We present results of a two-dimensional fully kinetic particle-in-cell simulation in order to shed light on the role of whistler waves in the scattering of strahl electrons and in the heat-flux regulation in the solar wind. We model the electron velocity distribution function as initially composed of core and strahl populations as typically encountered in the near-Sun solar wind as observed by Parker Solar Probe. We demonstrate that, as a consequence of the evolution of the electron velocity distribution function (VDF), two branches of the whistler heat-flux instability can be excited, which can drive whistler waves propagating in the direction oblique or parallel to the background magnetic field. First, oblique whistler waves induce pitch-angle scattering of strahl electrons, toward higher perpendicular velocities. This leads to the broadening of the strahl pitch-angle distribution and hence to the formation of a halo-like population at the expense of the strahl. Later on, the electron VDF experiences the effect of parallel whistler waves, which contributes to the redistribution of the particles scattered in the perpendicular direction into a more symmetric halo, in agreement with observations. Simulation results show a remarkable agreement with the linear theory of the oblique whistler heat-flux instability. The process is accompanied by a significant decrease of the heat flux carried by the strahl population.

In collision-poor plasmas from space, e.g., solar wind or stellar outflows, the heat-flux carried by the strahl or beaming electrons is expected to be regulated by the self-generated instabilities. Recently, simultaneous field and particle observations have indeed revealed enhanced whistler-like fluctuations in the presence of counter-beaming populations of electrons, connecting these fluctuations to the whistler heat-flux instability (WHFI). This instability is predicted only for limited conditions of electron beam-plasmas, and was not captured in numerical simulations yet. In this letter we report the first simulations of WHFI in particle-in-cell (PIC) setups, realistic for the solar wind conditions, and without temperature gradients or anisotropies to trigger the instability in the initiation phase. The velocity distributions have a complex reaction to the enhanced whistler fluctuations conditioning the instability saturation by a decrease of the relative drifts combined with induced (effective) temperature anisotropies (heating the core electrons and pitch-angle and energy scattering the strahl). These results are in good agreement with a recent quasilinear approach, and support therefore a largely accepted belief that WHFI saturates at moderate amplitudes. In anti-sunward direction the strahl becomes skewed with a pitch-angle distribution decreasing in width as electron energy increases, that seems to be characteristic to self-generated whistlers and not to small-scale turbulence.

The expansion of the solar wind plasma generates anisotropic particle distributions, so that the temperature in the direction parallel to the interplanetary magnetic field becomes higher than the temperature in the perpendicular direction. This configuration represents a source of free energy for the development of kinetic electromagnetic instabilities. Among them, the firehose instability is often considered to prevent the further increase of the temperature anisotropy in the particle velocity space and hence to shape the velocity distribution functions of electrons and protons in the solar wind. We present a non-linear modeling of the firehose instability, retaining a kinetic description for both the electrons and protons. Fully kinetic Particle-In-Cell simulations using the Energy Conserving semiimplicit method (ECsim) are performed to clarify the role of the electron temperature anisotropy in the development of the proton firehose instability. We found that in presence of an electron temperature anisotropy the onset of the proton firehose instability occurs earlier and its growth rate is faster. The enhanced wave fluctuations contribute to the particle scattering reducing the temperature anisotropy to the stable isotropic state. The simulation results compare well with linear theory confirming that the process responsible for particles isotropization is effectively initialized by the firehose instability.