On the bifurcation and non-uniqueness of MHD-equilibrium and tokamak transport

The mathematical models describing relevant problems in plasma physics, especially those of controlled nuclear fusion research, are generally nonlinear ones. The sensitivity of nonlinear differencial equations to the boundary conditions often leads to mathematically underdefinite problems, thus to the non-existence and/or non-uniqueness of the solutions. Such bifurcations of solutions are demonstrated and investigated in two analytically tractable cases: the magnetohydrodynamical equilibrium in an Astron configuration and the heat transport in tokamak systems. The features of non-uniqueness of the solutions are characterized and a practical procedure is proposed to unfold it. (D.Gy.)