  Nearly parallel vortex filaments are a generalization of point vortices and
describe many phenomena under conservation of angular momentum including
vortices forming in deep ocean convection, magnetically confined plasmas, and
the solar atmosphere. While point vortices represent perfectly straight,
parallel lines of circulation, nearly parallel vortex filaments have some
curvature due to internal viscosity. They interact logarithmically but have a
kinetic self-energy as well. In this letter, I present an exact solution of a
system of these filaments under angular momentum conservation in a mean-field
theory. I show that the filaments have an infinite order phase transition not
present in the point vortex model.
