Magnetohydrodynamics Basic MHD

What we will cover today1. Introduction2. Non-member survey3. Former member survey4. Lion survey highlights5. Key takeaways and next steps2

Now we can calculateThus we have foundexchange l and B –(the this term)= 0, becauseas assumedat the startIn ideal MHD two plasma elements that are on a common field line remain ona common field line. In this sense it is safe to consider ”moving” field lines.Another way to express the freezing:The magnetic flux through a closed loopdefined by plasma elements is constant(proof: exercise)The critical assumption was the ideal MHD Ohm’s law. This requires that theExB drift is faster than magnetic drifts (i.e., large scale convection dominates).As the magnetic drifts lead to the separation of electron and ion motions (J),the first correction to Ohm’s law in collisionless plasma is the Hall termso-called Hall MHDIt is a straightforward exercise to show that in Hall MHD the magnetic fieldis frozen-in to the electron motion andWhen two ideal MHD plasmas with different magnetic field orientations flowagainst each other, magnetic reconnection can take place. Magneticreconnection can break the frozen-in condition in an explosive way andlead to rapid particle accelerationWant to know more of reconnection, come to lectureson Space applications of plasma physics, II periodExample of reconnection:a solar flare4

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