Direct observations of energy transfer from resonant electrons to whistler-mode waves in magnetosheath of Earth

Electromagnetic whistler-mode waves in space plasmas play critical roles in collisionless energy transfer between the electrons and the electromagnetic field. Although resonant interactions have been considered as the likely generation process of the waves, observational identification has been extremely difficult due to the short time scale of resonant electron dynamics. Here we show strong nongyrotropy, which rotate with the wave, of cyclotron resonant electrons as direct evidence for the locally ongoing secular energy transfer from the resonant electrons to the whistler-mode waves using ultra-high temporal resolution data obtained by NASA's Magnetospheric Multiscale (MMS) mission in the magnetosheath. The nongyrotropic electrons carry a resonant current, which is the energy source of the wave as predicted by the nonlinear wave growth theory. This result proves the nonlinear wave growth theory, and furthermore demonstrates that the degree of nongyrotropy, which cannot be predicted even by that nonlinear theory, can be studied by observations.