Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

Abstract

We consider a nearly collisionless plasma consisting of a species of `test particles' in 1D-1V, stirred by an externally imposed stochastic electric field. The mean effect on the particle distribution function is stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant $C_2\propto \iint dxdv⟨f^2⟩$. We find that $C_2$ is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of $C_2$ in Fourier space, with $k$ and $s$ denoting spatial and velocity wavenumbers, respectively. Whereas even the linear phase mixing alone would lead to a constant flux of $C_2$ to high $s$ (towards the collisional dissipation range) at every $k$, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of $C_2$ is to both high $k$ and high $s$ simultaneously. Integrating over velocity (spatial) wavenumbers, the $k$-space ($s$-space) flux of $C_2$ is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the $(k,s)$ plane, with power-law asymptotics at large $k$ and $s$. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

arXiv commentMinor edits, final version accepted to PRE

References in corpus (46)

• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Particles and fields in fluid turbulence
• Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas
• The multi-scale nature of the solar wind
• Perpendicular Ion Heating by Low-Frequency Alfven-Wave Turbulence in the Solar Wind
• Non-diffusive transport in plasma turbulence: a fractional diffusion approach
• Recent progress in astrophysical plasma turbulence from solar wind observations
• Turbulence and Particle Heating in Advection-Dominated Accretion Flows
• 3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
• Dynamo theories
• Evidence for Electron Landau Damping in Space Plasma Turbulence
• A prescription for the turbulent heating of astrophysical plasmas
• The Properties of the Solar Corona and Its Connection to the Solar Wind
• Current Sheets and Collisionless Damping in Kinetic Plasma Turbulence
• The role of electron heating physics in images and variability of the Galactic Centre black hole Sagittarius A*
• Magnetic reconnection in the era of exascale computing and multiscale experiments
• Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence
• Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows
• Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection and electron heating in low-beta plasmas
• Gyrokinetic turbulence: a nonlinear route to dissipation through phase space
• Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
• Magnetosperic Multiscale (MMS) observation of plasma velocity-space cascade: Hermite representation and theory
• Diagnosing collisionless energy transfer using field-particle correlations: gyrokinetic turbulence
• A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU
• Dual phase-space cascades in 3D hybrid-Vlasov-Maxwell turbulence
• The Structure of Plasma Heating in Gyrokinetic Alfvénic Turbulence
• Fluidization of collisionless plasma turbulence
• A Prospectus on Kinetic Heliophysics
• Two-dimensional gyrokinetic turbulence
• Spatially Localized Particle Energization by Landau Damping in Current Sheets Produced by Strong Alfven Wave Collisions
• Turbulent Dissipation Challenge: A community Driven Effort
• Decay of scalar turbulence revisited
• Velocity-Space Cascade in Magnetized Plasmas: Numerical Simulations
• On stochastic heating and its phase-space signatures in low-$\beta$ kinetic turbulence
• The Enhancement of Proton Stochastic Heating in the near-Sun Solar Wind
• A model for the non-universal power-law of the solar wind sub-ion scale magnetic spectrum
• Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence
• Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
• The Importance of Electron Landau Damping for the Dissipation of Turbulent Energy in Terrestrial Magnetosheath Plasma
• A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
• Suppression of phase mixing in drift-kinetic plasma turbulence
• Universal decay of scalar turbulence
• Generalized entropy production in collisionless plasma flows and turbulence
• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Collisionless relaxation of a Lynden-Bell plasma
• Phase space dynamics of unmagnetized plasmas: collisionless and collisional regimes

Cited by in corpus (6)

• Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum
• Radiative cooling induced coherent maser emission in relativistic plasmas
• Turbulent heating in collisionless low-beta plasmas: imbalance, Landau damping, and electron-ion energy partition
• Minimum-entropy constraints on galactic potentials
• Relaxation of weakly collisional plasma: continuous spectra, discrete eigenmodes, and the decay of echoes
• External charged debris in a flowing plasma : charge fluctuation induced complexity