Amplitude limits and nonlinear damping of shear-Alfv\'en waves in
  high-beta low-collisionality plasmas
  This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the
effect of self-generated pressure anisotropy on linearly polarized
shear-Alfv\'en fluctuations in low-collisionality plasmas. Such anisotropies
lead to stringent limits on the amplitude of magnetic perturbations in
high-beta plasmas, above which a fluctuation can destabilize itself through the
parallel firehose instability. This causes the wave frequency to approach zero,
"interrupting" the wave and stopping its oscillation. These effects are
explored in detail in the collisionless and weakly collisional "Braginskii"
regime, for both standing and traveling waves. The focus is on simplified
models in one dimension, on scales much larger than the ion gyroradius. The
effect has interesting implications for the physics of magnetized turbulence in
the high-beta conditions that are prevalent in many astrophysical plasmas.
