Energy Transfer Between Various Electron Populations Via Resonant Interaction with Whistler Mode Wave

Electron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi-monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave-particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles. Apart from the Earth's magnetic field, the main objects in the Earth's magnetosphere are electromagnetic waves and charged plasma particles, mainly electrons and protons. Self-consistent interactions between waves and particles determine their dynamics that includes wave excitation and damping, particle acceleration and pitch-angle scattering leading to their precipitation into the atmosphere. It appears that not all particles interact with the waves equally efficient. Among them there are the so-called resonant particles that experience slowly varying force from the wave. Usually, those are quite energetic particles. Resonant wave-particle interaction may lead to particle energization and, by energy conservation, to the wave damping, or vice versa, to wave excitation at the expense of resonant particle energy. Both cases may take place in the magnetospheric plasma. While both processes are related to energy exchange between wave and particles, after all, they result in energy transfer between various particle populations. We consider an example of such energy transfer, in which a whistler mode wave is excited close to the equator by one group of resonant electrons and is absorbed at higher latitudes by another group of resonant electrons, which manifests the energy exchange between two groups of energetic electrons mediated by whistler mode wave. Energy transfer between various particle populations is an intrinsic feature of wave-particle interactionsIn non-equilibrium unstable plasma, wave-mediated energy transfer from lower energy to higher energy particles is possibleWhistler wave packet excited by the first cyclotron resonance particles may then energize the Landau resonance particles