I am curious about what kind of math is needed for studying plasma physics, especially for the magnetohrodynamics. I know there are lots of PDEs in plasma physics, but how about real analysis? Or topology, groups and rings from algebra? Can you give me some hints?
closed as primarily opinion-based by Qmechanic♦ Dec 11 '18 at 7:09
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MHD modeling is hard because the equations that describe the dynamics of a hot plasma are all coupled: heat transfer, bulk movement, current flow, magnetic field, pressure, temperature, and density are all significant and interactive, which makes the differential equations horribly hard to solve.
To the best of my knowledge, group theory/topology/algebraic theory and other tools of pure mathematics are of limited use here.
I am not an expert in plasma physics, but did study it a bit in graduate school. The relevant equations are extremely complicated; they are nonlinear "integro-differential equations". For an example of the math concepts needed in plasma physics, see this paper.