Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment

TL;DR

This paper develops analytical models for Alfvén wave reflection and turbulent heating in the solar wind, accounting for wave periods and solar wind velocity, to improve understanding of solar wind heating and acceleration.

Contribution

It introduces generalized analytical models for Alfvén wave reflection and turbulent heating that include solar wind velocity effects, extending previous phenomenological approaches.

Findings

Analytical expressions for wave amplitudes and heating rates as functions of heliocentric distance.

Comparison of models with observations shows good agreement for different wave periods.

Models enable incorporation of wave reflection and heating into solar wind simulations.

Abstract

We study the propagation, reflection, and turbulent dissipation of Alfven waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al, we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy, and assume that there is much more energy in waves propagating away from the Sun than waves propagating towards the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfven critical point - that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfven-wave reflection and turbulent heating into fluid models of the solar wind.