Dissipation of the Perpendicular Turbulent Cascade in the Solar Wind

Abstract

The core solar wind protons are observed to be heated perpendicularly to the magnetic field. This is taken to be a signature of the cyclotron damping of the turbulent fluctuations, which are thought to be responsible for the heating. At the same time, it is commonly accepted that the turbulent cascade produces mostly highly oblique (quasi-two-dimensional) fluctuations, which cannot be immediately cyclotron resonant with the ions because of their low frequencies and small parallel wavenumbers. To address this problem, we propose a new, indirect mechanism for damping the quasi-two-dimensional fluctuations. The mechanism involves a plasma instability, which excites ion cyclotron resonant waves. As the cascade proceeds to higher wavenumbers, it generates increasingly high velocity shear associated with the turbulent fluctuations. The shear eventually becomes unstable to waves near harmonics of the ion cyclotron frequency. Once the frequency of the waves is upshifted, they can heat ions perpendicularly, extracting the energy from the quasi-two-dimensional fluctuations. The dissipation rates of quasi-two-dimensional fluctuations are incorporated into a model of the energy transfer in the turbulent cascade. Our analysis of the observed spectra shows that the spectral break separating the inertial and dissipation ranges of the turbulence, where the dissipation sets in, corresponds to the same shear under a wide range of plasma conditions, in agreement with the prediction of the theory. The observed turbulence spectra often have power-law dissipation ranges with an average spectral index of -3. We demonstrate that this fact is simply a consequence of a marginal state of the instability in the dissipation range.