Weak turbulence theory of the non-linear evolution of the ion ring distribution

TL;DR

This paper develops a weak turbulence theory for the nonlinear evolution of ion ring distributions in low-beta magnetospheric plasmas, highlighting how nonlinear scattering processes extend wave saturation timescales.

Contribution

It introduces a new weak turbulence framework accounting for nonlinear wave-electron scattering, which alters the saturation dynamics of ion ring instabilities.

Findings

Nonlinear scattering by electrons dominates wave saturation.

Wave amplitude saturates at low levels due to nonlinear effects.

Quasilinear relaxation times are significantly extended.

Abstract

The nonlinear evolution of an ion ring instability in a low-beta magnetospheric plasma is considered. The evolution of the two-dimensional ring distribution is essentially quasilinear. Ignoring nonlinear processes the time-scale for the quasilinear evolution is the same as for the linear instability 1/t_ql gamma_l. However, when nonlinear processes become important, a new time scale becomes relevant to the wave saturation mechanism. Induced nonlinear scattering of the lower-hybrid waves by plasma electrons is the dominant nonlinearity relevant for plasmas in the inner magnetosphere and typically occurs on the timescale 1/t_ql w(M/m)W/nT, where W is the wave energy density, nT is the thermal energy density of the background plasma, and M/m is the ion to electron mass ratio, which has the consequence that the wave amplitude saturates at a low level, and the timescale for quasilinear relaxation is extended by orders of magnitude.