FITTING THE AE-8 ENERGY-SPECTRA WITH 2 MAXWELLIAN FUNCTIONS

In fitting the integral flux spectrum J(> E; B; L) of trapped energeti c particles above the energy threshold E, it is common practice to use either an exponential function exp(-E/E(o)) or a power law E(-7) wher e the energy constant E(o) or the index gamma are adjusted to obtain b est fits to the measured flux values J(i)(>E(i); B; L). These fit func tions have generally been chosen not on firm physical grounds, but bec ause of their mathematical simplicity. They have been used since 1960 in radiation belt modelling. However, a large number of mathematical f unctions can be selected to fit data with an equally good accuracy. No te that most of them have no physical meaning or relevance. In this wo rk, the discrete AE-8 energy spectra J(i)(E(i); B-o; L) have been fitt ed with a sum of two maxwellian functions. The slope of the differenti al flux J(d)(E) is then related to the characteristic temperature of t he maxwellian velocity distribution and the normalisation constant is proportional to the number density of the maxwellian population. Besid es its greater physical relevance, this new fit function has a non-sin gular behaviour in the limit E = 0. This is not the case for the power laws mentioned above which fit the data only in limited energy ranges . The fitting parameters have been determined for drift shells paramet ers ranging between L = 1.2 and L = 10. Their dependence on L is deter mined and discussed. The analytical fit of the energy spectra is good for energies smaller than 4 MeV, but it is not satisfactory at larger energies for reasons which are discussed. This work indicates that the energy spectra of the AE-8 model can be approximated rather well by t wo maxwellian distributions for electron energies smaller than 4 MeV, not only near geostationary orbit but also for a wide range of L value s. Copyright (C) 1996 Elsevier Science Ltd.