Empirical modeling of quasilinear evolution of electromagnetic ion cyclotron instability for finite beta plasmas

Electromagnetic ion-cyclotron (EMIC) waves are believed to be important for the loss of relativistic electrons in the radiation belt. On the basis of such a notion, scientists applied quasilinear diffusion theory to compute various diffusion time scales and so forth in order to assess the impact of EMIC waves in the electron loss process. In all these efforts, however, cold plasma dispersion relation is employed although it is well known that the plasma beta in the inner magnetosphere during storm times can reach values as high as the unity. The reason is because the numerical warm plasma dispersion relation makes the computation intractable. In the present paper we put forth an empirical model for the warm plasma dispersion relation, and compare the analytical model with exact solutions. The approximate but sufficiently accurate results are practical enough so that it might be possible to reformulate the classic radiation belt electron diffusion theory by means of the analytical warm plasma dispersion relation. Such a task is beyond the scope of the present paper, but in the present paper, we carry out quasi-linear analysis of the anisotropy-driven EMIC instability over a wide range of the anisotropy factor and plasma beta. Upon comparison with exact numerical solutions it is shown that the empirical model is an excellent substitute for a wide range of parameters.