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

Hall magnetohydrodynamics in a relativistically strong mean magnetic field

This Letter presents a magnetohydrodynamic model that describes the small-amplitude fluctuations with wavelengths comparable to ion inertial length in the presence of a relativistically strong mean magnetic field. The set of derived equations is virtually identical to the non-relativistic Hall reduced magnetohydrodynamics (Schekochihin et al. 2019), differing only by a few constants that take into account the relativistic corrections. This means that all the properties of kinetic Alfv\'en turbulence and ion cyclotron turbulence inherent in the non-relativistic Hall regime persist unchanged even in a magnetically dominated regime

Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: B\'{e}nard Convection and Zonal flow

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven

Energy partition between Alfv\'enic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfv\'enic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfv\'enic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfv\'enic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfv\'enic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.Comment: Accepted for publication in Journal of Plasma Physic

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.

Improved beta (local beta >1) and density in electron cyclotron resonance heating on the RT-1 magnetosphere plasma

This study reports the recent progress in improved plasma parameters of the RT-1 device. Increased input power and the optimized polarization of electron cyclotron resonance heating (ECRH) with an 8.2 GHz klystron produce a significant increase in electron beta, which is evaluated by an equilibrium analysis of the Grad–Shafranov equation. The peak value of the local electron beta βe is found to exceed 1. In the high-beta and high-density regime, the density limit is observed for H, D and He plasmas. The line-averaged density is close to the cutoff density for 8.2 GHz ECRH. When the filling gas pressure is increased, the density limit still exists even in the low-beta region. This result indicates that the density limit is caused by the cutoff density rather than the beta limit. From the analysis of interferometer data, we found that inward diffusion causes a peaked density profile beyond the cutoff density