Dynamics of fast magnetosonic wave turbulence

TL;DR

This paper investigates the dynamics of fast magnetosonic wave turbulence through numerical simulations of the kinetic equation, revealing cascade behaviors, anisotropic spectra, and providing theoretical insights relevant to solar wind observations.

Contribution

It introduces a detailed numerical analysis of fast magnetosonic wave turbulence, including decay laws, cascade directions, anisotropic spectra, and analytical constants, advancing understanding of plasma turbulence.

Findings

Identification of a mixture of forward and backward cascades with the forward being dominant.

Discovery of a $k^{-3/2}$ energy spectrum with anisotropy depending on the magnetic field angle.

Analytical derivation and numerical verification of the Kolmogorov-Zakharov constant.

Abstract

Fast magnetosonic waves are among the fundamental oscillation modes of astrophysical plasmas. To study their dynamics, we carry out numerical simulations of the wave turbulence kinetic equation, which describes the evolution of the energy spectrum of a set of weakly nonlinear fast magnetosonic waves. This kinetic equation, which involves three-wave interactions, has recently been derived from compressible magnetohydrodynamics in the low-$\beta$ limit (Galtier 2023). It has an exact stationary solution, the Kolmogorov-Zakharov spectrum, corresponding to a direct energy cascade. Here we perform free decay simulations of the kinetic equation for which we propose a Kolmogorov-type phenomenology to explain the temporal decay laws of energy and integral length scale. In the forced simulations, we show that the cascade is in fact composed of a mixture of a forward cascade for counter-propagating waves, and a backward cascade for co-propagating waves, with the former being stronger than the latter. The Kolmogorov-Zakharov energy spectrum in $k^{-3/2}$ is found in the radial direction with an anisotropy due to the amplitude that depends on the angle relative to the strong mean magnetic field. We give the analytical expression of the Kolmogorov-Zakharov constant, which is numerically verified in the high Reynolds number limit. Our study provides a theoretical explanation for certain observations in the solar wind plasma (Zhao et al. 2022), where a regime of weak turbulence has been identified for fast magnetosonic waves, alongside a critical balance regime for strong Alfv\'en wave turbulence.