Minimum dissipative processes in astrophysics

An alternative theory of relaxation, based on the principle of minimum dissipation rate (MDR) of energy is proposed. This principle is closely related to a well-known theorem of irreversible thermodynamics, viz. the principle of minimum entropy production rate. We perform self-consistent, time-dependent numerical simulations of a slightly dissipative turbulent plasmas at a high Lundquist number, using fully 3-D compressible MHD code with high numerical resolution. The time variation of global helicity, magnetic energy, and the dissipation rate are plotted. Is is seen that the global helicity remains approximately constant while magnetic energy decays faster and the dissipation rate decays even faster than the magnetic energy. This establishes that the principle of minimum dissipation rate under the constraint of (approximate) conservation of global helicity is a viable approach for plasma relaxation. Relaxation of a magnetized plasma based on MDR yields a magnetic field which can support a finite pressure gradient. Applications of such model in predicting arcade structures in solar coronal magnetic fields are discussed.