FLUCTUATING ENERGY STORAGE AND NONLINEAR CASCADE IN AN INHOMOGENEOUS CORONAL LOOP

Abstract

The dynamics and the energy balance of large-scale fluctuations in a coronal loop are studied. The loop is represented by a simplified structure where the curvature is neglected and the background magnetic field is uniform. In a previous paper, we studied a similar model where a uniform background density was assumed. The present paper represents a generalization of the previous one and it has the purpose of investigating possible modifications to the large-scale energy balance and dynamics due to a more realistic longitudinally nonuniform density. Large-scale fluctuations are dominated by coherent eigenmodes that nonlinearly couple to produce an energy cascade to smaller scales. Eigenmodes properties are calculated by a simplified linear dissipative model, deriving an expression for the input energy flux that is not substantially modified by the presence of the density inhomogeneity and is independent of dissipation. For typical values of the parameters, the derived input energy flux is comparable with that required to heat the active region corona. Nonlinear couplings are dominated by coherence effects due to the symmetry properties of eigenmodes; the consequences are that the system is in a weakly nonlinear regime that produces fluctuating energy storage in the loop, and that the kinetic and magnetic nonlinear energy fluxes are of the same order, despite the dominance of magnetic energy at large scales. From the energy balance, an expression for the velocity fluctuation is derived, which is valid in the more general case of a nonuniform background density; this estimate is in agreement both with measures of nonthermal velocities in the solar corona and with previous numerical results.