Effects of nonlinear wave growth on extreme radiation belt electron fluxes

Abstract

[1] We present new relativistic formulae for the self-limiting electron integral and differential fluxes in a planetary radiation belt. The formulae depend on the relativistic particle anisotropy, the power gain of electromagnetic whistler mode waves assumed to be generated near the equator, and the associated length scale for convective wave growth. The theoretical limit for the electron differential flux is compared with measured fluxes at geosynchronous orbit. Next we incorporate the effects of nonlinear wave growth into the calculation of extreme radiation belt electron fluxes. We assume that whistler mode waves undergo a linear growth phase, during which the frequency is constant, followed by a nonlinear growth phase during which the frequency is time increasing. We determine the total power gain GTOT as the sum of the linear wave gain gL during linear growth and the nonlinear wave gain gN during nonlinear growth. GTOT depends on the maximum values of the linear and nonlinear wave growth rates at the equator and is hence a function of the energetic electron number density Nh. For a specified value of GTOT, we can determine the value of Nh that corresponds to an extreme value for the electron (integral/differential) flux. Our new result for the extreme electron flux in the nonlinear regime can be regarded as a generalization of the Kennel-Petschek limit, which is based on linear wave growth. The extreme value for the electron flux depends on the parameters that characterize the plasma and the assumed particle distribution, as well as the convective length scales λLH and λNH for linear and nonlinear wave growth.