Nonlinear dynamics of small-scale Alfvén waves

Abstract

We study the nonlinear evolution of very oblique small-scale Alfvén waves with k⊥di≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k⊥di∼1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k⊥ρs, k⊥de, or k∥di becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than di. We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

Relativistic Alfvén Turbulence at Kinetic Scales

“…Energy cascade in the kinetic range arguably governs the energy dissipation and particle heating in a collisionless turbulent plasma, and it may be relevant for nonthermal particle acceleration. Kinetic-range modes play an important role in space and astrophysical plasmas, where they have been studied analytically, numerically, and, where possible, in in situ spacecraft measurements (e.g., Chen et al 2013;Sahraoui et al 2013;Chen & Sorriso-Valvo 2014;Told et al 2015;Chen & Boldyrev 2017;Roytershteyn et al 2019;He et al 2020;Mallet et al 2023;Vega et al 2023;Zhou et al 2023).…”