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We study the stability and the modes of non -- isothermal coronal loop modelswith different intensity values of the equilibrium twisted magnetic field.Weuse an energy principle obtained via non -- equilibrium thermodynamicarguments. The principle is expressed in terms of Hermitian operators andallows to consider together the coupled system of equations: the balance ofenergy equation and the equation of motion, to obtain modes and eigenmodes in aspectrum ranging from short to long--wavelength disturbances without having touse weak varying approximations of the equilibrium parameters. Long--wavelengthperturbations introduce additional difficulties because the inhomogeneousnature of the medium determines disturbances leading to continuous intervals ofeigenfrequencies which cannot be considered as purely sinusoidal.We analyze themodification of periods, modes structure and stability when the helicity, themagnetic field strength and the radius of the fluxtube are varied. Theefficiency of the damping due to the resonant absorption mechanism is analyzedin a context of modes that can either impulsively release or storage magneticenergy.We find that the onset of the instability is associated to a criticalvalue of the helicity and that the magnetic energy content has a determinantrole on the instability of the system with respect to the stabilizing effect ofthe resonant absorption mechanism.

astronomy and astrophysics

Stability and mode analysis of solar coronal loops using thermodynamic  irreversible energy principles II. Modes in twisted non--isothermal magnetic  field configurations