A Model for Dissipation of Solar Wind Magnetic Turbulence by Kinetic Alfvén Waves at Electron Scales: Comparison with Observations

Abstract

In hydrodynamic turbulence, it is well established that the length of the dissipation scale depends on the energy cascade rate, i.e., the larger the energy input rate per unit mass, the more the turbulent fluctuations need to be driven to increasingly smaller scales to dissipate the larger energy flux. Observations of magnetic spectral energy densities indicate that this intuitive picture is not valid in solar wind turbulence. Dissipation seems to set in at the same length scale for different solar wind conditions independently of the energy flux. To investigate this difference in more detail, we present an analytic dissipation model for solar wind turbulence at electron scales, which we compare with observed spectral densities. Our model combines the energy transport from large to small scales and collisionless damping, which removes energy from the magnetic fluctuations in the kinetic regime. We assume wave-particle interactions of kinetic Alfvén waves (KAW) to be the main damping process. Wave frequencies and damping rates of KAW are obtained from the hot plasma dispersion relation. Our model assumes a critically balanced turbulence, where larger energy cascade rates excite larger parallel wavenumbers for a certain perpendicular wavenumber. If the dissipation is additionally wave driven such that the dissipation rate is proportional to the parallel wavenumber -as with KAW -then an increase of the energy cascade rate is counter-balanced by an increased dissipation rate for the same perpendicular wavenumber leading to a dissipation length independent of the energy cascade rate.

Wave‐Particle Interaction of Alfvén Waves in Jupiter's Magnetosphere: Auroral and Magnetospheric Particle Acceleration

“…We use here a numerical solver for the general hot dispersion relationship, which considers the full plasma dispersion function. Details of the solver are described in the appendix of Schreiner and Saur ().…”

“…In Figure , we display the real part of the dispersion relationship in the magnetospheric plasma sheet at various distances from Jupiter. Here we use the full hot dispersion relationship (Schreiner & Saur, ; Stix, ) to include finite gyrofrequency effects. In accordance with our plasma scale study in section 2.2, we see that the dominant dissipation scale in the magnetosphere is the gyroperiod of the oxygen ion.…”

“…In Figure , we display the damping rate of the kinetic Alfvén waves in the acceleration region, which is represented by the imaginary part of ω , that is, γ =− I m [ ω ] normalized to R e [ ω ]. Averaged over several wave periods/wave lengths, the damping of the wave is proportional to 2 P ( k ⊥ ) γ ( k ⊥ ) with the wave spectral power density P ( k ) (e.g., Howes et al, ; Schreiner & Saur, ). We see that damping sets in around the electron inertial length scale.…”

Anisotropies of the Magnetic Field Fluctuations at Kinetic Scales in the Solar Wind: Cluster Observations

“…It is well-known that the electron to proton temperature ratio T e /T p is larger in the slow wind. A larger T e /T p increases the damping of KAW for several values of β p and k (Schreiner & Saur 2017) but reduces the damping of the slow-ion acoustic mode; so that we cannot exclude the presence of this last mode for f > 20 Hz, i.e. for kd e ≥ 0.3, a mode which would be less damped and more compressive than the KAW mode.…”

Chirality, extended magnetohydrodynamics statistics and topological constraints for solar wind turbulence

“…However, at even smaller scales below the observed k −4 regime, some dissipation mechanism may exist (even for 'collisionless' plasmas with 'huge' mean free path, the 'dissipation' might be caused, say, by the electron Landau damping: see, e.g., Schreiner & Saur 2017, for a recent discussion of SWT dissipation.) If this indeed is the case, and, as pointed out in the above, for the neutral-fluid-like character of the spectra in the this regime, the dissipation mechanism may seriously destroy OCSDS, leaving the so-called second order OCSDS with only the more persisting cascade flux of one chiral sector (Zhu, Yang & Zhu 2014).…”