Kinetic simulations of the interruption of large-amplitude
  shear-Alfv\'en waves in a high-beta plasma
  Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear
"interruption" of standing and traveling shear-Alfv\'en waves in collisionless
plasmas. Interruption involves a self-generated pressure anisotropy removing
the restoring force of a linearly polarized Alfv\'enic perturbation, and occurs
for wave amplitudes $\delta B_{\perp}/B_{0}\gtrsim \beta^{\,-1/2}$ (where
$\beta$ is the ratio of thermal to magnetic pressure). We use highly elongated
domains to obtain maximal scale separation between the wave and the ion
gyroscale. For standing waves above the amplitude limit, we find that the
large-scale magnetic field of the wave decays rapidly. The dynamics are
strongly affected by the excitation of oblique firehose modes, which transition
into long-lived parallel fluctuations at the ion gyroscale and cause
significant particle scattering. Traveling waves are damped more slowly, but
are also influenced by small-scale parallel fluctuations created by the decay
of firehose modes. Our results demonstrate that collisionless plasmas cannot
support linearly polarized Alfv\'en waves above $\delta B_{\perp}/B_{0}\sim
\beta^{\,-1/2}$. They also provide a vivid illustration of two key aspects of
low-collisionality plasma dynamics: (i) the importance of velocity-space
instabilities in regulating plasma dynamics at high $\beta$, and (ii) how
nonlinear collisionless processes can transfer mechanical energy directly from
the largest scales into thermal energy and microscale fluctuations, without the
need for a scale-by-scale turbulent cascade.
