Lossy radial diffusion of relativistic Jovian electrons

The radial diffusion equation with synchrotron lossess is solved by the Laplace transform method for near equatorially mirroring relativistic electrons. The evolution of a power law distribution function is found, and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient of the form D/sub L//sub L/=D0L/sup alpha/. The peaking of the 10.4-cm volume emissivity from Jupiter at Lapprox. =1.8 provides an estimte D0approx. =9 x 10-11 in the radiation belts; this value is suggested as the appropriate modification for an equatorial field strenght of 4.2 G of the Birmingham et al.(1974) result. Nonsynchrotron losses are included phenomenologically, and from the phase space densities reported by McIlwain and Fillius (1975) the particle lifetime is estimated as tauapprox.6 x 108L2-/sup alpha/ s. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided