Dynamic Optimization of Trajectory for Ramp-up Current Profile in Tokamak Plasmas

TL;DR

This paper develops a numerical framework using gradient-based optimization to control the current profile during tokamak plasma ramp-up, integrating PDE constraints and a user-friendly GUI for improved plasma control.

Contribution

It introduces a novel PDE-constrained optimization approach with a MATLAB GUI for optimizing tokamak plasma current profiles during ramp-up.

Findings

Effective control of plasma current profile achieved

Framework verified through numerical simulations

Potential application to broader chemical engineering problems

Abstract

In this paper, we consider an open-loop, finite-time, optimal control problem of attaining a specific desired current profile during the ramp-up phase by finding the best open-loop actuator input trajectories. Average density, total power, and plasma current are used as control actuators to manipulate the profile shape in tokamak plasmas. Based on the control parameterization method, we propose a numerical solution procedure directly to solve the original PDE-constrained optimization problem using gradient-based optimization techniques such as sequential quadratic programming (SQP). This paper is aimed at proposing an effective framework for the solution of PDE-constrained optimization problem in tokamak plasmas. A more user-friendly and efficient graphical user interface (GUI) is designed in MATLAB and the numerical simulation results are verified to demonstrate its applicability. In addition, the proposed framework of combining existing PDE and numerical optimization solvers to solve PDE-constrained optimization problem has the prospective to target challenge advanced control problems arising in more general chemical engineering processes.