Extremum-Seeking-Based Fluctuation Mitigation and Azimuthal Velocity Profile Regulation by $E\times B$ Actuation in HELCAT

Turbulence and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, destabilizing mechanisms, such as gradients and currents, and stabilizing mechanisms like shear. Active control of fluctuations is investigated in this paper via manipulation of flow profiles in a magnetized laboratory plasma device helicon-cathode (HELCAT). Fluctuations are monitored by electrostatic probes, and E×B flow profiles are controlled via bias ring electrodes. First, a nonmodel-based extremum-seeking optimal control algorithm is implemented in HELCAT to seek the bias ring voltages that minimize a cost function related to the fluctuation amplitude. The experimental results in HELCAT show that the proposed controller is able to not only suppress the fluctuations but also to regulate their average amplitude around a predefined desired level. It is anticipated that this controller can become a valuable tool for physics-oriented studies designed to elucidate the relationship between the shape of the azimuthal flow profile and the amplitude of the fluctuations once the capability of measuring the flow profile in real time becomes available in HELCAT. Second, with the assistance of a HELCAT-tailored transport code capable of predicting the evolution of the azimuthal flow at several radial points within the plasma, the potential of an extremum-seeking controller for directly regulating the azimuthal flow profile around a prescribed target profile is illustrated numerically.