A stringent limit on the amplitude of Alfv\'enic perturbations in
  high-beta low-collisionality plasmas
  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 $\beta \gtrsim 1$.
