Relationship between the shell-averaged energy spectrum and the frequency spectrum measured by a single spacecraft in the solar wind

Abstract

The relationship between the shell-averaged energy spectrum E(k) and the frequency spectrum P(f) measured by a single spacecraft is needed in studies of solar wind turbulence to allow comparisons between theory and experiment. This relationship is derived for a three-dimensional (scalar) wavevector spectrum of the power-law form that is either isotropic or cylindrically symmetric about the mean magnetic field. In the latter case, it is assumed that the power-law exponents in directions parallel and perpendicular to the mean magnetic field are the same, an assumption that allows the analysis to be performed analytically. The results show that the effects of anisotropy are small when the angle θBV between the solar wind velocity and the mean magnetic field is between approximately 35° and 90°. The largest effects occur near 0°where a significant correction factor is needed compared to the isotropic case due to the lower energy in the k ∥ direction compared to the k ⊥ direction. For solar wind spectra with an unknown degree of anisotropy, measurements of E(k) obtained when 35° ≤ θBV ≤ 90° should be reasonably accurate for most purposes since even if the spectrum is assumed to be isotropic and no corrections are made for spectral anisotropy, the resulting errors are typically less than 10% or 20%. © 2009. The American Astronomical Society. All rights reserved.