Dual cascade and its possible variations in magnetized kinetic plasma turbulence

TL;DR

This paper derives electrostatic gyrokinetic absolute equilibria in magnetized plasma turbulence, explaining discretization effects and suggesting potential variations in dual cascade behavior at different scales.

Contribution

It provides a theoretical derivation of equilibria with continuum velocity fields and clarifies previous discretization mistakes, exploring implications for cascade dynamics.

Findings

Equilibria derived via partition function and Green function methods.

Discretization effects can lead to invariants concentrating at low modes.

Potential variation of dual cascade picture in magnetized plasma turbulence.

Abstract

Electrostatic gyrokinetic absolute equilibria with continuum velocity field are obtained through the partition function and through the Green function of the functional integral. The new results justify and explain the prescription for quantization/discretization or taking the continuum limit of velocity. The mistakes in the Appendix D of our earlier work [J.-Z. Zhu and G. W. Hammett, Phys. Plasmas {\bf 17}, 122307 (2010)] are explained and corrected. If the lattice spacing for discretizing velocity is big enough, all the invariants could concentrate at the lowest Fourier modes in a negative-temperature state, which might indicate a possible variation of the dual cascade picture in two-dimension magnetized plasma turbulence.