The effects of bounce resonances on wave growth rates in the magnetosphere
Abstract
Expressions for the ULF wave growth rates are obtained by consistent study of the bounce and drift motions of geomagnetically trapped particles. Different cases depending on the relative values of bounce, drift and wave frequencies are examined. It is shown that the growth (damping) rate as a function of wave frequency has an oscillatory character with maxima associated with an averaged bounce frequency. The instability conditions are investigated. For wave frequencies exceeding the Larmor drift frequency, the instability appears if the derivative function with respect to the energy is positive over a sufficient period. If, however, the wave frequency is less than an effective Larmor drift frequency, the instability is possible even if this derivative is negative everywhere.
 Publication:

Planetary and Space Science
 Pub Date:
 June 1977
 DOI:
 10.1016/00320633(77)900642
 Bibcode:
 1977P&SS...25..573K
 Keywords:

 Earth Magnetosphere;
 Extremely Low Radio Frequencies;
 Magnetically Trapped Particles;
 Radiation Belts;
 Resonance Scattering;
 Wave Propagation;
 Damping;
 Drift Rate;
 Integral Equations;
 Kinetic Equations;
 Larmor Precession;
 Numerical Analysis;
 Geophysics