This study deals with the stability of a plasma in the field of a self-consistent Alfvén wave. Decay instabilities for a plasma with β ≫ 1 are considered, and the growth rate and widths of the instability zones are found. The problem of determining the critical wave amplitude is discussed.The solution as a whole was reached for two types of Alfvén waves – standing and travelling.An instability associated with the scattering of the Alfvén wave was found in the second approximation with respect to the parameter h0/H0 (h0 being the amplitude of the Alfvén wave and H0 the intensity of the constant magnetic field). The excitation conditions for this instability are less stringent than those for decay instabilities.Problems connected with the build-up of instabilities of the type under consideration in systems bounded along the magnetic field are discussed.
MHD surface waves in a cylindrical plasma with a spatial density variation