The Effective Mode Approximation for Analyzing Position Instability of a Tokamak Plasma

The effect of induced currents in the equilibrium field (EF) coils on ameliorating the instability of a small position perturbation of a rigid tokamak plasma is analyzed. A strong analogy between the position instability of the plasma and supercriticality of a fission reactor core is recognized. The position of the plasma corresponds to the neutron population, and the retardation of the displacement by the induced eddy currents to the suppression of population growth by delayed neutrons. The matrix equation of the dispersion relation for the position instability is diagonalized and factored into a form identical to the in-hour equation of fission reactor kinetics. An Effecitve Mode Approximation (EMA) similar to the one group of delayed neutron approximation has been introduced to greatly simplify the analysis of the position instability and feedback control. With this approximation the dispersion relation is reduced to a linear or cubic algebraic equation depending on the effectiveness of retardation by the eddy currents. The time constant of the unstable mode can be expressed in terms of the plasma parameters and the effective resistance and inductance of the current carriers, which can be conveniently computed. The vertical instability of a typical noncircular tokamak plasma is analyzed numerically as well as analytically by the EMA method. The results agree well within a negligible discrepancy.