Force-free Plasma Equilibria and Differential Operators Connecting Certain Equations
Differential operators connecting a linear case of the Grad--Shafranov equation and the axisymmetric Klein--Gordon equation are found. Differential operators linking another linear case of the Grad--Shafranov equation and the axisymmetric Helmholtz equation are also given. Infinite families of exact solutions to the Grad--Shafranov equation of both types and their corresponding force-free plasma equilibria are derived. General constructions of transforms among differential equations are presented.