A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space

Journal article

A class of simple kinetic systems is considered, described by the 1D Vlasov--Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analog of the Kraichnan--Batchelor model of chaotic advection. The solution of the model is found in Fourier--Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective dissipation channel at wave numbers below a certain cut off (analog of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The full Fourier--Hermite spectrum is derived. Its asymptotics are $m^{-3/2}$ at low wave numbers and high Hermite moments ($m$) and $m^{-1/2}k^{-2}$ at low Hermite moments and high wave numbers ($k$). The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

Authors: Adkins, T; Schekochihin, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Journal of Plasma Physics
• Volume: 84
• Issue: 1
• Article number: 905840107
• Publication date: 2018-01-25
• Acceptance date: 2017-11-29
• DOI: 10.1017/S0022377818000089
• EISSN: 1469-7807
• ISSN: 0022-3778
• Keywords: astro-ph.SR; physics.space-ph; physics.plasm-ph; plasma nonlinear phenomena