Abstract

Our research is aimed to derive the macroscopic equation of motion of a vortex-current filament, in which electric current and vorticity coaxially exist. The macroscopic equation of motion of vortex filaments without the electric current has been developed by D. W. Moore and P. G. Saffman. To derive the new equations of motion of the vortex-current filament, we follow their methods and obtain the result correct to the terms inversely proportionnal to the square of radius of curvature. The resulting equations of motion contain both the hydro- and magnetohydro-dynamic effects. Our result can be elucidated by comparing with the result obtained by V. S. Mukhovatov and V. D. Shafranov in the force balance analysis in Tokamak. The cut-off Biot-Savart integral approximation derived by E. D. Siggia is also useful in our MHD formulation.

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