Effect of field divergence on reflectivity of Alfvén waves at the transition region

One of the longstanding problems in solar physics and astrophysics is the mysterious heating of the atmosphere that maintains temperatures above 1 million degrees K. Over the past 70-years different scenarios have been put forward none of which has yet been confirmed. Alfven waves that were discovered during WW2 represent an interplay between the tension of the magnetic field lines and plasma inertia. They therefore resemble waves on a string instrument.

Previous studies of Alfven waves have demonstrated their ability to carry significant amounts of energy from the visible surface of the sun known as the photosphere into the atmosphere. Towards the end of their long distance journey Alfven waves can transfer their energy into heating through different mechanisms. Examples include Alfven waves turbulence, phase mixing, and shock heating through nonlinear coupling to compressional waves.

The latter mechanism has been shown to be efficient in 1 dimensional studies. These studies have been able to model the propagation of Alfven waves along 1 dimensional loop like structures from the photosphere into the atmosphere. As the waves reach the upper atmosphere of the sun known as the corona, their amplitudes increase which results in their conversion into compressional slow and fast waves.

The compressional waves rapidly steepen and turn into shocks resulting in heating of the atmosphere. The energy of the Alfven waves is thus converted into heating.The main advantage of the 1 dimensional studies is their ability to employ a high resolution numerical grid that gives the opportunity to investigate the detailed process of wave propagation, conversion, and steepening into shocks.

The drawback is the lack of realistic physics that includes an artificially rigid magnetic field, a simple prescribed field geometry with field lines that always remain in the vicinity of the symmetry axis of the loop.

We propose to investigate the propagation of Alfven waves and their role in heating the solar corona by using a 3 dimensional model that is based on an open source code http://pencil-code.nordita.org/. The model will have the ability to incorporate the important effects of thermal conduction and radiation, magnetic field curvature and expansion, gravity and stratification in the atmosphere.

The structure geometry will be determined by the interaction between the internal and external magnetic environments in a fully three dimensional physical model. It will become possible to address the propagation of the Alfven waves and their interactions with the longitudinal as well as the transverse waves. The resulting heating of the atmosphere through the processes of wave coupling will be investigated.

Our previous studies have demonstrated that plasma jets and surges replicating solar spicules enhance the process of wave amplification and provide important additional energy to the Alfven waves. We would therefore expect to find a similar contribution in a more complex geometry. We will be able to address the role of spicules in Alfven wave amplification and their indirect contribution to the heating process in a more realistic 3 dimensional model. Recent observations

with Hinode/EIS, SST, and other instruments have demonstrated the ubiquity of the Alfven waves in the solar atmosphere.

The proposed research project will contribute to our understanding of the physics of the sun. It will clarify the role of Alfven waves in the dynamics and energetics of the solar atmosphere. The work will be carried out under MPI on massively parallel shared memory computers using the national supercomputing research facility of Wales (SCW)