Optimal Control of the Plasma Azimuthal Velocity Profile by Feedback $E\times B$ Actuation in HELCAT

Active control of the flow shear, which is related to the radial derivative of the azimuthal flow, is a key factor in reducing the cross-field turbulence-driven particle transport in a magnetically confined plasma column. Once a desired radial azimuthal velocity profile and its associated level of turbulent fluctuations are identified, the challenge of systematically achieving and sustaining it still remains. In this paper, a model-based feedback controller is proposed to overcome this challenge in helicon-cathode (HELCAT). This linear, dual-source, magnetized-plasma, laboratory device employs concentric ring electrodes to mitigate the turbulent plasma transport by generating a sheared radial electric field and modifying the flow profiles by E×B actuation. A linear-quadratic-integral optimal feedback controller is designed to minimize a weighted combination of the tracking error and the control effort with an ultimate goal of regulating the radial azimuthal velocity profile around a prescribed desired profile even with external disturbances and perturbed initial conditions. Numerical simulations show the effectiveness of the proposed controller in shaping the azimuthal flow profile in HELCAT. The proposed control solution has the potential of being used as a systematic tool for physics-oriented studies in laboratory plasmas such as those achieved in HELCAT.