Temporal evolution of whistler instability due to cold plasma injection in the presence of perpendicular AC electric field in the magnetosphere of Uranus

Temporal evolution of whistler instability has been studied due to cold plasma injection in the presence of a perpendicular AC electric field in the magnetosphere of Uranus. A generalized distribution function with index j, which is a reducible to a bi-Maxwellian for j = 0 and to a loss-cone for j = 1, for a plasma in the presence of a perpendicular AC electric field, has been derived from a hot/warm background plasma and a time-dependent plasma described by a simple Maxwellian distribution has been considered to represent the injected cold plasma. An expression for the growth rate of a system with added time-dependent cold plasma injection has been calculated using the method of characteristics and kinetic approach The results obtained for representative value of the parameters suited to the Uranian magnetosphere in both cases have been compared and discussed. It is inferred that the temperature anisotropy remains the major source of free energy whereas a loss-cone background acts as an additional source of free energy for the instability. It is not the magnitude but the frequency of the AC field which Influences the growth rate. In comparison to the Uranian magnetosphere this effect is more significant in Earth's magnetosphere. As the ionisation time of the time-dependent injected cold plasma increases, the growth rate goes on increasing, this effect being much greater in a loss-cone background in comparison to a bi-Maxwellian background plasma time-dependence of the cold plasma has been considered since it represents a more realistic situation in injection experiments.