Existence of true plasma equilibria in asymmetric magnetic fields

The fundamental theoretical problem of the existence of plasma equilibrium in a nonsymmetric magnetic field with nested magnetic surfaces is resolved. The lack of examples of smooth solutions to the equilibrium equations with no symmetry of the configuration has for many years served as the argument supporting the hypothesis by Harold Grad that nondegenerated three-dimensional plasma equilibrium does not exist. This paper first presents explicit analytical counterexamples to Grad's hypothesis. Within the standard formulation of the plasma equilibrium problem, we obtain the family of smooth solutions to the equilibrium equations. These solutions describe the set of "true" nonsymmetric magnetic surfaces compatible with continuous profiles of plasma pressure and rotational transform. The convenient system of equilibrium equations is used in the form generalizing the Grad-Shafranov approach to the case of nonaxisymmetric magnetic configurations without involving the formalism of flux coordinates. The inapplicability of simple prototype models of slab or cylindrical topologies for the predictive conclusions about the equilibrium of toroidal plasma is also revealed and clearly demonstrated. The developed formalism proves the fallacy of Grad's hypothesis and opens opportunities for adequate modeling of three-dimensional equilibrium plasma configurations.