Non-resonant magnetohydrodynamics streaming instability near magnetized relativistic shocks

We present in this paper both a linear study and numerical relativistic MHD simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front restframe, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our calculation, we also perform relativistic MHD simulations describing the propagation of the aforementioned magneto-acoustic waves through the shock precursor. The numerical calculations confirm our linear analysis, which predicts that the growth rate of the instability is maximal for ultra-relativistic shocks and exhibits a wavenumber dependence $\propto k_x^{1/2}$. Our numerical simulations also depict the saturation regime of the instability where we show that the magnetic amplification is moderate but nevertheless significant ($\delta B/B\leq 10$). This latter fact may explain the presence of strong turbulence in the vicinity of relativistic magnetized shocks. Our numerical approach also introduces a convenient means to handle isothermal (ultra-)relativistic MHD conditions.Comment: 14 pages, 6 figures, MNRAS (in press

SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to fifth order). We validate our algorithm against several test problems -- thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.Comment: 26 pages, 19 figures, discussion about performance is added, published in Ap

Magnetohydrodynamic code for gravitationally-stratified media

Aims. We describe a newly-developed magnetohydrodynamic (MHD) code with the capacity to simulate the interaction of any arbitrary perturbation (i.e., not necessarily limited to the linearised limit) with a magnetohydrostatic equilibrium background. Methods. By rearranging the terms in the system of MHD equations and explicitly taking into account the magnetohydrostatic equilibrium condition, we define the equations governing the perturbations that describe the deviations from the background state of plasma for the density, internal energy and magnetic field. We found it was advantageous to use this modified form of the MHD equations for numerical simulations of physical processes taking place in a stable gravitationally-stratified plasma. The governing equations are implemented in a novel way in the code. Sub-grid diffusion and resistivity are applied to ensure numerical stability of the computed solution of the MHD equations. We apply a fourth-order central difference scheme to calculate the spatial derivatives, and implement an arbitrary Runge-Kutta scheme to advance the solution in time. Results. We have built the proposed method, suitable for strongly-stratified magnetised plasma, on the base of the well-documented Versatile Advection Code (VAC) and performed a number of one- and multi-dimensional hydrodynamic and MHD tests to demonstrate the feasibility and robustness of the code for applications to astrophysical plasmas

Mixed diffusive-convective relaxation of a broad beam of energetic particles in cold plasma

We revisit the applications of quasi-linear theory as a paradigmatic model for weak plasma turbulence and the associated bump-on-tail problem. The work, presented here, is built around the idea that large-amplitude or strongly shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are convective (ballistic-like). We cast this novel idea in the rigorous form of a self-consistent nonlinear dynamical model, which generalizes the classic equations of the quasi-linear theory to "broad" beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport; and essentially depend on nonlinear wave-particle interactions and phase-space structures. Taking into account modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution function and the fluctuation intensity spectrum.Comment: 25 pages, 15 figure

The Heating of Test Particles in Numerical Simulations of Alfvenic Turbulence

We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (``Alfvenic turbulence''); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle is comparable to the frequency of a turbulent fluctuation that is resolved on the computational domain. Particles with these frequencies nearly equal undergo strong perpendicular heating (relative to the local magnetic field) and pitch angle scattering. By contrast, particles with large gyrofrequency undergo strong parallel heating. Simulations with a finite resistivity produce additional parallel heating due to parallel electric fields in small-scale current sheets. Many of our results are consistent with linear theory predictions for the particle heating produced by the Alfven and slow magnetosonic waves that make up Alfvenic turbulence. However, in contrast to linear theory predictions, energy exchange is not dominated by discrete resonances between particles and waves; instead, the resonances are substantially ``broadened.'' We discuss the implications of our results for solar and astrophysics problems, in particular the thermodynamics of the near-Earth solar wind. We conclude that Alfvenic turbulence produces significant parallel heating via the interaction between particles and magnetic field compressions (``slow waves''). However, on scales above the proton Larmor radius, Alfvenic turbulence does not produce significant perpendicular heating of protons or minor ions.Comment: Submitted to Ap

Fast acoustic streaming in standing waves : Generation of an additional outer streaming cell

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30. Streaming velocity is measured by means of laser Doppler velocimetry in a cylindrical resonator filled with air at atmospheric pressure at high intensity sound levels. The compressible Navier-Stokes equations are solved numerically with high resolution finite difference schemes. The resonator is excited by shaking it along the axis at imposed frequency. Results of measurements and of numerical calculation are compared with results given in the literature and with each other. As expected, the axial streaming velocity measured and calculated agrees reasonably well with the slow streaming theory for small ReNL but deviates significantly from such predictions for fast streaming (ReNL > 1). Both experimental and numerical results show that when ReNL is increased, the center of the outer streaming cells are pushed toward the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes

Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics

The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStr\"om collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain ``benchmarks'' have been created that can later be used as test cases for atmospheric numerical model validation