Amplification of Whistler Waves by Losscone Instability in the Magnetosphere

Summary form only given. Relativistic electrons trapped in the radiation belts have a loss-cone velocity distribution. Loss-cone instability to amplify whistler waves by those electrons in the bulk of the energy distribution is studied. Doppler shifted cyclotron resonance interaction provides the energy transfer between electrons and the wave. The resonance condition is given by omega₀ = Omega/gamma₀ + kv_z0, where omega₀ and Omega are the wave frequency and the nonrelativistic electron cyclotron frequency; gamma₀ is the initial relativistic factor of the electron. Only small portion of total electrons are close to resonant interaction with a wave with frequency omega. Wave is experiencing cyclotron damping to those electrons, which are initially at exact cyclotron resonance with the wave, i.e., omega-omega₀ = Deltaomega₀ = 0. However, wave can exchange energy with those electrons having Deltaomega₀ slightly different from zero. For whistler waves, omega < Omega. To match the cyclotron resonance, it requires Doppler shift with kv_z<0. A differential-integral equation, which governs the temporal evolution of the whistler wave field amplitude, is derived. The numerical results show that whistler waves can be amplified by more than 20 dB, agreeing with the experimental results. This amplification process reduces considerably the required field intensity of injected whistler wave for the purpose of precipitating electrons in MeV range. This suggests an optimal approach applying the chaotic scattering process to reduce the population of very energetic electrons trapped in the magnetosphere. It is using less-energetic electrons (e.g., <100 keV electrons) to amplify injected whistler waves through loss-cone instability and then using the amplified waves to scatter undesired energetic electrons (e.g., MeV electrons) into the loss cone