A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation

Abstract

We present a new hybrid algorithm implemented in the code CHIEF ( Code Hybrid with Inertial Electron Fluid) for simulations of electron–ion plasmas. The algorithm treats the ions kinetically, modeled by the Particle-in-Cell (PiC) method, and electrons as an inertial fluid, modeled by electron fluid equations without any of the approximations used in most of the other hybrid codes with an inertial electron fluid. This kind of code is appropriate to model a large variety of quasineutral plasma phenomena where the electron inertia and/or ion kinetic effects are relevant. We present here the governing equations of the model, how these are discretized and implemented numerically, as well as six test problems to validate our numerical approach. Our chosen test problems, where the electron inertia and ion kinetic effects play the essential role, are: 0) Excitation of parallel eigenmodes to check numerical convergence and stability, 1) parallel (to a background magnetic field) propagating electromagnetic waves, 2) perpendicular propagating electrostatic waves (ion Bernstein modes), 3) ion beam right-hand instability (resonant and non-resonant), 4) ion Landau damping, 5) ion firehose instability, and 6) 2D oblique ion firehose instability. Our results reproduce successfully the predictions of linear and non-linear theory for all these problems, validating our code. All properties of this hybrid code make it ideal to study multi-scale phenomena between electron and ion scales such as collisionless shocks, magnetic reconnection and kinetic plasma turbulence in the dissipation range above the electron scales

A generalized quasi-neutral fluid-particle hybrid plasma model and its application to energetic-particle-magnetohydrodynamics hybrid simulation

“…The appearance of Bernstein waves clearly shows that the ion kinetic effect is correctly included. Similar results have been reported recently by [34].…”

“…We see that the nonlinear evolution of the FHI (Run-4A) was quite similar to the results already presented in the literature [39,34]. Namely, the parallel FHI dominated in an early nonlinear phase whereas the power of the oblique FHI became comparable and eventually larger than the parallel in a late nonlinear phase.…”

A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm

“…">Hybrid kinetic-ion fluid-electron plasma modelThere are a number of options for the choice of the electron fluid model, and it is appropriate to comment firstly on the choices that have been made here. Finite electron inertia has been included in several hybrid algorithms [1,20,37], where it can mitigate the stiffness of the whistler wave at short wavelength and in near vacuum regions. In such algorithms, electron inertia is often implemented with a reduced value of the ion-to-electron mass ratio to reduce the separation between the ion and electron scales.…”

Plasma waves as a benchmark problem

“…Details of the hybrid code are described in Muñoz et al. (2016). On a high level it computes the time evolution of the ions, just as a PIC code would, and determines the ions charge density and current density .…”