Dynamics of a Thin Twisted Flux Tube

Abstract

A set of dynamical equations are derived for a slender tube of isolated magnetic Ñux generalizing a model due to Spruit. The tube is assumed to consist of Ðeld lines that twist about the tubeÏs axis at some rate q. The equations describe the evolution of the axis and the evolution of the twist. They include the interaction between twist and motions of the axis described as writhing. Through this interaction, the motion of the axis can introduce twist into a previously untwisted tube. The twist so introduced will have a sign opposite to the local handedness of the axial curve. This may be important for the generation of current in emerging active regions. Tubes with sufficiently large twist are subject to an instability that distorts the axis into a helix of pitch similar to the tubesÏ Ðeld lines. Such an instability might be responsible for the observed morphology in d-spots on the Sun.