Nonlinear Magnetohydrodynamics

Alfvén effect Alfvén waves amplitude approximation arcade assumed B₁ B₂ behavior Biskamp boundary conditions configuration consider const convection corresponding current density current profile current sheet cylindrical decay diffusion discussed in section disruption dissipation rate dissipation scale dynamic eddies energy spectrum equilibrium evolution field line finite flow fluid flux tubes global gradient Hence ideal incompressible inertial range instability interaction inverse cascade island linear magnetic field magnetic helicity magnetic reconnection magnetohydrodynamic marginal stability MHD equations Navier-Stokes turbulence nonlinear numerical simulations obtained Ohm's law parameter perturbation photospheric Phys pinch plasma boundary Plasma Physics plasmoid poloidal probability distribution quantities r₁ radius rational surface reconnection reduced MHD region resistive kink mode resonant surface Reynolds number sawtooth collapse separatrix shear small-scale solar solution spatial spectral stability symmetry tearing mode temperature term theory tokamak toroidal two-dimensional vanishes velocity wavenumber X-point