Simulation of high‐frequency solar wind power spectra using Hall magnetohydrodynamics

Abstract

Solar wind frequency spectra show a distinct steepening of the ƒ−5/3 power law inertial range spectrum at frequencies above the Doppler‐shifted ion cyclotron frequency. This is commonly attributed to dissipation due to wave‐particle interactions. We consider the extent to which this steepening can be described, using a magnetohydrodynamic formulation that includes the Hall term. An important characteristic of Hall MHD is that although the ion cyclotron resonance is included, there is no wave‐particle dissipation of energy. In this study we use a compressible Hall MHD code with a constant magnetic field and a polytropic equation of state. Artificial dissipation in the form of a bi‐Laplacian operator is used to suppress numerical instabilities, allowing for a clear separation of the dissipative scales from the ion cyclotron scales. A distinct steepening appears in the simulation power spectra near the cyclotron resonance for certain types of initial conditions. This steepening is associated with the appearance of right circularly polarized fluctuations at frequencies above the ion cyclotron resonance. Similar steepenings and polarization enhancements are observed in solar wind magnetic field data.

Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer

“…Some authors argue that it does not [83][84][85][86][87][88][89] and argue that kinetic Alfvén waves provide the observed steepening, but some of these observations have been brought into question [90]. Dispersion is sometimes invoked as an explanation for the steepening of the power spectrum at ion dissipation scales [55,[91][92][93][94][95] and whistler waves are also discussed in the context of forming the dissipation range at ion scales [92,[96][97][98]. The central issue to that question rests with the dissipation processes that remove energy from the turbulence and produce heat.…”

Solar wind vs magnetosheath turbulence and Alfvén vortices

“…Some authors associate the spectral steepening to the dissipation range (Leamon et al, 1998Smith et al, 2006). Others suggest that beyond the spectral break another turbulent cascade takes place (Biskamp et al, 1996;Ghosh et al, 1996;Stawicki et al, 2001;Galtier, 2006;Galtier and Buchlin, 2007).…”

Wave turbulence in magnetized plasmas

“…Another important issue discussed in the literature is the relationship between perpendicular and parallel scales in anisotropic MHD turbulence (see e.g., Higdon, 1984;Goldreich and Sridhar, 1995;Boldyrev, 2006). In order to take into account anisotropy, Goldreich and Sridhar (1995) proposed a heuristic model based on a critical balance between the Alfvén time and the eddy-turnover time scale, respectively…”