Construction of substantially different solutions of inverse problem for toroidal plasma equilibrium equation

The paper is devoted to reconstruction of current density in toroidal plasma using experimentally measured data. The toroidal current density is characterized by two functions in the right hand side of Grad–Shafranov equation, which together with the poloidal flux are to be determined. The question about uniqueness of the solution of the inverse problem was usually not addressed in numerical methods developed over recent decades. However, theoretical study of this question for simplified models showed possibility of existence of substantially different solutions. For correct understanding of physical properties of a pulse it is necessary to analyze all possible solutions of the inverse problem in its physically correct formulation. This formulation is presented in the paper. A new numerical method for determining of all substantially different solutions of the inverse problem is proposed. Examples of existence of such solutions are constructed for close to experimental plasma parameters.