Turbulent disruptions from the Strauss equations

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Abstract
The Strauss equations of reduced resistive magnetohydrodynamics are solved pseudo-spectrally, inside a cylinder of square cross-section. Conducting, free-slip, boundary conditions are imposed at the boundaries normal to the direction of the imposed d.c. magnetic field and net current, and periodic boundary conditions are imposed in the third direction. The emphasis is on the development of disruptions. Initial conditions are not analytical equilibria, and are characterized by wide-band noise perturbations in many Fourier modes. Typical spatial resolution is 32 × 32 × 16. At this resolution, the code takes approximately 0·7 seconds per time step on a CRAY-1 computer. Lundquist numbers are limited by the need to resolve the small-scale turbulence which develops. Disruptions are characterized by (i) a burst of kinetic fluid activity which is roughly equipartitioned with the magnetic fluctuations at the small scales, but which involves overall kinetic energies which are much less than the magnetic energies; (ii) a helical ‘m = l, n = 1’ current filament which develops out of the wide-band turbulent noise and wraps itself around the magnetic axis; and (iii) relatively mild disturbances of the magnetic field lines, at least at these low values of Lundquist number (S ≃ 100). The results are compared with those from similar codes which solve the linearized Strauss equations.