  Context. For the last thirty years, most of the studies on the relaxation of
stressed magnetic fields in the solar environment have onlyconsidered the
Lorentz force, neglecting plasma contributions, and therefore, limiting every
equilibrium to that of a force-free field. Aims. Here we begin a study of the
non-resistive evolution of finite beta plasmas and their relaxation to
magnetohydrostatic states, where magnetic forces are balanced by
plasma-pressure gradients, by using a simple 2D scenario involving a
hydromagnetic disturbance to a uniform magnetic field. The final equilibrium
state is predicted as a function of the initial disturbances, with aims to
demonstrate what happens to the plasma during the relaxation process and to see
what effects it has on the final equilibrium state. Methods. A set of numerical
experiments are run using a full MHD code, with the relaxation driven by
magnetoacoustic waves damped by viscous effects. The numerical results are
compared with analytical calculations made within the linear regime, in which
the whole process must remain adiabatic. Particular attention is paid to the
thermodynamic behaviour of the plasma during the relaxation. Results. The
analytical predictions for the final non force-free equilibrium depend only on
the initial perturbations and the total pressure of the system. It is found
that these predictions hold surprisingly well even for amplitudes of the
perturbation far outside the linear regime. Conclusions. Including the effects
of a finite plasma beta in relaxation experiments leads to significant
differences from the force-free case.
