Coronal MHD waves excited by perturbations of magnetic field lines propagate upward, carrying with them the energy from the excitation. Under favorable conditions shocks form, and part of the wave energy is converted to plasma heating and motion. We use numerical simulations to accurately follow the shock formation and subsequent energy release. The model includes an adiabatic energy equation for the explicit evaluation of temperature increases and energy fluxes contributed by the shocks. Transverse, plane-polarized excitations are considered; they can be periodic, as in Alfvén wave trains, or pulsed, as might result from nanoflares. The model is tested with a set of validation runs that produce good agreement with theoretical predictions. Our results show that nonlinear waves moving along large magnetic fields with low plasma , with field amplitudes comparable to the background field, develop shocks that form important amounts of plasma heating and that mass outflow may occur. Fast and slow magnetoacoustic shocks are generated, each one making its own contribution. Most of the heating takes place in the low corona, but long-range distributed heating still occurs up to heights of several solar radii. The energy fluxes for the stronger cases are sufficient to compensate for thermal and convective losses, consistent with observations. We conclude that large-amplitude MHD shocks in low-regions could be a viable mechanism for coronal heating and wind acceleration in regions of open magnetic field lines.

a b s t r a c tAn E-CUSP (energy-convective upwind and split pressure) scheme is developed to solve the equations of magnetohydrodynamics. Fifth order WENO reconstructions are employed to calculate the fluxes in order to achieve high order spacial accuracy. A characteristic speed of sound by averaging the fast wave speed and the acoustic speed of sound is suggested to evaluate the Mach number, which will yield robust and accurate solutions. The numerical experiments have demonstrated the accuracy and the capability of the new scheme to capture complex interactions of multiple shocks and vortices.

The formation of stationary striations in an argon plasma due to the development of an instability is studied using the equations for the competing plasma population species. The nonlinear dynamic stability of the system is analyzed using a two-time perturbation procedure. The unstable uniform steady state bifurcates to a new state with a sinusoidal density variation in space leading to the formation of balls of glowing plasma. This is analogous to phenomena of structure formation that appear in chemical reactions and biological processes.

The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.

No abstract