“…In fact, the cold plasma approximation is inappropriate when the hot plasmas are present, such as the hot particle injection from magnetotail during active times (e.g., Chen et al, 2011Chen et al, , 2019Silin et al, 2011). It has been found that the presence of hot particles can seriously modify the cold plasma dispersion relation and consequently strongly affect the quasi-linear diffusion coefficients (Chen et al, 2013(Chen et al, , 2019Ni et al, 2018;Yu et al, 2019b). However, the effects of hot plasmas on the nonlinear interactions of electrons with electromagnetic waves remain unknown.…”