2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104009The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type $\vec {B}\cdot \nabla Φ=s$. We apply the necessary and sufficient criterion for the existence of the potential $Φ$ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry.11 pages, submitted for publication in: SIAM Journal for Applied MathematicsPlasma PhysicsClassical Physicstext