4.4 Feedback Experiments on a High Energy Plasma Contained in the Phoenix II Simple Mirror Machine

Feedback experiments on a high-energy plasma in the Phoenix mirror machine

“…As far as the frequency of the instability is concernedjfor loop gains 6 n < 1 the results of both series are in qualitative agreement with the theory developed in Ref. [21] taking into account the frequency response of the feedback loop,but the quantitative agreement is not as good as was found for the case of stable plasmas, due, at least in part, to the fact that a constant plasma density could not be maintained. When the loop gain was increased beyond 6 n ^ 1 the plasma suddenly changed to a new state in the wideband case; its density increased and the oscillations changed in frequency and mode.…”

“…This compares favourably with the predicted value of 6. 5 X 10 8 cm" 3 for the line density calculated from the results of electron drift wave experiments reported elsewhere [23].…”

“…The interest in feedback experiments with unstable plasmas is in its effects on plasma losses, normally caused by the flute instability. Experiments with stable plasmas [21] have shown that, though complete stability cannot be achieved with this feedback scheme in the linear regime, the frequency of the instability is a function of the feedback parameters as is the predicted growth rate. Non-linear effects limit the amplitude of the stability and plasma loss rate and the reported experiments concern themselves with these aspects.…”

Feedback Suppression of a Large-Growth-Rate Flute Mode

“…Most modes that have succumbed to external stabilization have been characterized by small growth rates, 1 " 3 including the flute mode of Ref. 3. This paper reports negative-feedback suppression of a grossly unstable magnetohydrodynamic (MHD) mode for which the growth time to nonlinear saturation is about a single perturbation period.…”

“…For resonant modes the relevant ion motion is determined by introducing the usual guidingcenter coordinates 3 and averaging the equations of motion over a cyclotron period. For a particle with phase-space coordinates (r, v) the substitutions r = R + p, v= V+3 are made where R and V are assumed slowly varying in a cyclotron period and p^ <J are coordinates perpendicular to the local B field, which account for the mod- Q is the ion-cyclotron frequency at R; and /i is the magnetic moment, ^mw 2 /B.…”