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Register a new userSelf-sustaining sound in collisionless, high-beta plasma
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Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $delta n/n_0 gtrsim 2/beta$ (where $betagg{1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more `fluid-like than kinetic. A nonlinear fluctuation-dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels, and weakly collisional thermodynamics when IAWs with $delta n/n_0 gtrsim 2/beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.
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In a magnetized, collisionless plasma, the magnetic moment of the constituent particles is an adiabatic invariant. An increase in the magnetic-field strength in such a plasma thus leads to an increase in the thermal pressure perpendicular to the field lines. Above a $beta$-dependent threshold (where $beta$ is the ratio of thermal to magnetic pressure), this pressure anisotropy drives the mirror instability, producing strong distortions in the field lines on ion-Larmor scales. The impact of this instability on magnetic reconnection is investigated using a simple analytical model for the formation of a current sheet (CS) and the associated production of pressure anisotropy. The difficulty in maintaining an isotropic, Maxwellian particle distribution during the formation and subsequent thinning of a CS in a collisionless plasma, coupled with the low threshold for the mirror instability in a high-$beta$ plasma, imply that the geometry of reconnecting magnetic fields can differ radically from the standard Harris-sheet profile often used in simulations of collisionless reconnection. As a result, depending on the rate of CS formation and the initial CS thickness, tearing modes whose growth rates and wavenumbers are boosted by this difference may disrupt the mirror-infested CS before standard tearing modes can develop. A quantitative theory is developed to illustrate this process, which may find application in the tearing-mediated disruption of kinetic magnetorotational channel modes.
Hybrid-kinetic numerical simulations of firehose and mirror instabilities in a collisionless plasma are performed in which pressure anisotropy is driven as the magnetic field is changed by a persistent linear shear $S$. For a decreasing field, it is found that mostly oblique firehose fluctuations grow at ion Larmor scales and saturate with energies $sim$$S^{1/2}$; the pressure anisotropy is pinned at the stability threshold by particle scattering off microscale fluctuations. In contrast, nonlinear mirror fluctuations are large compared to the ion Larmor scale and grow secularly in time; marginality is maintained by an increasing population of resonant particles trapped in magnetic mirrors. After one shear time, saturated order-unity magnetic mirrors are formed and particles scatter off their sharp edges. Both instabilities drive sub-ion-Larmor--scale fluctuations, which appear to be kinetic-Alfv{e}n-wave turbulence. Our results impact theories of momentum and heat transport in astrophysical and space plasmas, in which the stretching of a magnetic field by shear is a generic process.
Using hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvenic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfv{e}nic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale critical balance between their characteristic linear and nonlinear frequencies. Once the temperature anisotropy is sufficiently negative, the plasma becomes unstable to kinetic firehose instabilities, which excite rapidly growing magnetic fluctuations at ion-Larmor scales. The consequent pitch-angle scattering of particles maintains the temperature anisotropy near marginal stability, even as the turbulent plasma continues to expand. The resulting evolution of parallel and perpendicular temperatures does not satisfy double-adiabatic conservation laws, but is described accurately by a simple model that includes anomalous scattering. Our results have implications for understanding the complex interplay between macro- and micro-scale physics in various hot, dilute, astrophysical plasmas, and offer predictions concerning power spectra, residual energy, ion-Larmor-scale spectral breaks, and non-Maxwellian features in ion distribution functions that may be tested by measurements taken in high-beta regions of the solar wind.
In the previous works harmonic, phase-mixed, Alfven wave dynamics was considered both in the kinetic and magnetohydrodynamic regimes. Up today only magnetohydrodynamic, phase-mixed, Gaussian Alfven pulses were investigated. In the present work we extend this into kinetic regime. Here phase-mixed, Gaussian Alfven pulses are studied, which are more appropriate for solar flares, than harmonic waves, as the flares are impulsive in nature. Collisionless, phase-mixed, dispersive, Gaussian Alfven pulse in transversely inhomogeneous plasma is investigated by particle-in-cell (PIC) simulations and by an analytical model. The pulse is in inertial regime with plasma beta less than electron-to-ion mass ratio and has a spatial width of 12 ion inertial length. The linear analytical model predicts that the pulse amplitude decrease is described by the linear Korteweg de Vries (KdV) equation. The numerical and analytical solution of the linear KdV equation produces the pulse amplitude decrease in time as $t^{-1}$. The latter scaling law is corroborated by full PIC simulations. It is shown that the pulse amplitude decrease is due to dispersive effects, while electron acceleration is due to Landau damping of the phase-mixed waves. The established amplitude decrease in time as $t^{-1}$ is different from the MHD scaling of $t^{-3/2}$. This can be attributed to the dispersive effects resulting in the different scaling compared to MHD, where the resistive effects cause the damping, in turn, enhanced by the inhomogeneity. Reducing background plasma temperature and increase in ion mass yields more efficient particle acceleration.
We herein investigate shock formation and particle acceleration processes for both protons and electrons in a quasi-parallel high-Mach-number collisionless shock through a long-term, large-scale particle-in-cell simulation. We show that both protons and electrons are accelerated in the shock and that these accelerated particles generate large-amplitude Alfv{e}nic waves in the upstream region of the shock. After the upstream waves have grown sufficiently, the local structure of the collisionless shock becomes substantially similar to that of a quasi-perpendicular shock due to the large transverse magnetic field of the waves. A fraction of protons are accelerated in the shock with a power-law-like energy distribution. The rate of proton injection to the acceleration process is approximately constant, and in the injection process, the phase-trapping mechanism for the protons by the upstream waves can play an important role. The dominant acceleration process is a Fermi-like process through repeated shock crossings of the protons. This process is a `fast process in the sense that the time required for most of the accelerated protons to complete one cycle of the acceleration process is much shorter than the diffusion time. A fraction of the electrons is also accelerated by the same mechanism, and have a power-law-like energy distribution. However, the injection does not enter a steady state during the simulation, which may be related to the intermittent activity of the upstream waves. Upstream of the shock, a fraction of the electrons is pre-accelerated before reaching the shock, which may contribute to steady electron injection at a later time.
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