Title:

Magnetic helicity and forcefree equilibria in the solar corona and in laboratory devices

Forcefree equilibria are believed to be important in both an astrophysical and a laboratory context as minimumenergy configurations (see, for example, Woltjer, 1958; Taylor, 1974). Associated is the study of magnetic helicity and its invariance. In Chapter Two of this thesis we put forward a means of heating the corona by the rotation of the footpoints of a coronal "sunspot" magnetic field anchored in the photosphere. The method adopted is essentially that of Heyvaerts and Priest (1984), employing Taylor's Hypothesis (Taylor, 1974) and a magnetic helicity evolution equation. A characteristic of the ReversedField Pinch device is the appearance, at high enough values of the quantity "voltseconds over toroidal flux", of a helical distortion to the basic axisymmetric state. In Chapter Three we look for corresponding behaviour in the "sunspot equilibrium" of the previous chapter, with limited success. However, we go on to formulate a method of calculating general axisymmetric fields above a sunspot given the normal field component at the photosphere. Chapters Four, Five and Six are concerned with equilibrium forcefree fields in a sphere. The main aim here is the calculation minimumenergy configurations having magnetic flux crossing the boundary, and so we employ "relative helicity" (Berger and Field, 1984). In Chapter Four we consider the "P1(cosθ)" boundary radial field, finding that the minimumenergy state is always purely symmetric. In Chapter Five we treat the "P2(cosθ)" boundary condition. We find in this case that a "mixed state" is theoretically possible for high enough values of the helicity. In Chapter Six, we consider a general boundary field, which we use to model point sources of magnetic flux at the boundary of a spheromak, finding that in practice an axisymmetric configuration is always the minimumenergy state. Finally, in Chapter Seven we present an extension to the theorem of Woltjer (1958), concerning the minimization of the magnetic energy of a magnetic structure, to include the case of a free boundary subjected to external pressure forces. To illustrate the theory, we have provided three applications, the first to a finite cylindrical flux and the remainder to possible spheromak configurations.
