Parametric instabilities of circularly polarized Alfven waves in high-beta plasmas

CGL relations including the effect of finite ion Larmor radius are used to consider a class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in high-beta plasmas. The disperison relation governing the instabilities is a sixth-order polynomial which is solved numerically. There are two types of instabilities: a modulational instability at k is less than k(0) and a relatively weak and narrow bandwidth instability at k is less than approximately k(0), where k and k(0) are the wavenumbers of the unstable density fluctuation and the 'pump' wave, respectively. It is shown that these instabilities can occur for left-handed pump waves and that the modulational instability is unstable over a very broad band in k with a maximum growth rate at finite k is not equal to 0.