Excitation of Whistler Wave Instabilities Using a Spiraling Electron Beam in a Plasma

In the present manuscript, we present a local theory of whistler wave excitation by a spiraling electron beam in magnetoplasmas. Different excitation mechanisms have been studied with an electron beam injected parallel to the static magnetic field Bs and with a spiraling electron beam injected at an angle to the magnetic field. The whistler wave excitation by a parallel beam and an oblique beam has been studied analytically for parallel as well as oblique whistlers. The dispersion relation of the whistler modes has been derived for parallel beam–parallel whistlers interaction, oblique beam–parallel whistlers interaction, oblique beam and oblique whistler wave and parallel beam–oblique whistlers interaction. For whistler wave promulgating parallel to the applied magnetic field, only cyclotron resonance takes place, while for whistler wave promulgating at an angle to the applied magnetic field, both cyclotron and Cerenkov resonance occurred. The expression of growth rate and unstable wave frequencies of excited whistler waves are derived using the first-order perturbation theory. The numerical values of unstable wave frequencies and growth rate, both are found to increase with increasing value of wave number and beam density. Also, a rise in growth rate is reported even with increasing velocity of the electron beam. However, the growth rate value turns down with the increase in obliqueness of the wave. The growth rate value increases with increase in the value of the applied magnetic field in both Cerenkov and cyclotron interactions. The results presented in this manuscript may be useful to elucidate the excitation of whistler waves in complex plasmas.