Absolute and convective instabilities of circularly polarized Alfvén waves:  Decay instability

David Simpson, University of Sheffield

 The absolute and convective instabilities of a circularly polarized Alfvén wave propagating parallel to the ambient magnetic field are studied. 
We impose the restriction that the plasma beta is less than 1 and that the amplitude of the wave, a, is small in order to make analytical progress. 
We find an interval for the velocity of the reference frame with respect to the rest plasma where the wave absolutely unstable. 
When the wave is convectively unstable we show that spatially amplifying waves exist in two symmetric frequency bands of order a. 
The implication of the results on the interpretation of observational data is discussed.