Magnetohydrodynamics Basic MHD

Assume plasma isotropicand nearly homogeneous:Plasma beta ; small beta ; ”large” betaIn magnetized plasmas pressure and temperature can be anisotropicWrite:(train your brain: why 2 in the parallel equation?)Using these we can derive themacroscopic currents fromthe single particle drift motionswhereThe magnetization isSumming up J G , J C and J M we get the total currentMagnetohydrostaticequilibrium in anisotropicplasma is described byIn case of the pressure gradientis negligible and the equilibrium isforce-free field orfield-aligned currentNowa nasty non-linear equation! is constant along BIf is constant in all directions, the equationbecomes linear, the Helmholtz equationA force-free field and thecurrent in the same direction6