RELAXED STATES OF AN IDEAL MHD PLASMA WITH EXTERNAL MAGNETIC-FIELD

We study an ideal MHD plasma with the non-vanishing invariants energy, cross-helicity and magnetic helicity, confined in a cylinder with inf initely conducting walls and an externally applied magnetic field B-0. The magnetic and velocity fields are expanded in base vector fields, satisfying del x B-lambda = B lambda. Boundary conditions are imposed to make the curl a self-adjoint operator. The three invariants depend on the time-dependent coefficients of the base vector fields, and are used to construct the partition function to gather statistical informa tion about the equilibrium thermodynamic state to which the plasma rel axes after a turbulent transition. For zero external magnetic field bu t large magnetic helicity, the energy resides preferentially in magnet ic field fluctuations. A sizeable fraction of the kinetic energy initi ally present is transformed into magnetic energy. The energy condenses via an inverse cascade predominantly to the lowest energy eigenstate, in agreement with results obtained by Taylor. However, since we consi der the whole spectrum of eigenstates, the energy does not exclusively occupy the lowest eigenstate. If the eigenvalues are densely spaced ( as in a thin torus), the higher eigenmodes also contain appreciable am ounts of energy, resulting in a finite pressure of the plasma. For con stant and finite external magnetic field, the average induced magnetic field exactly cancels the external held. This indicates that, on a st atistical average, the plasma is diamagnetic or superconducting. Super imposed on the average statistical state are fluctuations that may bec ome large if the magnetic helicity is large.