Vortex filament dynamics in plasmas and superconductors

The dynamical description of a thin vortex filament in a perfect fluid is generalized to a charged fluid on a neutralizing background. The filament curvature and torsion evolve integrably according to a higher nonlinear Schr\"odinger equation, which is found using the Hasimoto transformation. Because of screening, local induction is accurate, and the logarithmic long-range divergency is removed. Linear waves, such as the Kelvin mode, are supported by the filament, as well as nonlinear waves and solitons. The effects of vortex stretching are briefly discussed. Applications of the results are found in electron magnetohydrodynamics and in type II superconductor theory.