A Concise Empirical Formula for the Field-aligned Distribution of Auroral Kilometeric Radiation based on Arase satellite and Van Allen Probes

Abstract Auroral kilometric radiations (AKR) are strong radio emission phenomena, and can prduce significant acceleration or scattering of radiation belt electrons. The variation of AKR wave amplitude with the latitude (λ) has not been reported so far owing to lack of measurements. Here, using observations of the Arase satellite and Van Allen Probes from 23 March 2017 to 31 July 2019, we present the first statistical study on the AKR electric field amplitude (Et) in the radiation belts for |λ| = 0° − 40° and L-shell L = 3.0−6.2. Results (totally 14,770 samples) show that Et can be described by a concise formula: Et(λ) = E0  exp(ξ sin |λ|), decreasing with decreasing latitude. Fitting parameters E0 and ξ are limited in the ranges: E0 = 0.054−0.340 mV/m and ξ = 3.0−4.2. Wave amplitudes are greater (smaller) under intense (weak) geomagnetic conditions. This study helps to better quantify the gyroresonance between AKR and radiation belt electrons.