Abstract

The hot beaming (or strahl) electrons responsible for the main electron heal flux in the solar wind are believed to be self-regulated by the electromagnetic beaming instabilities, also known as the heal dux instabilities. Here we report the first quasi-linear theoretical approach of the whistler unstable branch able to characterize the long-term saturation of the instability as well as the relaxation of the electron velocity distributions. The instability saturation is not solely determined by the drift velocities, which undergo only a minor relaxation, but mainly from a concurrent interaction of electrons with whistlers that induces (opposite) temperature anisotropies of the core and beam populations and reduces the effective anisotropy. These results might be able to (i) explain the low intensity of the whistler heat-flux fluctuations in the solar wind (although other explanations remain possible and need further investigation), and (ii) confirm a reduced effectiveness of these fluctuations in the relaxation and isotropization of the electron strahl and in the regulation of the electron heat flux.