Lorentz self-forces on curved current loops

A derivation is presented for the Lorentz self-force arising from the interaction of a slender current loop of arbitrary shape with its own magnetic field. The self-force on any loop segment depends explicitly on the global shape of the remainder of the loop. Calculations of the self-force are presented for various model loops. For loops having small to moderate noncircularity, it is shown that the self-force on a segment with local major (R) and minor (a) radii is approximately that for an axisymmetric torus having uniform R and a. These properties of the self-force critically influence the equilibrium and dynamics of thin current loops in solar and astrophysical plasmas.