On phase steepening as an intense plasma heating mechanism

Abstract

A new physical mechanism of the intense plasma heating is introduced, which may be designated as phase steepening: (i) it applies to velocity and/or magnetic field scaling like a power of the distance with a complex exponent; (ii) the imaginary part the exponent corresponds to a phase with a logarithmic singularity, which leads to oscillations with increasing diverging steepness; and (iii) the steep gradients, even with finite or moderately decaying amplitude, lead to intense dissipation and heating. The physical process of phase steepening is identified in a quite general case of steady magnetohydrodynamics of an incompressible fluid subject to rotation and gravity, in the combined presence of three dissipation mechanisms: electrical resistance, fluid viscosity, and thermal conduction (Fig. 1). The exact analytical solution of the problem leads to 13 cases, one of which suggests the possibility of phase steepening, with conditions that are not fully satisfied. Most of the cases assume the existence of an axisymmetric flow source or sink at the axis and also of a split-monopole magnetic field decaying like the inverse of the radial distance, with opposite directions in different angular sectors, so that the total magnetic flux across a cylindrical surface is zero. The possibility remains that all conditions for phase steepening could be met in other physical conditions.