THE CURL TRANSFORM OF A LINEAR FORCE-FREE MAGNETIC-FIELD

An expression is derived giving the curl transform of a linear force-f ree magnetic field in terms of the curl eigenfunction projection on th e sum of two integrals over the field in physical space. The result si verified by direct substitution of the curl eigenfunction expansion o f the field and exemplified by deriving the curl transform for the sim plest force-free magnetic field. This provides the means to compare th e curl transforms of previously-worked-out fields with those derived d irectly from the transform space representations, effectively completi ng the description of linear force-free magnetic fields in terms of th e curl eigenfunction expansion begun previously. The direct and invers e curl transforms provide a new approach to the practical and theoreti cal study of linear force-free magnetic fields (as well as Trkalian-Be ltrami flows) and their classification.