Plasma turbulence at ion scales: a comparison between PIC and Eulerian hybrid-kinetic approaches

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar-wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma model is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning about two decades in wavenumber - from MHD inertial range to scales well below the ion gyroradius - with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell (HPIC) simulations of freely-decaying Alfv\'enic turbulence, whereas the other consists of Eulerian hybrid Vlasov-Maxwell (HVM) simulations of turbulence continuously driven with partially-compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_\perp\rho_i\gtrsim1$ are observed. The system indeed self-consistently "reprocesses" the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter. Small-scale turbulence has been found to be mainly populated by kinetic Alfv\'en wave (KAW) fluctuations for $\beta\geq1$, whereas KAW fluctuations are only sub-dominant for low-$\beta$.Comment: 18 pages, 4 figures, accepted for publication in J. Plasma Phys. (Collection: "The Vlasov equation: from space to laboratory plasma physics"

Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: from fluid to kinetic modeling

The nonlinear evolution of collisionless plasmas is typically a multi-scale process where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic, Hall-MHD, two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects of small scale processes on the nonlinear evolution of collisionless plasmas. We illustrate how the evolution of a magnetized shear flow depends on the relative orientation of the fluid vorticity with respect to the magnetic field direction during the linear evolution when kinetic effects are taken into account. Even if we found that small scale processes differ between the different models, we show that the feedback from small, kinetic scales to large, fluid scales is negligable in the nonlinear regime. This study show that the kinetic modeling validates the use of a fluid approach at large scales, which encourages the development and use of fluid codes to study the nonlinear evolution of magnetized fluid flows, even in the colisionless regime

A Hybrid Gyrokinetic Ion and Isothermal Electron Fluid Code for Astrophysical Plasma

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl. \textbf{182}, 310 (2009)]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into {\tt AstroGK}, an Eulerian $\delta f$ gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Compute. Pays. \textbf{229}, 9347 (2010)]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant--Friedrichs--Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs $\sim 2\sqrt{m_\mathrm{i}/m_\mathrm{e}} \sim 100$ times faster than {\tt AstroGK}\ with a single ion species and kinetic electrons where $m_\mathrm{i}/m_\mathrm{e}$ is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron--ion temperature ratio and plasma beta

ViDA: a VlasovDArwin solver for plasma physics at electron scales

We present a Vlasov–DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the nonlinear regime to guarantee a clean description of the plasma dynamics at fine spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to the Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations of a non-relativistic fully kinetic collisionless plasma and it is expected to provide relevant insights into important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region

Electron Signatures of Reconnection in a Global eVlasiator Simulation

Geospace plasma simulations have progressed toward more realistic descriptions of the solar wind-magnetosphere interaction from magnetohydrodynamic to hybrid ion-kinetic, such as the state-of-the-art Vlasiator model. Despite computational advances, electron scales have been out of reach in a global setting. eVlasiator, a novel Vlasiator submodule, shows for the first time how electromagnetic fields driven by global hybrid-ion kinetics influence electrons, resulting in kinetic signatures. We analyze simulated electron distributions associated with reconnection sites and compare them with Magnetospheric Multiscale (MMS) spacecraft observations. Comparison with MMS shows that key electron features, such as reconnection inflows, heated outflows, flat-top distributions, and bidirectional streaming, are in remarkable agreement. Thus, we show that many reconnection-related features can be reproduced despite strongly truncated electron physics and an ion-scale spatial resolution. Ion-scale dynamics and ion-driven magnetic fields are shown to be significantly responsible for the environment that produces electron dynamics observed by spacecraft in near-Earth plasmas.Peer reviewe

A Lagrangian kinetic model for collisionless magnetic reconnection

A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression of the Lagrangian, rather then enforcing a zero electron mass in the equations of motion. This is done upon splitting the electron velocity into its mean and fluctuating parts, so that the latter naturally produce the corresponding pressure tensor. The model exhibits a new Coriolis force term, which emerges from a change of frame in the electron dynamics. Then, if the electron heat flux is neglected, the strong electron magnetization limit yields a hybrid model, in which the electron pressure tensor is frozen into the electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio

Instabilities, anomalous transport, and nonlinear structures in partially and fully magnetized plasmas.

Plasmas behavior, to a large extent, is determined by collective phenomena such as waves. Wave excitation, turbulence, and formation of quasi-coherent nonlinear structures are defining features of nonlinear multi-scale plasma dynamics. In this thesis, instabilities, anomalous transport, and structures in partially and fully magnetized plasmas were studied with a combination of analytical and numerical tools. The phenomena studied in this thesis are of interest for many applications, e.g., plasma reactors for material processing, electric propulsion, magnetic plasma confinement, and space plasma physics. Large equilibrium flows of ions and electrons exist in many devices with partially magnetized plasmas in crossed electric and magnetic fields. Such flows result in various instabilities and turbulence that produce anomalous electron transport across the magnetic field. We present first principle, self-consistent, nonlinear fluid simulations that predict the level of anomalous current generally consistent with experimental data. We also show that drift waves in partially magnetized plasmas (which we called Hall drift waves), destabilized by the electron drift along with density gradients, tend to form (via inverse energy cascade) shear flows similar to zonal flows in fully magnetized plasmas. These flows become unstable due to a secondary instability (similar to Kelvin–Helmholtz instability) and produce large-scale quasi-stationary vortices. Then, it was shown that in nonlinear regimes, the axial mode instability due to electron and ion flows (along the electric field) forms large-amplitude cnoidal type waves. At the same time, the strong electric field produced by axial modes affects Hall drift waves stability and provides a feedback mechanism on density gradient driven turbulence, creating a complex picture of interacting anomalous transport, zonal flows, vortices, and streamers. In the case where axial modes are destabilized by boundary effects, the nonlinear dynamics result in a new nonlinear equilibrium or standing oscillating waves. The formation of shear flows (zonal flows) was also studied in the framework of the Hasegawa-Mima equation and it was established that zonal flows can saturate due to nonlinear self-interactions. Lastly, a novel approach for high-fidelity numerical simulations of multi-scale nonlinear plasma dynamics is developed which is illustrated with the example of an unmagnetized plasma