Role of Whistler Waves in Regulation of the Heat Flux in the Solar Wind

The electron heat flux is one of the leading terms in energy flow processes in the collisionless or weakly-collisional solar wind plasma. The very first observations demonstrated that the collisional Spitzer-HÓ“rm law could not describe the heat flux in the solar wind well. In particular, in-situ observations at 1AU showed that the heat flux was suppressed below the collisional value. Different mechanisms of the heat flux regulation in the solar wind were proposed. One of these possible mechanisms is the wave-particle interaction with whistler-mode waves produced by the so-called whistler heat flux instability (WHFI). This instability operates in plasmas with at least two counter-streaming electron populations. Recent observations indicated that the WHFI operates in the solar wind producing predominantly quasi-parallel whistler waves with the amplitudes up to several percent of the background magnetic field. But whether such whistler waves can regulate the heat flux still remained an open question.

We present the results of simulation of the whistler generation and nonlinear evolution using the 1D full Particle-in-Cell code TRISTAN-MP. This code models self-consistent dynamics of ions and two counter-streaming electron populations:  warm (core) electrons and hot (halo) electrons. We performed two sets of simulations. In the first set, we studied the wave generation for the classical WHFI, so both core and halo electron distributions were taken to be isotropic. We found a positive correlation between the plasma beta and the saturated wave amplitude. For the heat flux, the correlation changes from positive to a negative one at some value of the heat flux. The observed wave amplitudes and correlations are consistent with the observations. Our calculations show that the electron heat flux does not change substantially in the course of the WHFI development; hence such waves are unlikely to contribute significantly to the heat flux regulation in the solar wind.

The classical WHFI drives only those whistler waves that propagate along the halo electron drift direction (consequently, parallel with respect to background magnetic field). Such waves interact resonantly with electrons that move in the opposite direction; hence, only a relatively small fraction of hot halo electrons is affected by these waves. On the contrary, anti-parallel whistler waves would interact with a substantial fraction of halo electrons. Thus, they could influence the heat flux more significantly. To test this hypothesis, we performed the second set of simulations with anisotropic halo electrons. Anisotropic distribution drives both parallel and anti-parallel waves. Our calculations demonstrate that anti-parallel whistler waves can decrease the heat flux. This indicates that the waves generated via combined whistler anisotropy and heat flux instabilities might contribute to regulation of the heat flux in the solar wind.

The work was supported by NSF grant 1502923. I. Kuzichev would also like to acknowledge the support of the RBSPICE Instrument project by JHU/APL sub-contract 937836 to the New Jersey Institute of Technology under NASA Prime contract NAS5-01072. Computational facility: Cheyenne supercomputer (doi:10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by NSF