Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wavenumber ranges in a $\beta \gtrsim 1$ plasma. The $k^{-5/3}$ inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfv\'en speed. At smaller wavelengths $k \rho_i \geq 1$ the electric spectrum is softer and is consistent with the expected dispersion relation of short-wavelength kinetic Alfv\'en waves. Kinetic Alfv\'en waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluid-like nature of the solar wind.