Analytical Calculation and Event Study of the Effect of High ULF-waves Mode Numbers on Diffusion Rate of Radiation Belt Electrons

Abstract:

Contrary to its crucial importance, estimating the realistic azimuthal wave (mode) number of Ultra Low Frequency (ULF) waves and its effect on diffusion rate of the energetic electrons have been a missing part in the quantification of radial diffusion coefficient D_LL for radiation belt electrons. A threshold mode number, m_th will be derived in this work as a characteristic value under which the mode structures are resolvable by MHD-based models, while resolving mode numbers above m_th would require kinetic models or high-resolution spacecraft data. It will be shown that high mode numbers (larger than m≈40) are beyond the capability of MHD models to resolve. It will be demonstrated that the ground magnetometers are not capable of resolving the kinetic structure of the ULF magnetic pulsations. An event study of 9 March 2018 is conducted as a proof of concept to estimate the realistic mode structure of ULF waves as well as m_th using in-situ magnetometers data of MMS spacecraft mission. The D_LL values will then be calculated with the resolved high-fidelity mode structures. Effect of high modes on the calculated diffusion rates will be studied. Specifically, we quantify the difference between the commonly used diffusion rate and the calculated rate that includes the high mode numbers. This difference in the calculated D_LL could be a potential reason for the limited performance of radiation belt models in simulating the relativistic electrons during some storms. In addition, we find that including only m=+1 in the diffusion rate of electrons, which is a commonly used in the literature, could overestimate the by at least 300 %.