Toroidal current profile control during low confinement mode plasma discharges in DIII-D via first-principles-driven model-based robust control synthesis

Abstract

In order for ITER to be capable of operating in advanced tokamak operating regimes, characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability and a non-inductively driven plasma current, for extended periods of time, several challenging plasma control problems still need to be solved. Setting up a suitable toroidal current density profile in the tokamak is key for one possible advanced operating scenario characterized by non-inductive sustainment of the plasma current. At the DIII-D tokamak, the goal is to create the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintain this target profile for the remainder of the discharge. The evolution in time of the toroidal current profile in tokamaks is related to the evolution of the poloidal magnetic flux profile, which is modelled in normalized cylindrical coordinates using a first-principles, nonlinear, dynamic partial differential equation (PDE) referred to as the magnetic diffusion equation. The magnetic diffusion equation is combined with empirical correlations developed from physical observations and experimental data from DIII-D for the electron temperature, the plasma resistivity and the non-inductive current drive to develop a simplified, control-oriented, nonlinear, dynamic PDE model of the poloidal flux profile evolution valid for low confinement mode discharges. In this work, we synthesize a robust feedback controller to reject disturbances and track a desired reference trajectory of the poloidal magnetic flux gradient profile by employing the control-oriented model of the system. A singular value decomposition of the static gain matrix of the plant model is utilized to identify the most relevant control channels and is combined with the dynamic response of system around a given operating trajectory to design the feedback controller. A general framework for real-time feedforward + feedback control of magnetic and kinetic plasma profiles was implemented in the DIII-D Plasma Control System and was used to demonstrate the ability of the feedback controller to control the toroidal current profile evolution in the DIII-D tokamak. These experiments constitute the first time ever a first-principles-driven, model-based, closed-loop magnetic profile controller was successfully implemented and tested in a tokamak device.

Control-oriented modeling of the plasma particle density in tokamaks and application to real-time density profile reconstruction

“…with the radial particle flux Γ given by (3) and the net electron source S given by (4). First, we approximate the electron density by By substituting the electron density parameterization (A.2) in (A.1), (3) and (4), the electron density continuity is written as…”

“…ASTRA [30], CRONOS [43]) are not directly suitable for the task of real-time density reconstruction, since their execution time generally exceeds the discharge duration. It has been shown in [2][3][4][5]39,40] that low-complexity 1D models can be used for reconstruction and control of the temperature and safety factor profiles.…”

“…Plasma control has expanded in recent years from control of bulk plasma quantities (such as total plasma current, average particle density and average temperature) to control of the spatial distributions of these quantities, e.g. the profiles of temperature, safety factor and rotation [2][3][4][5][6].…”

Robust control of the safety factor profile and stored energy evolutions in high performance burning plasma scenarios in the ITER tokamak

“…The volumeaveraged plasma stored energy is related to these kinetic profiles and can be controlled to regulate the fusion power. Recent experiments at DIII-D [4]- [6] represent the first successful demonstration of first-principles-driven (FPD), model-based, closed-loop control of the entire q-profile in a tokamak, where the control strategy employed was a feedforward + feedback scheme. Other advances towards designing FPD controllers to control the plasma magnetic profile are discussed in [7]- [9].…”

“…In the DIII-D experiments, the closedloop control was chosen to be performed in low confinement (L-mode) [1] scenarios due to the reduced complexity of the plasma dynamics in this regime. In this work, we extend the control strategy employed in [4]- [6] to control the q-profile and stored energy in high performance, high confinement (Hmode) [1] burning plasma, i.e., one with a significant number of fusion reactions occurring, regimes in ITER. A profile control algorithm based on real-time estimation of linearized plasma profile response models for ITER is discussed in [10].…”