Transport and turbulence modeling of solar wind fluctuations

Abstract

Magnetohydrodynamic (MHD) activity, including waves and turbulence, has been a focus of attention in solar wind research for several decades, owing to the wealth of available relevant spacecraft observations. Characterizations of the turbulence have generally been based on incompressible homogeneous turbulence theory. However, recent observations show that the fluctuations undergo systematic temporal evolution, suggesting couplings to large‐scale plasma and magnetic field inhomogeneities. Here we present in detail, and further develop, a theory of transport of small‐scale solar wind MHD turbulence, the preliminary results of which have been recently reported (Zhou and Matthaeus, Geophysical Research Letters, 16, 755, 1989). Large‐scale plasma velocity and magnetic fields are specified, and small‐scale incompressible turbulence evolves in response to the associated inhomogeneities, as well as in accordance with modeled local nonlinear couplings. Dynamical equations based on a two length scale expansion are derived, from which the evolution of various wave number spectra may be computed, including magnetic and kinetic energies, cross helicity, induced electric field, and the corresponding helicities. Several simple analytic solutions predict, with increasing heliocentric distance, a decrease of the preponderance of outward traveling type Alfvénic fluctuations and a lowering of the small‐scale kinetic to magnetic energy ratio of small scale. Both of these are consistent with Helios and Voyager observations. The theory provides a basis for further computations that may be compared with statistical features of solar wind observations.

Wave‐driven Turbulent Coronal Heating in Open Field Line Regions: Nonlinear Phenomenological Model

“…An initial population of upward waves can give rise to a "" reÑected ÏÏ population of downward waves owing to the presence of these terms. This e †ect is entirely analogous to the what has been called a "" mixing ÏÏ e †ect (Zhou & Matthaeus 1990) in transport equations developed for solar wind turbulence (see also Marsch & Tu 1993 ;Tu & Marsch 1989). The main di †er-ence between the two cases is that in the corona the largescale (wind) speed U is presumably much smaller than the speed Thus terms of have been neglected Alfven V A .…”

“…We consider a model based on the theory of transport of 482 small-scale MHD turbulence developed by Zhou & Matthaeus (1990) (see also Tu & Marsch 1989 ;Marsch & Tu 1993). The approach focuses on the dynamics of the smallscale Ñuctuations as inÑuenced by speciÐed large-scale inhomogeneities as well as by local nonlinear couplings.…”

Transport of solar wind fluctuations: A two-component model

“…Assuming that there is scale separation between the fluctuations and the large-scale fields, transport equations for general incompressible fluctuations can be readily derived [Zhou and Matthaeus, 1990;Zank et al, 1996;Matthaeus et al, 1996;Tu and Marsch, 1993]. A comprehensive derivation and discussion of the approximations used is given by Breech et al [2008].…”

Solar Wind Electrons Alphas and Protons (SWEAP) Investigation: Design of the Solar Wind and Coronal Plasma Instrument Suite for Solar Probe Plus

“…Two competing acceleration possibilities are (a) resonant statistical acceleration by waves, including quasi-linear 2nd order Fermi acceleration and transit-time damping (Fisk et al 1974;Miller 1998), and (b) non-resonant stochastic acceleration by turbulent fluid compressions and rarefactions (Ptuskin 1988;Webb et al 2003;Le Roux et al 2002;Cho and Lazarian 2006;Fisk and Gloeckler 2006). Key measurements by SWEAP will include (i) suprathermal ion spectra; (ii) wave modes, density, and velocity vectors, amplitudes and polarization properties, and correlating with magnetic field observations; (iii) plasma turbulence, power spectra (up to the dissipation range of frequencies greater than the proton gyro-frequency, ∼ tens of Hz at ∼ 20R s ), the outer scale, wavevectors (slab/2D), cross-correlations between velocity and density, structure functions, helicity and cross-helicity (Roberts et al 1987;Bavassano et al 2000), and (iv) the radial evolution of turbulent power and relevant length scales (Zhou and Matthaeus 1990;Zank et al 1996) and identification of driving mechanisms (fast/slow stream interactions, shear, and compressions). Requirements: e-strahl: energy range: 70-1000 eV, angular resolution, < 10 • ; Bi-directional electrons: energy range, ≥ 80 eV; Pitch angle distributions in at least 10 energy channels, angular resolution: 20 • ; Detect ion halos with energy up to 20 keV.…”