PAPER Related content - Central safety factor and N control on Modeling and control of plasma rotation for NSTX NSTX-U via beam power and plasma boundary shape modification, using TRANSP for closed loop simulations using neoclassical toroidal viscosity and neutral M.D. Boyer, R. Andre, D.A. Gates et al. beam injection - Topical Review M S Chu and M Okabayashi To cite this article: I.R. Goumiri et al 2016 Nucl. Fusion 56 036023 - Rotation and momentum transport in tokamaks and helical systems K. Ida and J.E. Rice View the article online for updates and enhancements. Recent citations - Design and simulation of the snowflake divertor control for NSTX–U P J Vail et al - Real-time capable modeling of neutral beam injection on NSTX-U using neural networks M.D. Boyer et al - Resistive wall mode physics and control challenges in JT-60SA high scenarios L. Pigatto et al This content was downloaded from IP address 128.112.165.144 on 09/09/2019 at 19:26 IOP Nuclear Fusion International Atomic Energy Agency Nuclear Fusion Nucl. Fusion Nucl. Fusion 56 (2016) 036023 (14pp) doi:10.1088/0029-5515/56/3/036023 56 Modeling and control of plasma rotation for 2016 NSTX using neoclassical toroidal viscosity © 2016 IAEA, Vienna and neutral beam injection NUFUAU I.R. Goumiri1, C.W. Rowley1, S.A. Sabbagh2, D.A. Gates3, S.P. Gerhardt3, M.D. Boyer3, R. Andre3, E. Kolemen3 and K. Taira4 036023 1 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA I.R. Goumiri et al 2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA 3 Princeton Plasma Physics Laboratory, Princeton, NJ 08544, USA Modeling and control of plasma rotation using NTV and NBI 4 Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Printed in the UK E-mail: [email protected] Received 29 September 2015, revised 22 December 2015 NF Accepted for publication 26 January 2016 Published 19 February 2016 10.1088/0029-5515/56/3/036023 Abstract A model-based feedback system is presented to control plasma rotation in a magnetically confined toroidal fusion device, to maintain plasma stability for long-pulse operation. This Paper research uses experimental measurements from the National Spherical Torus Experiment (NSTX) and is aimed at controlling plasma rotation using two different types of actuation: momentum from injected neutral beams and neoclassical toroidal viscosity generated by three- 0029-5515 dimensional applied magnetic fields. Based on the data-driven model obtained, a feedback controller is designed, and predictive simulations using the TRANSP plasma transport code show that the controller is able to attain desired plasma rotation profiles given practical 3 constraints on the actuators and the available measurements of rotation. Keywords: magnetic confinement, feedback control, rotation Control, neutral beam injection, neoclassical toroidal viscosity, NSTX (Some figures may appear in colour only in the online journal) 1. Introduction a model-based approach to controlling the rotation profile in spherical tokamaks, and to apply the approach to a predictive Spherical tokamaks such as the National Spherical Torus model based on experimental data from NSTX. Experiment (NSTX [1]) are toroidal magnetic fusion devices The effect of the rotation profile on MHD instabilities has that have been proven experimentally to realize theoretical been well studied in recent years. For instance, greater stability expectations of efficient and compact advanced tokamak of tearing modes has been associated with increased rotation operation, producing high plasma pressures in relation to shear [2, 3], while rotation profile shapes that lead to stronger the pressure of the magnetic field used to create the plasma kinetic resonances lead to stabilization of kink/ballooning equilibrium. In certain circumstances, these high pressures modes and resistive wall modes [4, 5]. Furthermore, rotational can cause rapidly growing magnetohydrodynamic (MHD) shear can affect plasma turbulence and consequently can have plasma instabilities that can lead to undesirable effects such as an impact on transport processes and the energy confinement reducing the plasma pressure, or even terminating the plasma performance of tokamak plasmas [6–8]. In present-day pulsed (disruption). Many of these instabilities are sensitive to the tokamaks, plasma rotation can evolve, through normal heat shear, so the rotation profile plays a key role in regulating and momentum transport processes, toward profiles for which these instabilities. The goal of the present study is to describe certain MHD modes are unstable. Even if these profiles evolve 0029-5515/16/036023+14$33.00 1 © 2016 IAEA, Vienna Printed in the UK Nucl. Fusion 56 (2016) 036023 I.R. Goumiri et al by chance to a steady-state profile that is stable, transient Once the model is satisfactorily developed, a further step processes including edge-localized modes (ELMs), internal consists of applying a spectral decomposition method, line- transport barriers, and different heating mechanisms can alter arizing the equation about an equilibrium and projecting onto plasma profiles further and make them less stable, or unstable a subspace spanned by Bessel functions, in order to obtain an [9]. In future large fusion-power-producing tokamak opera- approximate linear model consisting of just 5 ordinary differ- tion (e.g. the fusion nuclear science facility, FNSF [10–12]), ential equations. The resulting reduced model is then used to disruptions caused by macroscopic instabilities can generate design a controller using standard techniques from optimal electromagnetic forces and heat loads large enough to damage control. The advantage of using a reduced-order model is that device components, so it is particularly important to avoid the resulting controller is also low dimensional, so that it is such disruptions, for instance through control of the rotation computable in real time, as well as being easier to tune and profile. design. There is an abundant literature on plasma control such as The paper is organized as follows. Section 2 describes the kinetic profile control (density and temperature) [13, 14], data-driven model definition with details about the actuators burn control [13–2, 15, 17–19], toroidal current profile con- used, model reduction process and comparison to exper- trol [20–24], safety factor profile control [25–27], direct imental data. Section 3 describes the optimal control method control of tearing modes [28, 29] and resistive wall modes used to track a desired rotation profile, using both NTV and [9, 30]. Rotation control in tokamaks has been demonstrated NBI as actuators, and its implementation through numerical using momentum input from injected neutral beams (NBI) simulation. Section 4 presents the results of the designed con- as an actuator [31, 32]. A new and unique aspect of the troller on a more complete rotation model that can be found present work is the use of non-axisymmetric (three-dimen- in TRANSP, a time dependent code developed at Princeton sional) magnetic fields as another actuator in closed-loop Plasma Physics Laboratory for both prediction and analysis of feedback control to supplement the neutral beam actuator. tokamak experimental data [39, 40]. Conclusions and future Rotation alteration by non-resonant, three-dimensional work are discussed in section 5. magnetic fields allows more precise, continuous control of the plasma rotation alteration than NBI, as the momentum 2. A simplified model of the toroidal momentum delivered by the latter occurs in significantly large, discrete balance increments. The physical process creating the force on the plasma rota- 2.1. Model definition tion generated by the applied three-dimensional field, termed neoclassical toroidal viscosity (NTV) [33–35], has been used Consider the transport of toroidal angular plasma momentum successfully to affect plasma rotation in a pre-programmed in a tokamak with the assumption of axisymmetry. To facili- manner on NSTX over a wide range of plasma operation, with tate the analysis, an arbitrary flux surface averageρ ∈ []0, 1 is quantitative agreement of the experimentally generated torque used, where ρ = 0 and 1 denote the center and the boundary to theory [36]. NTV is caused by non-ambipolar diffusion of of the plasma, respectively. plasma ions and electrons caused by the magnetic field comp- Using the work of Goldston [41] and Callen [42], the onents that break the usual toroidal symmetry of tokamak angular velocity of the plasma ω can be described dynami- confinement field. As NTV depends on several important cally by the flux surface average ⋅ of the toroidal momentum plasma parameters including temperature, and the plasma equation rotation itself, its use in closed-loop feedback leads to weak 2 22∂ω ∂ni ∂ R nonlinearities which must be investigated to ensure successful ∑∑nmiiR + ωωRmi + ∑ nmii control. Details of such elements will be shown throughout i ∂t i ∂t i ∂t this work. −1 2 ⎛∂V ⎞ ∂ ∂V The present work defines a model-based algorithm for + ∑ nmiiR ω⎜ ⎟ i ⎝ ∂ρρ⎠ ∂t ∂ plasma rotation control based on experimental data from −1 ⎡ ⎤ NSTX [1], that measures the rotational (toroidal) momentum ⎛∂VV⎞ ∂ ∂ 22∂ω = ⎜ ⎟ ⎢ ∑ nmiiχρφ R ()∇ ⎥ transport in the tokamak. More details about how to measure ⎝ ∂ρρ⎠ ∂ ⎣ ∂ρ i ∂ρ ⎦ rotation profile in real-time can be found in [36, 37]. Data- −1 ⎡ ⎤ ⎛∂VV⎞ ∂ ∂ 22vρ driven modeling techniques have been successfully used