Alfven Waves and Turbulence in the Inner Corona

Alfv ́enic turbulence is believed to play a fundamental role in the inner corona since the wave flux emerg- ing from the transition region can accelerate the wind directly (wave pressure) and indirectly (plasma heating). The stratification of the solar atmosphere causes the reflection of Alfv ́en waves propagating up- ward and trigger nonlinear interactions. In a high Reynolds number plasma this leads to a turbulent cascade which, in presence of a strong, large scale, magnetic field, develops in the perpendicular (to the mean magnetic field) wave numbers. We adopt a 2D shell-model coupled to wave propagation in a stratified atmosphere to study the efficiency of such a reflection sustained turbulence and the evolution of the spectra in the perpendicular wave numbers. It turns out that magnetic energy far exceeds the kinetic energy in the fluctuations, their spectra are approximately equal and show a power-law behav- ior with slope -2 in all the domain considered (up to 10 R⊙). Most of the heating occurs in the first 3 solar radii where reflection is stronger (correspond- ing to the minimum of the normalized cross helicity). The heating rate is still too low, compared to the en- ergy available in the system; however, an enhanced heating can be achieved injecting more power at low frequency or increasing the stratification of the at- mosphere.