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 (λ) 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 (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. Plain Language Summary Auroral kilometric radiation (AKR) is a strong radio emission phenomenon which is generated in the low density polar cavity. They can propagate downward into radiation belts and produce significant acceleration or pitch angle scattering of energetic electrons. Those electrons can yield serious damage to spacecraft or ozone destruction. Because wave‐particle interaction generally occurs at each point along the field line and diffusion coefficients are directly proportional to the square of wave amplitude, it is necessary to specify the field‐aligned wave amplitude. However, previous calculations of AKR‐electron interaction were based on the assumption of the constant field‐aligned wave amplitude. Here, using observations of the Arase satellite and Van Allen Probes from March 23, 2017 to July 31, 2019, we report a field‐aligned distribution of AKR wave amplitude for the first time. Gaussian fitting for the electric field power spectral density is performed to obtain the wave amplitude of each AKR sample. We calculate averaged wave amplitudes of total 14,770 samples on the dayside and nightside. Results show that wave amplitude can be described by a concise formula, decreasing obviously with decreasing latitude. Wave amplitudes are greater (smaller) under intense (weak) geomagnetic condition. This paper provides the further understanding of AKR‐electron interaction. Key Points The field‐aligned distribution of AKR wave amplitude is presented for the first time based on Arase satellite and Van Allen Prob