It is shown that low-collisionality plasmas can not support linearly polarized shear-Alfvén 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-Alfvén-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 .