Bounce resonant interaction between pulsations and trapped particles
Abstract
The exchange of energy between a given wave and the energetic particle population is investigated, with emphasis on waves with a rapid East-West variation of phase. Reasons are given why these are of particular interest, but the field disturbance has yet to be computed in detail and here a physical account is presented leading to rough estimates for the damping or amplification. The techniques applied to gyroresonance are followed as closely as possible, but bounce resonance is more complicated, and great simplifications are made, particularly in neglecting harmonics. Transformation to the rotating frame of the wave gives a simple way of calculating the change in energy of a single particle for a given change in L. The resonance condition including the Doppler shift due to the East-West particle drift is a quadratic for the particle energy. Typically there is a low energy for which the bounce frequency almost equals the wave frequency and a high energy for which the Doppler shifted frequency is much higher than the wave frequency. The high energy resonance is more favourable for wave amplification by the kind of particle distribution known to exist. Typically the high energy electrons are relativistic and here attention is given to the high energy proton resonance. For westward travelling waves, protons which move out lose energy and the outer edge of a proton belt could supply energy to such a wave via bounce resonance. Calculations are based on the strongest known mechanism. This requires a disturbance in Br at the equator, which has been observed by Coleman. Because of ignorance of the wave fields it was found convenient to use quasilinear theory rather than linear theory in estimating the damping or growth rate. The resulting expressions for the exchange in energy are easier to interpret physically. The results show that the damping is quite powerful and the conditions required for amplification are discussed. It is pointed out that the East-West component of the group velocity of such waves is small and this may be important in applications to the magnetosphere.
- Publication:
-
Planetary and Space Science
- Pub Date:
- March 1969
- DOI:
- 10.1016/0032-0633(69)90068-3
- Bibcode:
- 1969P&SS...17..349S