A theoretical study of the whistler mode instability at the Uranian bow shock

Relativistic whistler wave mode with a perpendicular AC electric field has been studied for generalized distribution function with an index j, which i s reducible to bi-Maxwellian for j = 0, loss-cone for j = 1 and delta funct ion for j = infinity. Based on particle trajectories, the dispersion relati on is obtained using the techniques of a kinetic approach and a method of c haracteristic solutions Calculations are compassed with observations of low frequency waves of Voyager 2 The growth rates for the plasma parameters su ited to the magnetosphere of Uranus are obtained. It is inferred that, not the magnitude but the frequency of the AC field, influences the growth rate . In addition to the temperature anisotropy, plasma particles having a loss -cone provide an additional source of energy. The relativistic electrons al ong with increasing the growth rate, widen the band width so as to cover a wide frequency range thus may explain the entire spectrum of whistler emiss ions at Uranian bow shock.