We present a new hybrid kinetic model to simulate the response of plasmaspheric drainage plumes to impulsive interplanetary pressure pulses. Since particle distributions attending the interplanetary pulses and in the drainage plume are non-Maxwellian, wave-particle interactions play a crucial role in energy transport within and outside the plumes. Finite gyroradius effects become important in mass loading of the transmitted impulse with the drainage plume ions. A forward-reverse shock structure develops from the initial step-like transmitted shock. First results show that the impulse causes strong deformations in the global structure of the plume. The anisotropic ion velocity distribution functions at the impulse front and inside the plume help us determine energy transport via wave-particle interactions throughout the Earth's inner magnetosphere.