Plasma internal inductance dynamics in a tokamak

TL;DR

This paper introduces a novel, exact lumped parameter model for tokamak plasma current and internal inductance dynamics, suitable for control system design, validated with experimental data from JET.

Contribution

The paper presents a new formulation for plasma inductance and current dynamics, expressed in state space form, enabling advanced control system applications in tokamaks.

Findings

Model accurately predicts plasma inductance and current dynamics.

Excellent agreement with JET experimental data.

Facilitates control system design using modern control theory.

Abstract

A lumped parameter model for tokamak plasma current and inductance time evolution as function of plasma resistance, non-inductive current drive sources and boundary voltage or poloidal field (PF) coil current drive is presented. The model includes a novel formulation leading to exact equations for internal inductance and plasma current dynamics. Having in mind its application in a tokamak inductive control system, the model is expressed in state space form, the preferred choice for the design of control systems using modern control systems theory. The choice of system states allow many interesting physical quantities such as plasma current, inductance, magnetic energy, resistive and inductive fluxes etc be made available as output equations. The model is derived from energy conservation theorem, and flux balance theorems, together with a first order approximation for flux diffusion dynamics. The validity of this approximation has been checked using experimental data from JET showing an excellent agreement.