Shafranov's virial theorem and magnetic plasma confinement

Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.