Numerical MHD Simulation of the Coupled Evolution of Plasma and Magnetic Field in the Solar Chromosphere. I. Gradual and Impulsive Energisation

The dynamical coupling between solar chromospheric plasma and the magnetic field is investigated by numerically solving a fully self-consistent, two-dimensional initial-value problem for the nonlinear collisional MHD equations including electric resistivity, thermal conduction, and, in some cases, gas-dynamic viscosity. The processes in the contact zone between two horizontal magnetic fields of opposite polarities are considered. The plasma is assumed to be initially motionless and to have a temperature of 50,000 K uniform throughout the plasma volume; the characteristic magnetic field corresponds to a plasma β ≳ 1 . In a physical time interval of 17 seconds typically covered by a computational run, the plasma temperature gradually increases by a factor of two to three. Against this background, an impulsive (in 0.1 seconds or less) increase in the current-aligned plasma velocity occurs at the site of the current-layer thinning (sausage-type deformation, or m = 0 pinch instability). This velocity burst can be interpreted physically as an event of suprathermal-proton generation. Further development of the sausage instability results in an increase in the kinetic temperature of the protons to high values, even to those observed in flares. The form of our system of MHD equations indicates that this kind of increase is a property of the exact solution of the system for an appropriate choice of parameters. Magnetic reconnection does not manifest itself in this solution: it would generate flows forbidden by the chosen geometry. Therefore, the pinch-sausage effect can act as an energiser of the upper chromosphere and be an alternative to the magnetic-reconnection process as the producer of flares.