Numerical demonstration of injection locking of the sawtooth period by means of modulated EC current drive

In this paper the sawtooth period behaviour under periodic forcing by electron cyclotron waves is investigated. The deposition location is kept constant while the gyrotron power is modulated with a certain period and duty cycle. Extensive simulations on a representative dynamic sawtooth model show that when this modulation is properly chosen, the sawtooth period quickly synchronizes to the same period and remains locked at this value. It is shown that the range of modulation periods and duty cycles over which sawtooth period locking occurs, depends on the deposition location, but is particularly large for depositions near the q = 1 surface. The simulation results reveal a novel approach to control the sawtooth period in open loop, based on injection locking, which is a well-known technique to control limit cycles of non-linear dynamic oscillators. The locking and convergence results are therefore used in a simple open-loop locking controller design, with which accurate sawtooth period tracking to any desired value is indeed demonstrated. Injection locking appears to let the sawtooth period converge to the modulation period quickly, partly because it does not suffer from slow EC mirror launcher dynamics. Moreover, simulations show that the method has a relatively large robustness against general uncertainties and disturbances. Hence, injection locking is expected to outperform conventional sawtooth control methods using a variable deposition location and constant gyrotron power. Finally, the recent result with sawtooth pacing is shown to be a special case of the general locking effect.