Energy dependence of the radial diffusion coefficient and spectra of inner radiation belt particles: analytic solutions and comparison with numerical results

We present a theoretical method by which the energy dependence of the radial diffusion coefficient D/sub L/L may be deducted from spectral observations of the particle population at the inner edge of the earth's radiation belts. This region has previously been analyzed with numerical techniques (for a review see, e.g., Walt (1971)); in this report we give an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (Lapprox.1--2). We demonstrate both analytically and numerically that the particle spectra there are shaped by the energy dependence of D/sub L/L regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. We report excellent agreement between analytic and numerical results