Abstract Details
Abstracts
Author: Michael L. Nastac
Requested Type: Consider for Invited
Submitted: 2025-02-15 08:46:47
Co-authors: R. J. Ewart, J. Juno, M. Barnes, A. A. Schekochihin
Contact Info:
University of Oxford
Parks Road
Oxford, OX1 3PU
United Kingdom
Abstract Text:
The thermal fluctuation spectrum of the electric field arising due to particle noise in a quiescent Vlasov–Poisson plasma was derived in the 1960s. Here, we derive the universal fluctuation spectrum of the electric field, at Debye and sub-Debye scales, for a turbulent Vlasov–Poisson plasma. This spectrum arises from what is likely to be the 'final cascade'—a universal regime to be encountered at the extreme small-scale end of any turbulent cascade in a nearly collisionless plasma. The cascaded invariant is C_2, the quadratic Casimir invariant of the particle distribution function. C_2 cascades to small scales in both position and velocity space via both linear and nonlinear phase mixing, in such a way that the time scales associated with the two processes are critically balanced at every scale. We develop a scaling theory of the spectrum of C_2 in (k, s) space—and hence of the electric field in k space—in arbitrary dimensions, where k and s are the spatial and velocity wavenumbers, respectively. The conclusions of our theory are confirmed by direct numerical simulations of 1D-1V turbulence. The cascade is ultimately terminated at the (spatial) wavenumber where the turbulent electric-field spectrum gives way to the fluctuation spectrum associated with thermal noise; this transition scale is set by the amplitude of the turbulent electric fields and the plasma parameter. The characteristic time scale for this small-scale cutoff to be reached is the dynamical time of phase-space mixing times a logarithmic factor in the plasma parameter—this is the first concrete demonstration of this property of Vlasov–Poisson turbulence, analogous to how fluid turbulence dissipates energy at a rate (nearly) independent of molecular diffusion. In the presence of the phase-space cascade—a scenario that may be ubiquitous—standard collisional plasma theory ceases to be valid. This calls for the development of new collision operators suited to such turbulent environments.
Characterization: 4.0
Comments:
This work is dedicated to the memory of Bill Dorland (1965-2024).