Determination of turbulent heating rate and relaxed states in finite Larmor radius magnetohydrodynamic turbulence with helicity barrier

TL;DR

This paper derives exact laws for energy and helicity cascades in FLR-MHD turbulence, revealing a helicity barrier that influences ion heating and the structure of relaxed states in plasma turbulence.

Contribution

It introduces new exact laws for FLR-MHD turbulence, accounting for the helicity barrier and providing insights into energy cascades and relaxed states across scales.

Findings

Identifies the helicity barrier causing separate energy cascades.

Derives exact laws enabling calculation of ion heating rates.

Shows relaxed states exhibit velocity-magnetic field alignment but no Beltrami alignment.

Abstract

Finite Larmor radius magnetohydrodynamics (FLR-MHD) provides a hybrid model of plasma that explains how turbulent energy cascade extends to sufficiently small parallel length scales, potentially leading to perpendicular heating of the ions in the solar corona and the solar wind. In this work, we derive exact laws for the cascades of energy and generalized helicity in fully developed FLR-MHD turbulence. In large and small scale limits, we obtain the exact laws for reduced MHD and electron reduced MHD turbulence respectively. Unlike ordinary or reduced MHD turbulence, a global stationary state is shown to be absent in the case of a strong imbalance between the Elsasser variables. This is due to the so-called helicity barrier, which leads to two separate stationary energy cascades with different cascade rates. Our derived exact laws enable us to calculate these two cascade rates and therefore their difference, which effectively provides the heating rate of the ions. In addition, we also derive alternative Banerjee-Galtier forms for the exact laws and hence obtain the relaxed states of FLR-MHD turbulence using the framework of recently proposed principle of vanishing nonlinear transfer. The relaxed states show alignment between the velocity and magnetic field fluctuations. However, due to strong anisotropy, no Beltrami alignment is possible for velocity and magnetic fields. Similarly to the exact laws, the relaxed states of reduced and electron reduced MHD emerge in the large and small scale limits, respectively.