Optimal control of a Vlasov-Poisson plasma by fixed magnetic field coils

TL;DR

This paper studies the optimal control of a plasma described by the Vlasov-Poisson system using magnetic fields generated by fixed coils, aiming to steer the plasma to a desired state at a final time.

Contribution

It extends previous control models to account for fixed coil-generated magnetic fields, providing a more realistic framework for plasma control applications.

Findings

Formulation of an optimal control problem with fixed coil magnetic fields.

Analysis of the control problem within the superposition of fixed coil fields.

Potential methods for achieving desired plasma distributions at final time.

Abstract

We consider the Vlasov-Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control itself has already been investigated in [arXiv:1708.02464] and [arXiv:1708.02753]. However, in real technical applications it will not be possible to choose the control field in such a general fashion as it will be induced by fixed field coils. In this paper we will use the fundamentals that were established in [arXiv:1708.02464] and [arXiv:1708.02753] to analyze an optimal control problem where the magnetic field is a superposition of the fields that are generated by N fixed magnetic field coils. Thereby, the aim is to control the plasma in such a way that its distribution function matches a desired distribution function at some certain final time T as closely as possible.