Parametric instabilities of the circularly polarized Alfven waves including dispersion
Abstract
A class of parametric instabilities of largeamplitude, circularly polarized Alfven waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixthorder polynomial which is solved numerically. As a function of K identically equal to k/ksub0 (where ksub0 and k are the wave number of the 'pump' wave and unstable sound wave, respectively), there are three regionals of instability: a modulation instability at K less than 1, a decay instability at K greater than 1, and a relatively weak and narrow instability at K close to squared divided by vsubA squared (where csubs and vsubA are the sound and Alfven speeds respectively), the modulational instability occurs when beta is less than 1 (more than 1) for lefthand (righthand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). The growth rate of the decay instability of lefthand waves is greater than the modulational instability at all values of beta. Applications to largeamplitude wave observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.
 Publication:

Journal of Geophysical Research
 Pub Date:
 May 1986
 DOI:
 10.1029/JA091iA05p05617
 Bibcode:
 1986JGR....91.5617W
 Keywords:

 Circular Polarization;
 Magnetohydrodynamic Waves;
 Solar Wind;
 Space Plasmas;
 Wave Dispersion;
 Computerized Simulation;
 Ion Beams;
 Magnetohydrodynamic Stability;
 Shock Wave Propagation;
 Wave Equations;
 Astrophysics