Coronal heating by relaxation in a sunspot magnetic field

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Abstract
The heating by resistive turbulence of solar coronal magnetic fields is evaluated by means of the Taylor-Heyvaerts hypothesis, which enables one to calculate the evolution of the magnetic helicity and magnetic field in the corona in response to prescribed motions of the photospheric footpoints. The relationship between the photospheric velocity field and the helicity generation rate is considered for a coronal arcade and the energy release is proved to be positive definite in general. Also, the evolution and dissipation is determined for the axisymmetric magnetic field above a single sunspot which is being twisted up from below.