Stability conditions of feedback control system of vertical plasma position in tokamaks with a resistive shell

Abstract

Stability conditions of axisymmetric instabilities in tokamaks with a resistive shell and an active feedback control system are examined analytically, assuming a ring-shaped plasma. Using equations of plasma motion and equivalent circuits, the basic properties of the feedback control system are discussed. Above a critical n-index, the fast-growing mode is stabilized; the slow-growing mode is stabilized when the feedback loop gain is larger than the critical value, which is proportional to the n-index. The dependence of the stability condition on the positions and time constants of the shell and the control windings is discussed.

Stability limit of feedback control of vertical plasma position in the JFT-2M tokamak

“…7. If power supply is used in the AMP mode, the voltage of the control coil (5 V c ) is given by: 8 V = g G ( s ) A ^r c f - (7) where Ai// re f, g, and G(s) are a reference signal of the vertical position control, a transfer function of the P controller of the minor loop, and the transfer function of the PD circuit, respectively. Ai///I p Z p represents the sensitivity of Z p detection.…”

“…The real parts of all eigenvalues of this system (Eqs (4), ( 5), (7), and (8)) must be negative for stability to occur. These eigenvalues and the full stability conditions can be obtained from numerical calculations.…”

“…One of the necessary conditions, which is not a sufficient one and is equivalent to the condition derived in Ref. [7] for a more simple configuration of the vacuum vessel, is obtained analytically as follows: where r c is the resistance of the feedback coils and the power supply. These conditions imply that the open loop gain of the position control at s = 0 must be larger than unity.…”

“…If the passive shell current is approximated by a single passive coil element in the analysis such as in Ref. [7], the maximum £ is given by £ £s max r c + r s V 3…”

“…The limits of feedback stabilization were studied in several small tokamaks [7,9]. Power for the feedback control was supplied by transistor circuits in these experiments; so, the response time of the whole system could be about 100 /is.…”