A principal pressure limit in tokamaks is set by the onset of neoclassical tearing modes (NTMs), which are destabilized and maintained by helical perturbations to the pressure-gradient driven “bootstrap” current. The resulting magnetic islands break up the magnetic surfaces that confine the plasma. The NTM is linearly stable but nonlinearly unstable, and generally requires a “seed” to destabilize a metastable state. In the past decade, NTM physics has been studied and its effects identified as performance degrading in many tokamaks. The validation of NTM physics, suppressing the NTMs, and/or avoiding them altogether are areas of active study and considerable progress. Recent joint experiments give new insight into the underlying physics, seeding, and threshold scaling of NTMs. The physics scales toward increased NTM susceptibility in ITER, underlying the importance of both further study and development of control strategies. These strategies include regulation of “sawteeth” to reduce seeding, using static...

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Neoclassical Tearing Modes and Their Control

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. This manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches.

Routine reaction to approaching disruptions in tokamaks is currently largely limited to machine protection by mitigating an ongoing disruption, which remains a basic requirement for ITER and DEMO [1]. Nevertheless, a mitigated disruption still generates stress to device. Additionally, in future fusion devices, high-performance discharge time itself will be very valuable. Instead of reacting only on generic features, occurring shortly before the disruption, the ultimate goal is to actively avoid approaching disruptions at an early stage, sustain the discharges whenever possible and restrict mitigated disruptions to major failures. Knowledge of the most relevant root causes and the corresponding chain of events leading to disruption, the disruption path, is a prerequisite. For each disruption path, physics-based sensors and adequate actuators must be defined and their limitations considered. Early reaction facilitates the efficiency of the actuators and enhances the probability of a full recovery. Thus, sensors that detect potential disruptions in time are to be identified. Once the entrance into a disruption path is detected, we propose a hierarchy of actions consisting of (I) recovery of the discharge to full performance or at least continuation with a less disruption-prone backup scenario, (II) complete avoidance of the disruption to sustain the discharge or at least delay it for a controlled termination and, (III), only as last resort, a disruption mitigation. Based on the understanding of disruption paths, a hierarchical and path-specific handling strategy must be developed. Such schemes, testable in present devices, could serve as guideline for ITER and DEMO operation. For some disruption paths, experiments have been performed at ASDEX Upgrade and TCV. Disruptions were provoked in TCV by impurity injection into ELMy H-mode discharges and in ASDEX Upgrade by forcing a density limit in H-mode discharges. The new approach proposed in this paper is discussed for these cases. For the H-mode density limit sensors used so far react too late. Thus a plasma-state boundary is proposed, that can serve as an adequate early sensor for avoiding density limit disruptions in H-modes and for recovery to full performance.

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Path-oriented early reaction to approaching disruptions in ASDEX Upgrade and TCV in view of the future needs for ITER and DEMO

The successful performance of a model predictive profile controller is demonstrated in simulations and experiments on the TCV tokamak, employing a profile controller test environment. Stable high-performance tokamak operation in hybrid and advanced plasma scenarios requires control over the safety factor profile (q-profile) and kinetic plasma parameters such as the plasma beta. This demands to establish reliable profile control routines in presently operational tokamaks. We present a model predictive profile controller that controls the q-profile and plasma beta using power requests to two clusters of gyrotrons and the plasma current request. The performance of the controller is analyzed in both simulation and TCV L-mode discharges where successful tracking of the estimated inverse q-profile as well as plasma beta is demonstrated under uncertain plasma conditions and the presence of disturbances. The controller exploits the knowledge of the time-varying actuator limits in the actuator input calculation itself such that fast transitions between targets are achieved without overshoot. A software environment is employed to prepare and test this and three other profile controllers in parallel in simulations and experiments on TCV. This set of tools includes the rapid plasma transport simulator RAPTOR and various algorithms to reconstruct the plasma equilibrium and plasma profiles by merging the available measurements with model-based predictions. In this work the estimated q-profile is merely based on RAPTOR model predictions due to the absence of internal current density measurements in TCV. These results encourage to further exploit model predictive profile control in experiments on TCV and other (future) tokamaks.

https://iopscience.iop.org/article/10.1088/1741-4326/aa8c48/pdf

Profile control simulations and experiments on TCV: a controller test environment and results using a model-based predictive controller

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear and computationally intensive and can be difficult to interpret, while often only approximating the true dynamics. In this work, data-driven techniques recently developed in the field of fluid dynamics are leveraged to develop interpretable reduced-order models of plasmas that strike a balance between accuracy and efficiency. In particular, dynamic mode decomposition (DMD) is used to extract spatio-temporal magnetic coherent structures from the experimental and simulation datasets of the helicity injected torus with steady inductive (HIT-SI) experiment. Three-dimensional magnetic surface probes from the HIT-SI experiment are analyzed, along with companion simulations with synthetic internal magnetic probes. A number of leading variants of the DMD algorithm are compared, including the sparsity-promoting and optimized DMD. Optimized DMD results in the highest overall prediction accuracy, while sparsity-promoting DMD yields physically interpretable models that avoid overfitting. These DMD algorithms uncover several coherent magnetic modes that provide new physical insights into the inner plasma structure. These modes were subsequently used to discover a previously unobserved three-dimensional structure in the simulation, rotating at the second injector harmonic. Finally, using data from probes at experimentally accessible locations, DMD identifies a resistive kink mode, a ubiquitous instability seen in magnetized plasmas.

Characterizing Magnetized Plasmas with Dynamic Mode Decomposition

The biorthogonal decomposition analysis of signals from an array of Mirnov coils is able to provide the spatial structure and the temporal evolution of magnetohydrodynamic (MHD) instabilities in a tokamak. Such analysis can be adapted to a data acquisition and elaboration system suitable for fast real time applications such as instability detection and disruption precursory markers computation. This paper deals with the description of this technique as applied to the Frascati Tokamak Upgrade (FTU).

http://iopscience.iop.org/article/10.1088/0741-3335/56/11/114012/pdf

Development of real-time MHD markers based on biorthogonal decomposition of signals from Mirnov coils

Experiments on real time control of magneto-hydrodynamic (MHD) instabilities using injection of electron cyclotron waves (ECW) are being performed with a control system based on only three real time key items: an equilibrium estimator based on a statistical regression, a MHD instability marker (SVDH) using a three-dimensional array of pick-up coils and a fast ECW launcher able to poloidally steer the EC absorption volume with dρ/dt = 0.1/30 ms maximum radial speed. The MHD instability, usually a tearing mode with poloidal mode number m and toroidal mode number n such that m/n = 2/1 or 3/2 is deliberately induced either by neon gas injection or by a density ramp hitting the density limit. No diagnostics providing the radial localization of the instabilities have been used. The sensitivity of the used MHD marker allows to close the control loop solely on the effect of the actuator's action with little elaboration. The nature of the instability triggering mechanism in these plasma prevents that the stabilization lasts longer than the ECW pulse. However when the ECW power is switched on, the instability amplitude shows a marked sensitivity to the position of the absorption volume with an increase or decrease of its growth rate. Moreover the suppression of the dominant mode by ECRH performed at high plasma density even at relatively low power level facilitates the development of a secondary mode. This minimized set of control tools aim to explore some of the difficulties which can be expected in a fusion reactor where reduced diagnostic capabilities and reduced actuator flexibility can be expected. © 2015 EURATOM.

Experiments on magneto-hydrodynamics instabilities with ECH/ECCD in FTU using a minimal real-time control system

Various active control strategies of the Neoclassical tearing modes are being studied in present tokamaks using established detection techniques which exploit the measurements of the fluctuations of the magnetic field and of the electron temperature. The extrapolation of such techniques to the fusion reactor scale is made problematic by the neutron fluence and by the physics conditions related to the high plasma temperature and density which degrade the spatial resolution of such measurements.

M. Mosconi

Papers

Development of real-time MHD markers based on biorthogonal decomposition of signals from Mirnov coils

Experiments on magneto-hydrodynamics instabilities with ECH/ECCD in FTU using a minimal real-time control system

Towards the detection of magnetohydrodynamics instabilities in a fusion reactor