PARAMETRIC INSTABILITY OF WHISTLER WAVES IN THE ELECTRON MAGNETOHYDRODYNAMICS

Using an electron magnetohydrodynamic model, we investigate the parametric decay among three whistler waves. A nonlinear equation to describe both linear and nonlinear properties of whistler waves is derived. Then we discuss the growth rate of the parametric decay of whistler waves in the long-wavelength region and show that the growth rate for two reverse decay waves is larger than that for two decay waves in the same direction. The nonlinear interaction among the long-wavelength and short-wavelength waves is also studied in this paper. This wave-wave interaction implies that long-wavelength waves can be decayed to short-wavelength waves and then dissipate their energy in the short-wavelength region. The possibility of applying our results to account for the generation of sunward propagating whistler waves is also discussed.