Benjamin T. MacBride

The Turbulent Cascade at 1 AU: Energy Transfer and the Third-Order Scaling for MHD

We perform a test of MHD turbulent cascade theory in the solar wind and directly evaluate the contribution of local turbulence to heating the solar wind at 1 AU. We look at turbulent fluctuations in the solar wind velocity V and magnetic field B, using the vector Elsasser variables Z ± ≡ V ± B/(4πρ)1/2 as measured at the ACE spacecraft stationed at the Earths L1 point. We combine the fluctuations δZ± over time lags in the inertial range, from 64 s to several hours, to form components of the mixed vector third moments, and we adopt the work of Politano & Pouquet, who derive an exact scaling law, similar to the Kolmogorov 4/5 law, but valid in anisotropic MHD turbulence, for these components. We demonstrate that the scaling is reasonably linear, as is expected for the inertial range. The total turbulent energy injection/dissipation rate that we derive this way agrees with the in situ heating of the solar wind that is inferred from the temperature gradient, whereas methods using the power spectra only seldom agree with the heating rates derived from gradients of the thermal proton distribution. We derive expressions of the third-order moments that are applicable to the spectral cascades parallel and perpendicular to the mean magnetic field. We apply these expressions to fast- and slow-wind subsets of the data, with additional subsetting for mean field direction. We find that both the fast wind and the slow wind exhibit an active energy cascade over the inertial range scales. Furthermore, we find that the energy flux in the parallel cascade is consistently smaller than in the perpendicular cascade.

SPECTRAL INDICES FOR MULTI-DIMENSIONAL INTERPLANETARY TURBULENCE AT 1 AU

We examine Advanced Composition Explorer and Helios 1 data in search of evidence for an anisotropic spectrum of interplanetary magnetic and velocity field fluctuations. Specifically, we focus on the power-law indices of the fluctuation spectra and associated second-order structure functions and ask whether the index varies systematically with the angle between the mean magnetic field and the wind velocity. We extend previous results to show convincingly that it does not. Several popular theories for magnetohydrodynamic turbulence predict a significant variation as part of the turbulent cascade dynamic. We offer some observations on why the predicted anisotropy is not present.

THE TURBULENT CASCADE AND PROTON HEATING IN THE SOLAR WIND AT 1 AU

We examine the convergence of third-order structure function expressions derived to measure the rate of turbulent energy cascade within the solar wind using Advanced Composition Explorer observations from 1 AU over the years 1998 through 2007. We find that a minimum of a year of data is normally required to get good convergence and statistically significant results. We then apply these findings to 10 years of observations spanning both solar minimum and solar maximum conditions. We compare the computed energy cascade rates with previously determined rates of proton heating at 1 AU as determined from the radial gradient of the proton temperature to be proportional to the product of wind speed and proton temperature. We find good agreement with a moderate excess of energy within the cascade that is consistent with previous estimates for thermal electron heating in the solar wind. In keeping with earlier analyses of the dissipation spectrum, we postulate that electron heating by the turbulent cascade is less than and at most equal to the rate of proton heating.

THE TURBULENT CASCADE FOR HIGH CROSS-HELICITY STATES AT 1 AU

We apply third-moment theory that describes the energy cascade within the inertial range of magnetohydrodynamic turbulence to observations of large cross-helicity states at 1 AU. We find that in contrast to intervals with smaller helicity that form the bulk of the observations, large helicity states demonstrate a significant back-transfer of energy from small to large scales. This occurs in such a manner as to reinforce the dominance of the outward-propagating fluctuations. We find no evidence of a significant anisotropy in the back-transfer dynamics and conclude that the process must be short-lived in order to be consistent with solar wind observations. We offer this as partial explanation for large helicity states in the solar wind.

Turbulence spectrum of interplanetary magnetic fluctuations and the rate of energy cascade

There is growing evidence that a turbulent cascade of energy from large to small scales accounts for the dissipation of fluid energy (magnetic and velocity fluctuations) that heats the background plasma. However, much remains to be done to understand the dynamics of that cascade. We apply a structure function formalism originally derived for hydrodynamic turbulence and recently extended to include magnetohydrodynamics (MHD) to map the cascade of energy in the inertial range at 1 AU. We also examine the anisotropies associated with inertial range magnetic fluctuations in the hope of better understanding inertial‐ and dissipation‐range dynamics.

Using Third‐Order Moments of Fluctuations in V and B to Determine Turbulent Heating Rates in the Solar Wind

The inertial range scaling of certain mixed third‐order moments of velocity and magnetic field fluctuations in a turbulent MHD plasma such as the solar wind is related to the energy dissipation rate of the turbulence. We have used this relation to measure energy dissipation rates in the solar wind and other statistical methods to estimate the accuracy of these measurements. This paper reviews results we and others have recently published, and some new results.