Nonlinear Excitation of Fast Waves by Dispersive Alfven Waves and Solar Coronal Heating

This paper presents the study of a nonlinear process in the solar corona where dispersive Alfven waves (DAWs) may lead to coronal heating. We present the model equations governing the nonlinear excitation of the fast waves (FWs) by DAWs in low-beta plasmas (beta << m(e)/m(i) as applicable to the solar corona). By properly considering the ponderomotive nonlinearity, we have derived the equations for the decay waves, namely the FWs and other DAWs. The expressions for the coupling coefficients of the three-wave interaction have been derived. The growth rate of the instability is also calculated; we have found that the value of the decay growth time turns out to be of the order of milliseconds at the pump DAW amplitude B-0y/B-0 = 10 (3). This time scale is much shorter than the observed time scales (a minute or less) for coronal heating, as inferred from images obtained by instruments on board Yohkoh and the Solar and Heliospheric Observatory (SOHO).