Robust feedback control of collisional plasma dynamics in presence of uncertainties

TL;DR

This paper develops a robust feedback control method for collisional plasma in magnetic fusion devices, effectively managing uncertainties to improve confinement and stability using a Vlasov-Poisson-BGK model.

Contribution

It introduces a novel control strategy that is independent of uncertain parameters, enhancing plasma confinement robustness in complex fusion environments.

Findings

Control strategy successfully confines plasma despite uncertainties.

Numerical simulations demonstrate improved stability and confinement.

Method is applicable to realistic fusion device conditions.

Abstract

Magnetic fusion aims to confine high-temperature plasma within a device, enabling the fusion of deuterium and tritium nuclei to release energy. Due to the very large temperatures involved, it is essential to isolate the plasma from the device walls to prevent structural damage and the external magnetic fields play a fundamental role in achieving this confinement. In realistic settings, the physical mechanisms governing plasma behavior are highly complex, involving numerous uncertain parameters and intricate particle interactions, such as collisions, that significantly affect both confinement efficiency and overall stability. In this work, we address particularly these challenges by proposing a robust feedback control strategy designed to steer the plasma towards a desired spatial region, despite the presence of uncertainties. From a modeling perspective, we consider a collisional plasma described by a Vlasov-Poisson-BGK system, which accounts for a self-consistent electric field and a strong external magnetic field, while incorporating uncertainty in the model. A key feature of the proposed control strategy is its independence from the random parameter, making it particularly suitable for practical applications. A series of numerical simulations confirms the effectiveness of our approach and demonstrates the ability of external magnetic fields to successfully confine plasma away from the device boundaries, even in the presence of uncertain conditions.