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Context. For the last thirty years, most of the studies on the relaxation ofstressed magnetic fields in the solar environment have onlyconsidered theLorentz force, neglecting plasma contributions, and therefore, limiting everyequilibrium to that of a force-free field. Aims. Here we begin a study of thenon-resistive evolution of finite beta plasmas and their relaxation tomagnetohydrostatic states, where magnetic forces are balanced byplasma-pressure gradients, by using a simple 2D scenario involving ahydromagnetic disturbance to a uniform magnetic field. The final equilibriumstate is predicted as a function of the initial disturbances, with aims todemonstrate what happens to the plasma during the relaxation process and to seewhat effects it has on the final equilibrium state. Methods. A set of numericalexperiments are run using a full MHD code, with the relaxation driven bymagnetoacoustic waves damped by viscous effects. The numerical results arecompared with analytical calculations made within the linear regime, in whichthe whole process must remain adiabatic. Particular attention is paid to thethermodynamic behaviour of the plasma during the relaxation. Results. Theanalytical predictions for the final non force-free equilibrium depend only onthe initial perturbations and the total pressure of the system. It is foundthat these predictions hold surprisingly well even for amplitudes of theperturbation far outside the linear regime. Conclusions. Including the effectsof a finite plasma beta in relaxation experiments leads to significantdifferences from the force-free case.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. I. Parallel untwisted magnetic fields in 2D