Why Nuclear Fusion?

1. FDM PDE FEM Bo Uo Time FL p SM j y x Time z CAREER: Nonlinear Control of Plasmas in Nuclear Fusion Eugenio Schuster Lehigh University, Bethlehem, PA, USA The toroidal& poloidalmagnetic fields combine to produce a helicalmagnetic field Rotation Profile: NBI, I-coil, CER Why Nuclear Fusion? Control Needs Current, (Kinetic), (Rotation) Profile Control Magnetohydrodynamic (MHD) Flow Control • Currently, more than 80% of the energy produced worldwide is derived from burning fossil fuels, driving potentially catastrophic climate changes and polluting the environment. The U.S. Energy Information Administration predicts in its International Energy Outlook 2010 that the total world consumption of marketed energy will increase by 49 percent from 2007 to 2035. The time remaining to develop new energy sources and avoid a chaotic energy shortage, and a period of severe economic hardship worldwide, is growing short. • As fossil fuel depletes and the environmental impact of their use starts to be felt, fusion arises as an economically affordable, environmentally sustainable, and politically acceptable source of energy that can supply the increasing world population with electricity and hydrogen for transportation fuel. For approximately 50 years, researchers around the world have worked toward understanding how to control nuclear fusion. Although controlled fusion is a very challenging technology, a fusion power reactor would offer significant advantages over existing energy sources, including no air pollution or greenhouse gases, no risk of nuclear accident, no generation of material for nuclear weapons, low-level radioactive waste, and a world-wide available, nearly infinite supply of fuel, which would thus eliminate international tensions caused by imbalance in fuel supply. • In 2008 the National Academy of Engineering has identified the generation of energy from fusion as one of the Engineering’s Grand Challenges. An optimal control problem must be solved, where time evolution for three actuators (line-averaged density, total plasma current, total non-inductive power) are sought to match as close as possible a desired current density profile. Average density Parameterization Repetitive simulation of PDE Cost functional checking Parameter modification • Increase fusion reactivity • Increased current, pressure  increased fusion reactions • Stabilize resulting instabilities • Increased current, pressure  more unstable plasma (NTM, RWM, ELM, etc.) • Maintain desired plasma state • Magnetic Control: Current, distances/locations (MHD Equilibrium) • Kinetic Control: Density, temperature, pressure, confinement level (β). • Maintain desired plasma spatial profiles • Current density, temperature, density, pressure, toroidal rotation. • Mitigate effects of uncontrolled events • Instabilities  disruptions, which can ablate wall materials, damage structures from dissipation of magnetic and thermal energy • Loss of actuator  loss of control • Loss of coolant  device damage Time Total Current Overall control combines open-loop [10, 14] + closed- loop [6, 7, 8] optimal controllers: • Open-loop admits highly complex models • Closed-loop needs reduced-ordered models [3] Total Power Navier-Stokes Equation Trajectory in parameter space Finite difference Finite element Spectral/Pseudo Lorentz Force Cooling Blanket  Liquid Lithium (Tritium Breeding + Heat Transfer) Electrically conducting fluid flows under effect of magnetic fields Magnetic Induction Equation POD: proper orthogonal decomposition MOR: model order reduction E. Schuster and M. Ariola, “The Role of Controls in Nuclear Fusion,” Proceedings of the 2006 IEEE Conference on Decision and Control, San Diego, California, December 13-15, 2006. M.L. Walker, E. Schuster, D. Mazon and D. Moreau, “Open and Emerging Control Problems in Tokamak Plasma Control”, Proceedings of the 2008 IEEE Conference on Decision and Control, Cancun, Mexico, December 10-12, 2008. Nonlinear Programming / Extremum Seeking Iterative Learning Control / Minimal Surface Theory Why Controls? CAREER Overall Organization Current, (Kinetic), (Rotation) Profile Control Magnetohydrodynamic (MHD) Flow Control A week magnetic field is imposed Active control is started As more of the fundamental physics problems are solved, the fusion community is moving beyond the realm of physics research toward the production of fusion energy. The best example of this is ITER, a multibillion tokamak whose construction has just started as the result of an unprecedented cooperative effort by governments around the world. With the construction of ITER as the next step in the international fusion roadmap, the engineering aspects of fusion are becoming increasingly important. Tokamaks, which are the major and most promising magnetic confinement approach to fusion being pursued around the world, are high order, distributed parameter, nonlinear systems with a large number of instabilities, so there are many extremely challenging control problems that must be solved before a fusion power system becomes a viable entity. There is consensus in the fusion community that active control will be one of the key enabling technologies. research outcomes Research Education mentoring • Neoclassical Tearing Modes • Dynamic modeling • Code integration • Non-model & model based adaptive control • Resistive Wall Modes • Control structure definition • Robust control • Adaptive control • Graduate • Interdisciplinary team • Courses on nonlinear & distributed control • Course on nuclear energy • Labs in graduate courses • Undergraduate • REU research • Semester research credit • Summer research • Courses on nonlinear and distributed control • Course on nuclear energy t Model Order Reduction (MOR) • Profile Control • Dynamic modeling • Optimal control in ramp-up • Regulation in flat-top • Plasma Flow Control • Electromagnetic control • CFD code development • Extension to electrically-conducting-fluid flows Two Boundary Value Problem (TBVP) research assistance RoboSoccer Lab Upgrade • Bilinear optimal control problem ↔ Picard iteration. • Bilinear system → quasi-linear system where the system matrices depend nonlinearly on the state variable (previous iteration). • Scheme is convergent under certain conditions (Construction of a contraction mapping + Fixed point theorem in Banach space) [5]. • Scheme based on quasilinearization of system dynamics does NOT converge to a solution of the TBVP. Iterative solution of the TBVP is required. • Iterative solution of the Riccati equation is NOT required. • Outreach • SDIS: Fusion (Star Power) • STAR: Controls (RoboSoccer) • Controls Lab: • Local G6-12 teachers • LVAIC Colleges • Local Industries • Others • Curriculum enhancement • Controls Lab upgrade • Project website • Application-driven Theory • Viscosity control of PDE’s • Optimal open/closed-loop PDE control • Structured robust control • Experimental Validation • CFD/Predictive Codes • Lab experiments • Field test: DIII-D, NSTX The laminar flow evolves to a fully developed state. A magnetic field is then imposed, laminarizing the flow and flattening the velocity profile. Active control overcomes MHD effects, increasing mixing and heat transfer, using mechanical and electromagnetic actuation [1, 2, 15, 16]. ITER is the experimental step between today’s machines (focused on plasma physics studies) and tomorrow's fusion power plants. Its mission is to demonstrate the scientific and technological feasibility of fusion energy (burning plasmas). This is a partnership between EU, Japan, Russia, US, India Korea, China. Site: Cadarache, France. Time: ~2008-2018. Cost: ~ $10B. research outcomes technical advice & feedback General Atomics (DIII-D) MIT (ALCATOR C-MOD) Princetion Plasma Physics Laboratory (NSTX) Experimental Facility Development Plasma Flow Control Experiments student feedback internship, industrial exposure, job networking What is Nuclear Fusion? CAREER Research Plan Resistive Wall Modes (RMW’s) Control CAREER Education Plan • The campus-wide plasma physics/fusion educational and research activity at Lehigh University (LU) is being strengthened, through this CAREER plan, by incorporating a currently missing engineering aspect of fusion, and by establishing a close collaboration with researchers in the Department of Physics at LU. • The CAREER plan is playing a prominent role in facilitating the transition for the current Energy Research Center at LU to a new structure focused on non-fossil energy research. • The research plan evolves around the following four central topics, which have been carefully selected to maximize the impact of the research on the domestic and international fusion program: (1) Current and Kinetic Profile Control [6, 7, 8, 9, 10, 14, 17, 18]; (2) Resistive Wall Mode (RWM) Control [11, 12]; (3) Neoclassical Tearing Mode (NTM) Stabilization [4, 13]; (4) Control of Plasma Flows [1, 2, 15, 16]. • The application-driven theoretical research activity developed within this CAREER plan are significantly impacting controls by addressing novel and challenging modeling and control problems such as (1) viscosity control of parabolic partial differential equations [5], (2) implementable closed-loop optimal control of distributed parameter systems [3], (3) robust and adaptive control of systems with structured uncertainties [12]. • The research plan makes emphasis on experimental validation of the control solutions at the most important fusion facilities in the country such as DIII-D (General Atomics) and NSTX (Princeton Plasma Physics Laboratory). The Resistive Wall Mode (RWM) is a form of plasma kink instability driven by pressure whose growth rate is moderated by the influence of a resistive wall. The word “kink” is used to characterize the behavior because it is similar to a garden hose kinking when pressurized. • A direct spin-off of the multidisciplinary proposed research is the education of students at the boundary of plasma/fusion physics, computational techniques, and theoretical and applied controls. This education is enhanced by experimental work at the most important fusion facilities in the U.S. Beyond this natural byproduct of the proposed research, an ambitious education plan is carried out to maximize the impact of the PI’s activity: • The Interdisciplinary Automatic Controls Laboratory is being upgraded. • Two new control senior/graduate courses on Nonlinear Analysis and Control, and Control of Distributed Parameter Systems has been developed. • An engineering senior/graduate course on Nuclear Fusion Energy has been created to complement the plasma physics courses currently taught at LU. • Outreach, with active participation of undergraduate and master students, will be achieved by: • Remote access capability of the Interdisciplinary Automatic Controls Laboratory, which will facilitate the use of this facility by G6-12 teachers, non-PhD granting colleges members of the Lehigh Valley Association of Independent Colleges (LVAIC), and local industries. • Exciting activities in fusion and controls for the “Science Demonstration in Schools” (SDIS)and “Students That Are Ready” (STAR) programs at LU. These programs at LU are designed to encourage underrepresented groups to participate in engineering and science at a young age, and to prepare disadvantaged students for higher education. • Recognizing the important role that diversity plays in the educational experience, underrepresented minority students are part of this endeavor. (extracted from water) (14.1 MeV) In a nuclear fusion reaction, light nuclei are brought together within the range of strong nuclear interactions to fuse in heavier element with energy release due to mass fraction loss. Outside View Wall Interaction Magnetic Feedback (neutron activation of Lithium) 1 gram of DT = 2,400 gallons of oil (3.5 MeV) • Like-charge particles repel one another. • Coulomb barrier → kinetic energy (heating • Reaction probability maximized at 108 degrees • At lower temperatures → plasma • Scattering still much more probable than fusion • Nuclei must be confined for many interaction times • Magnetic confinement (no end losses → torus) Notice the nonaxisymmetric distortion in the figures. Growth rate (): s  ms. Feedback control is possible. Plasma Rotation: Neutral beams provide momentum for rotation Magnetic Feedback: Non-axisymmetric coils generate magnetic fields opposing deformation Dynamic Modeling: How do plasma rotation and non-axisymmetric magnetic fields affect the RWM growth rate? Model-based Control: Can we design robust and adaptive controllers for a predefined range for ? [11, 12]. What is a Tokamak? Current, (Kinetic), (Rotation) Profile Control Neoclassical Tearing Modes (NTM’s) Control References High plasma pressure can cause ideally nested magnetic flux surfaces to tear and reconnect, leading to the formation of magnetic islands. The neoclassical tearing mode (NTM) instability drives the islands to grow to their saturated widths  poor confinement. Magnetic diffusion equation: [1] L. Luo and E. Schuster, “Heat Exchange Enhancement by Extremum Seeking Boundary Feedback Control in 3D Magnetohydrodynamic Channel Flow,” Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, USA, December 15-17, 2010 (journal paper in preparation). [2] L. Luo and E. Schuster, “Mixing Enhancement in 3D MHD Channel Flow by Boundary Electrical Potential Actuation,” Proceedings of the 2010 American Control Conference, Baltimore, Maryland, USA, June 30-July 2, 2010 (journal paper in preparation). [3] C. Xu, L. Luo and E. Schuster, “On Recursive Proper Orthogonal Decomposition Methods and Applications to Distributed Sensing in Cyber-Physical Systems,” Proceedings of the 2010 American Control Conference, Baltimore, Maryland, USA, June 30-July 2, 2010 (journal paper in preparation). [4] W. Wehner and E. Schuster, “Stabilization of Neoclassical Tearing Modes in Fusion Plasmas via Extremum Seeking,” Proceedings of the 3rd IEEE Multi-conference on Systems and Control, Saint Petersburg, Russia, July 8-10, 2009 (journal paper in preparation). [5] C. Xu, Y. Ou, E. Schuster, “Sequential Linear Quadratic Control for Bilinear Parabolic PDEs based on POD Model Reduction,” Automatica, in press. [6] Y. Ou, C. Xu, E. Schuster, T. C. Luce, J. R. Ferron, M. L. Walker and D. A. Humphreys, “Optimal Tracking Control of Current Profile in Tokamaks,” IEEE Transactions on Control Systems Technology, in press. [7] Y. Ou, C. Xu, E. Schuster, T. C. Luce, J. R. Ferron, M. L. Walker and D. A. Humphreys, “Receding-Horizon Optimal Control of the Current Profile Evolution During the Ramp-Up Phase of a Tokamak Discharge ,” Control Engineering Practice, in press. [8] Y. Ou, C. Xu and E. Schuster, “Robust Control Design for the Poloidal Magnetic Flux Profile Evolution in the Presence of Model Uncertainties,” IEEE Trans. on Plasma Science, vol.38, no.3, p.375, 2010. [9] C. Xu, Y. Ou and E. Schuster, “Transport Parameter Estimations of Plasma Transport Dynamics using the Extended Kalman Filter,” IEEE Trans. on Plasma Science, vol.38, no.3, p.359, 2010. [10] C. Xu, J. Dalessio, Y. Ou, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker and D.A. Humphreys, “Ramp-Up Phase Current Profile Control of Tokamak Plasmas via Nonlinear Programming,” IEEE Trans. on Plasma Science, vol.38, no.2, p.163, 2010. [11] J. Dalessio, E. Schuster, D.A. Humphreys, M.L. Walker, Y. In, J-S. Kim, “Model-based Control of the Resistive Wall Mode in DIII-D: A Comparison Study,” Fusion Eng. & Design 84 (2009) p.641. [12] J. Dalessio, E. Schuster, D.A. Humphreys, M.L.Walker, “Model-based Robust Control of Resistive Wall Modes via μ-synthesis,” Fusion Science & Technology, v.55, no.2, p.163, 2009. [13] J. Woodby, E. Schuster, G. Bateman, A. Kritz, “Model for Current Drive Stabilization of NTM’s,” Physics of Plasmas 15, 092504 (2008). [14] Y. Ou, C. Xu, E. Schuster, T.C. Luce, J.R. Ferron, M.L. Walker and D.A. Humphreys, “Design and Simulation of Extremum-Seeking Open-Loop Optimal Control of Plasma Current Profile at the DIII-D Tokamak,” Plasma Physics and Controlled Fusion 50 (2008) 115001. [15] E. Schuster, L. Luo, and M. Krstic, “MHD channel flow control in 2D: Mixing enhancement by boundary feedback,” Automatica 44 (2008) p. 2498. [16] C. Xu, E. Schuster, R. Vazquez, M. Krstic, “Stabilization of Linearized 2D Magnetohydrodynamic Channel Flow by Backstepping Boundary Control,” Systems & Control Letters 57 (2008) p. 805. [17] Y. Ou, E. Schuster, J. Ferron and M.L. Walker, “Equilibrium Reconstruction Improvement via Kalman-Filter-based Vessel Current Estimation at DIII-D,” Fusion Eng. & Design 82 (2007) p.1144. [18] Y. Ou, E. Schuster, T. Luce, J. Ferron, M.L. Walker and D.A. Humphreys, “Towards Model-based Current Profile Control at DIII-D,” Fusion Eng. & Design 82 (2007) p.1153. Tokamak - “toroidal chamber with magnetic coils” island Electron Cyclotron Current Drive (ECCD): A narrow microwave beam is sent into the plasma, replacing the missing current in the island and forcing it to shrink. O-pt injection is stable, X-pt injection is unstable. Positions island and beam unknown. Island width known (highly noisy). Poloidal coils in the donut hole are used to induce an electric current in the highly conducting plasma : poloidal magnetic flux [9, 18] 3/2 NTM Normal flux surfaces (good confinement) Perturbed flux surfaces (leaky confinement) 2/1 NTM RADIO FREQEUNCY HEATING - energy of electromagnetic waves generated by an antenna outside the chamber can be transferred to plasma particles at certain frequency. The electric current produces a poloidal magnetic field and heats the bulk plasma (Ohmic Heating) OHMIC HEATING - the induced current heats the plasma due to the resistance (less than 30 million K) Dynamic Modeling: How does the beam interacts with the island? [4, 13]. NEUTRAL BEAM INJECTION - inject high energy neutral particles into the plasma. The particles are trapped, ionize and transfer energy through repeated collisions. Extremum Seeking is used for optimal beam/island alignment, modulation, synchronization [4]. Toroidal coilsgenerate a toroidal magnetic field