Exact global plasma equilibria

Exact global axisymmetric and helically symmetric plasma equilibria are derived. These two families of exact solutions of the plasma equilibrium equations are not translation-invariant, depend on arbitrarily many parameters, and contain special $z$-invariant equilibria. All plasma equilibria constructed are smooth and localized in the sense that they have finite magnetic energy in each layer $c_1<z<c_2$. Furthermore, these exact solutions provide counterexamples to Parker's well-known theorem.