Stringent limits on the amplitude of Alfvénic perturbations at high-beta

It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfvén fluctuations above a critical amplitude δB⊥/B0 ∼ β-1/2, where β 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 interesting implications for magnetized turbulence in weakly collisional plasmas, in particular for the solar wind at 1AU where β 1.