Checking Key Assumptions of the Kennel-Petschek Flux Limit with ELFIN CubeSats

In planetary radiation belts, the Kennel-Petschek flux limit is expected to set an upper limit on trapped electron fluxes at 80-600 keV in the presence of efficient electron loss through pitch-angle diffusion by whistler-mode chorus waves generated around the magnetic equator by the same 80-600 keV electron population. Comparisons with maximum measured fluxes have been relatively successful, but several key assumptions of the Kennel-Petschek model have not been experimentally tested. The Kennel-Petschek model notably assumes an exponential growth of chorus waves as the trapped electron flux increases, and a fixed maximum wave power gain of about 3. Here, we describe a method for inferring the near-equatorial wave power gain using only measurements of trapped, precipitating, and backscattered electron fluxes at low altitude. Next, we make use of Electron Losses and Fields Investigation (ELFIN) CubeSats measurements of such electron fluxes during two moderate geomagnetic storms with sustained electron injections to infer the corresponding chorus wave power gains as a function of time, energy, and equatorial trapped electron flux. We show that wave power increases exponentially with trapped flux, with a wave power gain roughly proportional to the theoretical linear convective gain, and that the maximum inferred gain near the upper flux limit is roughly 10, with a factor of 2 uncertainty. Therefore, two key theoretical underpinnings of the Kennel-Petschek model are borne out by the present results, although the strong inferred gains should correspond to higher flux limits than in traditional estimates. A method for inferring equatorial wave power gain from low altitude electron flux measurements based on quasi-linear theory is described The inferred chorus wave power gain increases roughly linearly with equatorial 180-300 keV trapped electron flux during moderate storms Inferred chorus wave power gains typically reach 10 near the upper flux limit