Evidence of Critical Balance in Kinetic Alfven Wave Turbulence Simulations

A numerical simulation of kinetic plasma turbulence is performed to assess the applicability of critical balance to kinetic, dissipation scale turbulence. The analysis is performed in the frequency domain to obviate complications inherent in performing a local analysis of turbulence. A theoretical model of dissipation scale critical balance is constructed and compared to simulation results, and excellent agreement is found. This result constitutes the first evidence of critical balance in a kinetic turbulence simulation and provides evidence of an anisotropic turbulence cascade extending into the dissipation range. We also perform an Eulerian frequency analysis of the simulation data and compare it to the results of a previous study of magnetohydrodynamic turbulence simulations.Comment: 10 pages, 9 figures, accepted for publication in Physics of Plasma

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetised, turbulent plasma---and, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion discs around black holes. In the context of discs, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfv\'enic turbulence: collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, $\beta_\mathrm{i}$: it ranges from $\sim0.05$ at $\beta_\mathrm{i}=0.1$ to at least $30$ for $\beta_\mathrm{i} \gtrsim 10$. This energy partition is approximately insensitive to the ion-to-electron temperature ratio $T_\mathrm{i}/T_\mathrm{e}$. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfv\'enic turbulence will tend towards a nonequilibrium state in which one of the species is significantly hotter than the other, viz., hotter ions at high $\beta_\mathrm{i}$, hotter electrons at low $\beta_\mathrm{i}$. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high $\beta_i$ and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when $\beta_\mathrm{i}\lesssim1$ and by linear phase mixing (Landau damping) when $\beta_\mathrm{i}\gg1

Inertial range turbulence in kinetic plasmas

The transfer of turbulent energy through an inertial range from the driving scale to dissipative scales in a kinetic plasma followed by the conversion of this energy into heat is a fundamental plasma physics process. A theoretical foundation for the study of this process is constructed, but the details of the kinetic cascade are not well understood. Several important properties are identified: (a) the conservation of a generalized energy by the cascade; (b) the need for collisions to increase entropy and realize irreversible plasma heating; and (c) the key role played by the entropy cascade--a dual cascade of energy to small scales in both physical and velocity space--to convert ultimately the turbulent energy into heat. A strategy for nonlinear numerical simulations of kinetic turbulence is outlined. Initial numerical results are consistent with the operation of the entropy cascade. Inertial range turbulence arises in a broad range of space and astrophysical plasmas and may play an important role in the thermalization of fusion energy in burning plasmas.Comment: 11 pages, 2 figures, submitted to Physics of Plasmas, DPP Meeting Special Issu

Ion versus electron heating in compressively driven astrophysical gyrokinetic turbulence

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio Q_\rmi/Q_\rme as a function of the compressive-to-Alfv\'enic driving power ratio P_\compr/P_\AW, of the ratio of ion thermal pressure to magnetic pressure \beta_\rmi, and of the ratio of ion-to-electron background temperatures T_\rmi/T_\rme. It is shown that Q_\rmi/Q_\rme is an increasing function of P_\compr/P_\AW. When the compressive driving is sufficiently large, Q_\rmi/Q_\rme approaches \simeq P_\compr/P_\AW. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfv\'en waves is absent for both low and high \beta_\rmi, meaning that the compressive driving is directly connected to the ion entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low \beta_\rmi and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.Comment: Accepted for publication in Phys. Rev.

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

Temporal Properties of the Compressible Magnetohydrodynamic Turbulence

The temporal property of the compressible magneto-hydrodynamic (MHD) turbulence remains a fundamental unsolved question. Recent studies based on the spatial-temporal analysis in the global frame of reference suggest that the majority of fluctuation power in turbulence does not follow any of the MHD wave dispersion relations but has very low temporal frequency with finite wavenumbers. Here, we demonstrate that the Lorentzian broadening of the dispersion relations of the three MHD modes where the nonlinear effects act like the damping of a harmonic oscillator can explain many salient features of frequency spectra for all MHD modes. The low frequency fluctuations are dominated by modes with the low parallel wavenumbers that have been broadened by the nonlinear processes. The Lorentzian broadening widths of the three MHD modes exhibit scaling relations to the global frame wavenumbers and are intrinsically related to energy cascade of each mode. Our results provide a new window to investigate the temporal properties of turbulence which offers insights for building a comprehensive understanding of the compressible MHD turbulence.Comment: 15 pages, 4 figures, submitte

Particle acceleration at magnetized, relativistic turbulent shock fronts

The efficiency of particle acceleration at shock waves in relativistic, magnetized astrophysical outflows is a debated topic with far-reaching implications. Here, for the first time, we study the impact of turbulence in the pre-shock plasma. Our simulations demonstrate that, for a mildly relativistic, magnetized pair shock (Lorentz factor $\gamma_{\rm sh} \simeq 2.7$, magnetization level $\sigma \simeq 0.01$), strong turbulence can revive particle acceleration in a superluminal configuration that otherwise prohibits it. Depending on the initial plasma temperature and magnetization, stochastic-shock-drift or diffusive-type acceleration governs particle energization, producing powerlaw spectra $\mathrm{d}N/\mathrm{d}\gamma \propto \gamma^{-s}$ with $s \sim 2.5-3.5$. At larger magnetization levels, stochastic acceleration within the pre-shock turbulence becomes competitive and can even take over shock acceleration

Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] (which reduce to the standard Reduced-MHD equations in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., Astrophys. J. Suppl. 182:310 (2009)]. Two main applications of these equations are magnetised (Alfvenic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme composed of the combination of a total variation diminishing (TVD) third order Runge-Kutta method for the time derivative with a 7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, including a detailed analysis of 2D and 3D Orszag-Tang-type decaying turbulence, both in fluid and kinetic regimes.Comment: 42 pages, 15 figures, submitted to J. Comp. Phy