[Paper Review] Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. I. Parallel untwisted magnetic fields in 2D

Jorge Fuentes-Fernández, C. E. Parnell+1 more|St Andrews Research Repository (St Andrews Research Repository)|Oct 24, 2011

Solar and Space Plasma Dynamics23 references10 citations

TL;DR

This study investigates the non-resistive magnetohydrodynamic (MHD) relaxation of a 2D coronal plasma with finite beta, showing that plasma pressure gradients significantly alter equilibrium states compared to traditional force-free models. Using viscously damped magnetoacoustic waves, the system relaxes to a non force-free magnetohydrostatic equilibrium where magnetic and plasma forces balance, with analytical predictions matching numerical results even far beyond the linear regime.

ABSTRACT

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.

Motivation & Objective

• To investigate the role of finite plasma beta in MHD relaxation of coronal magnetic fields, moving beyond the standard force-free approximation.
• To determine how plasma pressure gradients affect the final equilibrium state during relaxation, particularly when magnetic forces are balanced by plasma pressure and magnetic tension.
• To assess the validity of linear analytical predictions for non-linear relaxation processes in a viscously damped MHD system.
• To examine the thermodynamic evolution of the plasma during relaxation, especially the transfer of energy from plasma to magnetic fields.
• To establish that the final equilibrium state depends only on initial perturbations and total pressure, not on viscosity or the nature of the initial disturbance (density, temperature, or internal energy).

Proposed method

• Numerical simulations using a full 2D MHD code with viscous dissipation to drive relaxation of perturbed magnetic and plasma states.
• Initial perturbations introduced as localized changes in plasma pressure, density, or internal energy, maintaining frozen-in magnetic field conditions.
• Viscous damping of magnetoacoustic waves (fast and slow) acts as the sole dissipation mechanism, enabling relaxation to a final MHD equilibrium.
• Linear analytical solutions derived using adiabatic assumptions and wave propagation along and across field lines to predict final pressure, density, and magnetic field distributions.
• Comparison of analytical predictions (based on conservation of total pressure and adiabatic evolution) with numerical results across varying initial perturbation amplitudes and plasma beta values.
• Use of a 2D Gaussian pressure perturbation to test non-linear regime behavior and quantify deviations from adiabatic predictions, particularly in plasma density.

Experimental results

Research questions

• RQ1 How does including finite plasma beta alter the final equilibrium state of a relaxed coronal magnetic field compared to the force-free assumption?
• RQ2 To what extent do analytical predictions based on linear adiabatic evolution hold in the non-linear regime of MHD relaxation?
• RQ3 What role does viscous dissipation play in determining the final equilibrium, and does it affect the final state or only the relaxation timescale?
• RQ4 How is energy transferred between plasma and magnetic fields during the relaxation process in a finite-beta plasma?
• RQ5 Can the final magnetohydrostatic equilibrium be uniquely determined by initial perturbations and total pressure, independent of the type of initial disturbance?

Key findings

• The final equilibrium is a non force-free magnetohydrostatic state where plasma pressure gradients balance magnetic Lorentz forces, with no residual magnetic tension.
• Analytical predictions based on adiabatic evolution and total pressure conservation match numerical results remarkably well, even for large initial perturbations far outside the linear regime.
• The final plasma density and pressure distributions depend only on the initial perturbation and total pressure, not on the nature of the initial disturbance (density, temperature, or internal energy change).
• Viscosity affects only the relaxation timescale, not the final equilibrium state, as long as viscous damping is sufficient to dissipate waves.
• Non-ideal effects grow slowly relative to initial perturbations, so linear predictions remain valid even in strongly non-linear regimes.
• A non-negligible amount of energy is transferred from plasma to magnetic fields during relaxation, indicating significant thermodynamic coupling in coronal environments, especially near magnetic null points.