Filamentary magnetohydrodynamic plasmas

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Abstract
A filamentary construct of magnetohydrodynamical plasma dynamics based on the Elsässer variables is developed. This approach is modeled after discrete vortex models of hydrodynamical turbulence, which cannot be expected in general to produce results identical to those based on a Fourier decomposition of the fields. In a highly intermittent plasma, the induction force is small compared to the convective motion, and when this force is neglected, the plasma vortex system is described by a Hamiltonian. A statistical treatment of a collection of discrete current‐vorticity concentrations is given. Canonical and microcanonical statistical calculations show that both the vorticity and the current spectra are peaked at long wavelengths, and the expected states revert to known hydrodynamical states as the magnetic field vanishes. These results differ from previous Fourier‐based statistical theories, but it is found that when the filament calculation is expanded to include the inductive force, the results approach the Fourier equilibria in the low‐temperature limit, and the previous Hamiltonian plasma vortex results in the high‐temperature limit. Numerical simulations of a large number of filaments are carried out and support the theory. A three‐dimensional vortex model is presented as well, which is also Hamiltonian when the inductive force is neglected. A statistical calculation in the canonical ensemble and numerical simulations show that a nonzero large‐scale magnetic field is statistically favored, and that the preferred shape of this field is a long, thin tube of flux. Possible applications to a variety of physical phenomena are suggested.