Coronal heating by Alfvén waves

Abstract

If Alfvén waves are responsible for the heating of the solar corona, what are the various dissipation processes, under what conditions are they important, and what observational consequences may be expected? For wave periods longer than roughly one minute, the corona appears to the waves as turbulent and dissipation is efficient, but little more can be said. For shorter wave periods, a bend or twist in the magnetic field can convert Alfvén waves into fast-mode waves, which then dissipate. But, if the waves travel nearly along the field, the main dissipation occurs via nonlinear interactions among Alfvén waves, near the top of magnetic loops. Once the wave intensity is sufficient so that wave dissipation exceeds radiative energy losses, the temperature rise (ΔT) is limited by electron heat conduction. The basic result is that ΔT is independent of the wave intensity and it is also independent of the electron density. Therefore, regions high and low in the corona are heated similarly. Since ΔT is also proportional to the magnetic pressure, the heating by Alfvén waves naturally outlines regions (loops) of enhanced magnetic fields. A numerical approximation, for wave period τ≲100 s, is

$$\frac{{\Delta T}}{T} \approx 10^{ - 2.5} B^2 \left( {\frac{{2 \times 10^6 }}{T}} \right)^{5/2} \frac{\tau }{{30s}}$$

.