The Transport and Evolution of MHD Turbulence throughout the Heliosphere: Models and Observations

Abstract

A detailed study of solar wind turbulence throughout the heliosphere in both the upwind and downwind directions is presented. We use an incompressible magnetohydrodynamic (MHD) turbulence model that includes the effects of electrons, the separation of turbulence energy into proton and electron heating, the electron heat flux, and Coulomb collisions between protons and electrons. We derive expressions for the turbulence cascade rate corresponding to the energy in forward and backward propagating modes, the fluctuating kinetic and magnetic energy, the normalized cross-helicity, and the normalized residual energy, and calculate the turbulence cascade rate from 0.17 to 75 au in the upwind and downwind directions. Finally, we use the turbulence transport models to derive cosmic ray (CR) parallel and perpendicular mean free paths (mfps) in the upwind and downwind heliocentric directions. We find that turbulence in the upwind and downwind directions is different, in part because of the asymmetric distribution of new born pickup ions in the two directions, which results in the CR mfps being different in the two directions. This is important for models that describe the modulation of cosmic rays by the solar wind.

MHD Turbulent Power Anisotropy in the Inner Heliosphere

“…Anisotropy is one of the important properties of solar wind turbulence. Anisotropy has been studied via (i) the power spectral indices of the perpendicular k ⊥ and parallel k || wavenumbers, i.e., spectral anisotropy (Horbury et al 2008;Podesta 2009;Wicks et al 2010;Narita et al 2010;He et al 2013;Bruno & Telloni 2015;Zhao et al 2022); (ii) turbulent power in directions parallel and perpendicular to the mean magnetic field or variance anisotropy (Montgomery 1982;Matthaeus et al 1990;Bieber et al 1996;Milano et al 2004;Smith et al 2006;Osman & Horbury 2009a, 2009bRuiz et al 2011;Weygand et al 2011;Horbury et al 2012;Weygand et al 2013;Pine et al 2020;Adhikari et al 2021a;Zank et al 2021;Zhao et al 2022), and (iii) the correlation length in directions parallel and perpendicular to the mean magnetic field i.e., correlation anisotropy (Dasso et al 2005;Matthaeus et al 2005;Osman & Horbury 2007;Dasso et al 2008;Weygand et al 2009;Wang et al 2019;Bandyopadhyay & McComas 2021). In the presence of a large-scale magnetic field, the variance anisotropy is determined by the relative magnitudes of the fluctuations in directions parallel and perpendicular to the mean magnetic field, and spectral anisotropy is determined with respect to the direction of k. These measures are therefore unique, and there is no dependence between them (Matthaeus et al 1996;Oughton et al 2015).…”

Density Turbulence and the Angular Broadening of Outer Heliospheric Radio Sources at High Latitudes and in the Ecliptic Plane

“…) of turbulence (Adhikari et al 2021b(Adhikari et al , 2021a. The larger l u implies a larger l i and lower cascade rate at the 45°latitude than that in the ecliptic plane.…”

“…In the downwind direction, the solar wind is less affected by the PUIs than that in the upwind direction. As a result, turbulence properties are different in the upwind and downwind directions, yielding different turbulence cascade rates and cosmic-ray diffusion tensors (Adhikari et al 2021a). This leads to different solar wind speeds and temperature profiles in the upwind and downwind directions (Nakanotani et al 2020;Adhikari et al 2021a).…”

“…As a result, turbulence properties are different in the upwind and downwind directions, yielding different turbulence cascade rates and cosmic-ray diffusion tensors (Adhikari et al 2021a). This leads to different solar wind speeds and temperature profiles in the upwind and downwind directions (Nakanotani et al 2020;Adhikari et al 2021a). Previous studies also showed that the solar wind and turbulence properties are different in the high-latitude region than in the ecliptic region (McComas et al 1998;Shiota et al 2017;Usmanov et al 2012Usmanov et al , 2014.…”

Turbulent Cosmic Ray–Mediated Shocks in the Hot Ionized Interstellar Medium

“…For balanced slab turbulence, that is, with equal intensities in forward and backward Elsässer fluctuations, ĒC0 is zero. However, balanced fully developed turbulence is infrequently observed in the solar wind (e.g.,Zank et al 2021b;Adhikari et al 2021), so the assumption ¯» E 0 C0 is unlikely to be very accurate, although it should be considered. Since the normalized cross helicity σ C = E C /E T and −1 σ C 1, we can write ¯s = consider two possible choices of normalized cross helicity, σ C = 0.05 or σ C = 0.5.…”