On the Solvability of Magnetic Differential Equations

Details On the Solvability of Magnetic Differential Equations On the Solvability of Magnetic Differential Equations

2005-10-14

arxiv.org/abs/physics/0510140v1

Physics

Plasma Physics

11 pages, submitted for publication in: SIAM Journal for Applied Mathematics

Scientific paper

The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type $\vec {B}\cdot \nabla \Phi =s$. We apply the necessary and sufficient criterion for the existence of the potential $\Phi$ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry.

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