Magnetic Shell Tracing: A Simplified Approach.

Abstract : We consider the adiabatic motion of electrons trapped in the model geomagnetic field derived from a scalar potential. The drift shell is specified analytically (i.e., by an approximation given in closed form) in terms of the equatorial pitch angle. The 'radial gradient' is inferred from the diurnal variation of particle flux. This procedure offers an internal test for the absence of time-varying coefficients in the expansion of V. The pitch-angle distribution is directly observed at the noon meridian. The parameters thus determined allow the pitch-angle distribution at other longitudes to be obtained from Liouville's theorem. The results, at least for a well-studied test case, are comparable in quality to those obtained by more difficult methods, using a more complicated field model and the data from two spacecraft, i.e., are in similarly good agreement with the observational data obtained at other longitudes. In particular, we find that the maximum flux at alpha sub 0 = pi/2 occurs at noon (phi = pi) and that the maximum flux j(alpha sub 0, phi = 0) at midnight (phi = 0) occurs at alpha sub 0 not = pi/2.

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