A stringent limit on the amplitude of Alfv\'enic perturbations in high-beta low-collisionality plasmas

TL;DR

This paper establishes a fundamental amplitude limit for shear-Alfvén waves in high-beta, low-collisionality plasmas, showing that exceeding this limit triggers instabilities that prevent large fluctuations, impacting astrophysical plasma turbulence.

Contribution

It introduces a critical amplitude threshold for shear-Alfvén fluctuations in high-beta plasmas, revealing a self-limiting mechanism due to pressure anisotropy and firehose instability.

Findings

Fluctuations above _0 \, eta^{-1/2} are unstable.

Pressure anisotropy causes wave damping and restructuring.

Magnetic fields form zig-zag structures after cutoff.

Abstract

It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfv\'en fluctuations above a critical amplitude $\delta B_{\perp}/B_{0} \sim \beta^{\,-1/2}$, where $\beta$ is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound on shear-Alfv\'en-wave amplitudes has far-reaching implications for the physics of magnetized turbulence in the high-$\beta$ conditions prevalent in many astrophysical plasmas, as well as for the solar wind at $\sim 1 \mathrm{AU}$ where $\beta \gtrsim 1$.