Stability and mode analysis of solar coronal loops using thermodynamic irreversible energy principles

II. Modes in twisted non-isothermal magnetic field configurations

¹ Instituto de Astronomía Teórica y Experimental (IATE-CONICET), Córdoba, Argentina e-mail: acosta@mail.oac.uncor.edu
² Instituto de Astronomía y Física del Espacio (IAFE-CONICET) Buenos Aires, Argentina
³ Universidad Nacional de General Sarmiento (UNGS), Argentina
⁴ Departamento de Física (FCEyN-UBA) Buenos Aires, Argentina

Received: 12 November 2007
Accepted: 26 June 2008

Abstract

Aims. We study the stability and modes of non – isothermal coronal loop models with different intensity values of equilibrium twisted magnetic field.

Methods. We use an energy principle obtained by means of non – equilibrium thermodynamic arguments. The principle is expressed in terms of Hermitian operators and enables us to consider the coupled system of equations, the balance of energy equation and the equation of motion, to obtain modes and eigenmodes in a spectrum ranging from short to long-wavelength disturbances without using weak varying approximations of the equilibrium parameters. Long-wavelength perturbations introduce additional difficulties because the inhomogeneous nature of the medium produce disturbances corresponding to continuous intervals of eigenfrequencies, which cannot be considered as purely sinusoidal.

Results. We analyze the modification of periods, modes structure, and stability when the helicity, the magnetic field strength, and the radius of the fluxtube are varied. The efficiency of the damping due to the resonant absorption mechanism is analyzed in terms of modes that can either impulsively release or store magnetic energy.

Conclusions. We find that the onset of the instability is associated with a critical value of the helicity and the magnetic energy content has a determinant role on the instability of the system with respect to the stabilizing effect of the resonant absorption mechanism.