A Concise Empirical Formula For The Field-Aligned Distribution Of Auroral Kilometeric Radiation Based On Arase Satellite And Van Allen Probes

Auroral kilometric radiations (AKR) are strong radio emission phenomena, and can produce significant acceleration or scattering of radiation belt electrons. The variation of AKR wave amplitude with the latitude (lambda) has not been reported so far owing to lack of measurements. Here, using observations of the Arase satellite and Van Allen Probes from March 23, 2017 to July 31, 2019, we present the first statistical study on the AKR electric field amplitude (E-t) in the radiation belts for vertical bar lambda vertical bar = 0 degrees - 40 degrees and L-shell L = 3.0-6.2. Results (totally 14,770 samples) show that E-t can be described by a concise formula: E-t(lambda) = E-0 exp(xi sin vertical bar lambda vertical bar), decreasing with decreasing latitude. Fitting parameters E-0 and xi are limited in the ranges: E-0 = 0.054-0.340 mV/m and xi = 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.