Limiting Energy Spectrum of a Saturated Radiation Belt.
Abstract
A reformulation of the nonrelativistic Kennel Petschek problem for electrons and protons enables a limiting energy spectrum to be derived, such that (for specified pitch angle anisotropy s of the energetic particle population) electromagnetic cyclotron waves at each frequency less than a fraction s/(s+1) of the equatorial gyrofrequency are marginally stable against spontaneous generation. The limiting spectrum is given in closed form for integer values of s and computed numerically for non integer values of s. Asymptotic expansions for energies E barely above and much greater than the minimum resonant energy E provides estimates of the limiting energy spectrum J sub 4 pi (E) in these extremes, regardless of whether s is an integer. A reconsideration of the original Kennel Petschek problem, in which the differential energy spectrum is not calculated but specified as a certain power law (J sub 4 pi E to the 1-l power), enables the wave frequency corresponding to maximum spatial growth rate, as well as the limiting integral flux I sub 4p above the minimum resonant energy E, to be calculated in closed form as functions of l and s. Keywords: trapped particles; wave particle interactions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 30, 1986
- Accession Number
- ADA176009
Entities
People
- D. T. Davidson
- Michael Schulz
Organizations
- The Aerospace Corporation