Study of relativistic beam of electron on whistler mode waves for subtracted distribution in Saturnian magnetosphere

Very low frequency electromagnetic waves in the magnetosphere of Saturn are the focus of the present study. Hot injected beam effect on these waves like whistler mode waves for relativistic and non-relativistic subtracted bi-Maxwellian distribution function have been studied in the presence of perpendicular A.C electric field. By using the method of characteristics solutions and kinetic approach, expression for dispersion relation and growth rate has been derived via detailed calculations and derivations. By changing parameters of plasma like: ac frequency, thermal anisotropy, number density, parametric analysis has been done. The influence of AC frequency on Doppler shift is analyzed, and the comparative study of the effects of oblique and parallel propagating waves on the growth rate has been done. Some different results were found using the subtracted bi-Maxwellian distribution function discussed with the results of bi-Maxwellian distribution function. It can be seen that the effective parameters for generating whistler mode waves are not only temperature anisotropy, but also relativistic factor, alternating field frequency, subtracted distribution amplitude and the width of the loss cone distribution function, which have been discussed in the results and discussion section.