A major problem in astrophysical plasma physics is to explain how the outer atmosphere, the corona, of the Sun is heated to temperatures of millions of degrees Kelvin. It is accepted that the heating mechanism is magnetic, with the energy source being turbulent motions below the solar surface. Two classes of theory are proposed, according to the timescale of the driving motions in relation to the Alfven timescale of the coronal plasma. Fast motions generate MHD waves which propagate up into the corona carrying energy and can heat the corona if the waves are damped. Slow motions move the footpoints of the coronal field, generating field-aligned currents which may dissipate to provide heat. In each case, the main difficulty is in finding an adequate means of dissipation in the highly-conducting coronal plasma. Some proposed heating mechanisms are outlined, which present a number of interesting plasma physics problems closely related to those arising for fusion plasma; in particular, Alfven wave propagation and absorption in a nonuniform medium, and anomalous heating by reconnection, turbulence and relaxation.
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