State Diagrams of Tokamaks and State Transitions

In a simple one-fluid cylindrical model of the transport and of the dissipative effects, the family of the magnetic states of the tokamak which correspond to a vanishing entropy production in the confinement region (according to the configurational magnetic entropy introduced in previous work) are characterised by a definite relation or "state equation" involving the relevant parameters of the discharge. We investigate how the entropy production is changing when the current density profile is rearranged by a perturbation which conserves the poloidal magnetic flux. It is shown that, for a sufficiently short time interval, that is to say t2 << τEτs where τE is the energy confinement time and τs is the resistive time, neighbouring bifurcating equilibria exist which can be reached with a flux conserving transition and with increase of the magnetic entropy. The family of these new states can also be characterised by a state equation involving the relevant discharge parameters. When the state equations of the two families are simultaneously satisfied by the same set of parameter values, a flux conserving, entropy increasing transition may take place between states of the two families. We investigate the modifications of the current density and of the temperature profiles involved in the transition and the conditions that the discharge parameters should satisfy in order that the transition could occur.