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Computation of plasma equilibria with semifree and free boundary

Besides the solution of the Grad-Shafranov equation for the fixed and semifree boundary value problem, the solution of the free boundary value problem is of particular interest because it provides the possibility to account for the passive conductors and the driving voltages. These voltages are in general composed of two parts, one with prescribed time dependence and the other used as feedback part. Hence the performance properties of the feedback control of the plasma position and the shape parameters can be assessed. The solution of the semifree boundary value problem can be used for comparison.

Combining the approach of Shafranov concerning the time evolution of equilibria with the circuit equations, the transport equations for the particle and energy inventory and the equilibrium constraint, the time evolution and the discharge can be tracked during the current rise and the flat top phase. The solution indicates that the numerical procedure for the proportional control of the plasma position and shape parameters should be supplemented by terms describing the respective differential or integral control. In this way the accuracy can be improved, the oscillations may be damped and the optimum control achieved.

Reported by

Kernforchungsanlage Juelich GmbH
52428 Juelich
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