microinstabilities governing its structure. In high-Mach-number shocks, such as those associated with supernova remnants, the ion Weibel instability is believed to provide the dominant dissipation mechanism. In this work, we investigate the ion Weibel instability driven by counterstreaming beams in the presence of an external perpendicular magnetic field. We employ hybrid simulations, in which ions are treated kinetically while electrons are modeled as a charge-neutralizing fluid. Although hybrid models are widely employed to study collisionless shocks, the resolution requirements needed to accurately capture ion-scale instabilities remain poorly understood. We address this issue by developing a linear theory of the ion Weibel instability tailored to the massless electron assumption of hybrid models and validating it with one- and two-dimensional simulations over a wide range of Alfvénic Mach numbers. We show that hybrid simulations can reliably reproduce the growth, saturation, and polarization of Weibel-generated magnetic fields in weakly magnetized regimes, provided that the relevant ion-scale modes are properly resolved. From the scaling of the dominant mode, we derive a minimum spatial resolution required as a function of Alfvénic Mach number. We also demonstrate that excessive resolution introduces unphysical small-scale whistler modes inherent to the massless-electron approximation. We validate the analysis by comparing the results with full particle-in-cell simulations. Together, these results provide practical guidance for hybrid simulations of collisionless shocks and beam-driven plasma systems.

9 pages, 5 figures. Few comments and simulations added, results unchanged. Matches version published by PoP

References in corpus (33)

• Particle acceleration in relativistic collisionless shocks: Fermi process at last?
• Simulations of Ion Acceleration at Non-relativistic Shocks. I. Acceleration Efficiency
• Interpenetrating plasma shells: near-equipartition magnetic field generation and non-thermal particle acceleration
• On the structure of relativistic collisionless shocks in electron-ion plasmas
• Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows
• Magnetic Field Generation in Collisionless Shocks; Pattern Growth and Transport
• Filamentation instability of counter-streaming laser-driven plasmas
• Simulations of Ion Acceleration at Non-relativistic Shocks. II. Magnetic Field Amplification
• Non-relativistic Collisionless Shocks in Unmagnetized Electron-Ion Plasmas
• Non-Fermi Power law Acceleration in Astrophysical Plasma Shocks
• Saturation mechanism of the Weibel instability in weakly magnetized plasmas
• Simulations of Ion Acceleration at Non-relativistic Shocks. III. Particle Diffusion
• Collisionless shock formation, spontaneous electromagnetic fluctuations and streaming instabilities
• dHybrid: a massively parallel code for hybrid simulations of space plasmas
• Relativistic Collisionless Shocks in Unmagnetized Electron-Positron Plasmas
• Nonrelativistic collisionless shocks in weakly magnetized electron--ion plasmas: two-dimensional particle-in-cell simulation of perpendicular shock
• Kinetic Simulations of Cosmic-Ray-Modified Shocks I: Hydrodynamics
• Electron Accelerations at High Mach Number Shocks: Two-Dimensional Particle-In-Cell Simulations in Various Parameter Regimes
• Magnetic field amplification by the Weibel instability at planetary and astrophysical high-Mach-number shocks
• Nonlinear dynamics of the ion Weibel-filamentation instability: an analytical model for the evolution of the plasma and spectral properties
• Kinetic simulation of magnetic field generation and collisionless shock formation in expanding laboratory plasmas
• dHybridR: a Hybrid--Particle-in-Cell Code Including Relativistic Ion Dynamics
• Generalized Fluid Models of the Braginskii Type
• A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation
• Stability analysis of a periodic system of relativistic current filaments
• Electron heating in high Mach number collisionless shocks
• Enhanced Magnetic Field Amplification by Ion-Beam Weibel Instability in Weakly Magnetized Astrophysical Shocks
• Saturation Level of Ion Weibel Instability and Isotropization Length Scale in Electron-Ion Weibel-Mediated Shocks
• A non-local fluid closure for modeling cyclotron resonance in collisionless magnetized plasmas
• Critical comparison of collisionless fluid models: Nonlinear simulations of parallel firehose instability
• Criteria for ion acceleration in laboratory magnetized quasi-perpendicular collisionless shocks: when are 2D simulations enough?
• Acceleration of Heavy Ions at Non-Relativistic Collisionless Shocks
• The role of three-dimensional effects on ion injection and acceleration in perpendicular shocks