Optimal confinement of collisionless plasmas by localized time-varying electric fields†

Abstract

The problem of optimal confinement of collisionless plasmas by means of external amplitude-limited time-varying electric fields localized to an outer layer enclosing the confinement region (a specified closed bounded spatial domain) is considered. To confine the plasma, the external electric field (control) establishes a finite potential barrier for the escaping particles. The field direction for confinement depends on the sign of the electrical charge of the escaping particles inside the layer. The paper begins with a formal development of the plasma equations. Then, the existence and uniqueness of solutions of these equations are established. This is followed by the formulation of the optimal confinement problem along with a discussion of the existence of an optimal electric field (control). By introducing additional assumptions to simplify the problem, sub optimal feedback controls are obtained. Finally, the effectiveness of the derived feedback controls is determined numerically using a computer-simulated plasma.

Notes

†This work was supported in part by a U.K. National Research Council Senior Post-Doctoral Fellowship at the Control Theory Centre, University of Warwick, Coventry during the summer of 1971, and in part by AFOSR Grant No. AFOSR-72-2303.