Simulation in Fusion: Foundation and Basic Theory

1. Simulation in Fusion and its Foundation on Basic Theory Don Batchelor Fusion Power Associates Annual Meeting Sept 27-28, 2006 Washington, DC Emphasis on simulation in Fusion research has increased recently – why? Simulation requires a foundation of basic theory – what does this mean? Where are we now? DBB

2. A constellation of recent events has resulted in a re-emphasis on simulation in fusion research • Community recognition of need to revitalize simulation • FESAC Priorities and Balance … (Knoxville, 1999) – “fully integrated capability for predicting…” • 2002 Snowmass summer study – “Fusion Plasma Simulator” • ISOFS committee – “… that a major initiative be undertaken, referred to here as the Fusion Simulation Project (FSP). • FESAC – “FESAC believes that this initiative would bring huge benefits to fusion research and to the fusion energy goal …” • ITER returns • Theory/simulation perceived as US competitive advantage • Cost effective way to play major role in ITER research • Big DOE investment in super-computers – SciDAC • Can these be used to make fusion go faster, get better use of experiments? • Similar needs in other fields – multi-scale mathematics, HPC initiatives Improved simulation capability is a cost effective way to increase the productivity of the worldwide fusion research effort. DBB

3. Simulation directly supports the experiments – scenario development, data interpretation ITER simulations now Tokamak Simulation Code (TSC) Time Dependent Simulation Of Hybrid Discharge in DIII-D and Hybrid in ITER Using GLF23 • What are desirable operating modes? • Can the available heating and control systems produce the desired state? • How should these systems be operated to achieve this state? • Can the effect we want to study be observed with the available diagnostics? DBB

4. Simulation is essential in designing new experimental facilities ITER auxiliary systems, diagnostics now  operation Plasma optimizations using extensive simulations have allowed unprecedented stellarator design improvements – NCSX, QPS • Compact systems with transport and  limits competitive to tokamaks • Stable to neoclassical tearing modes • Reduced current drive requirements for steady state Quasi Poloidal Stellarator (QPS) Naturally developing poloidal shear flowPotential for turbulence suppression Validated simulation is critical to determine what follows ITER DBB

5. Simulation, as well as the whole conceptual framework we use to formulate experiments, rests on a foundation of basic theory • A theory is a collection of concepts and equations relating those concepts. • Solve analytically in limiting cases to yield concepts and qualitative understanding. • Alfven wave, external kink mode, Spitzer resistivity, bootstrap current … • A simulation is a bunch of numbers from solving equations • Can be compared to theory in limiting cases • Can be compared to experiments in cases too complicated for human solution • May confirm theories, bring understanding to experiments, and even predict the future – after extensive validation and verification DBB

6. Simulation, as well as the whole conceptual framework we use to formulate experiments, rests on a foundation of basic theory • A theory is a collection of concepts and equations relating those concepts. • Solve analytically in limiting cases to yield concepts and qualitative understanding. • Alfven wave, external kink mode, Spitzer resistivity, … • A simulation is a bunch of numbers from solving equations • Can be compared to theory in limiting cases • Can be compared to experiments in cases too complicated for human solution • May confirm theories, bring understanding to experiments, and even predict the future – after extensive validation and verification Two things that simulation is not:  A replacement for theory  A replacement for experiment DBB

7. Understanding the basic theory requires simulationUnderstanding the simulation requires basic theory • Approximate, 1D, analytic theory (F.W. Perkins, 1977) • Provided valuable paradigms for mode conversion • Indicated several conversions were possible • Did not give quantitative information for real 2D situations • High-resolution simulations across the full plasma cross section • Includes arbitrary cyclotron harmonics • Very short wavelength structures – limited by computer size and speed, not by theoretical formulation 2D RF simulation gives complete, quantitative picture. Understood by comparison with theory, compared and verified in detail with experiment DBB

8. Simulation in fusion is scientifically challenging There are a number of fundamental issues: • High dimensionality • Basic description of plasma is 7D f(x, v, t) • Extreme range of time scales • wall equilibration/electron cyclotron O(1014) • Extreme range of spatial scales • machine radius/electron gyroradius O(104) • Extreme anisotropy • mean free path in magnetic field parallel/perp O(108) • Many non-linearly coupled phenomena • Sensitivity to geometric details Developing computable formulations dealing with these fundamental issues depends on basic theory DBB

9. We have been able to make progress by separating out the different phenomena and time scales into separate disciplines SLOW MHD INSTABILITY, ISLAND GROWTH CYCLOTRON PERIODce-1 ci-1 MICRO- TURBULENCE ENERGY CONFINEMENT, tE CURRENT DIFFUSION 10-10 10-8 10-6 10-4 10-2 100 102 104 SEC. PARTICLE COLLSIONS, tC ELECTRON TRANSIT, tT GAS EQUILIBRATION WITH VESSEL WALL FAST MHD INSTABILITY,SAWTOOTH CRASH RF Codes: wave-heating and current-drive Gyrokinetics Codes: micro-turbulence Extended MHD Codes: device scale stability Transport Codes: discharge time-scale DBB

10. We have a portfolio of SciDAC and other computational projects addressing the separated phenomena and time scales Center for Extended MHD Modeling Gyrokinetic Particle Simulation Center Nonlicar dynamics of: • Sawteeth • Neoclassical tearing modes • Edge localized modes • Energetic particle modes • Micro-stability • Turbulence and turbulent transport • Long mean-free-path collisional transport Center for Simulation of Wave-Plasma Interactions Edge Simulation Laboratory • Divertor performance • Heat and particle loads • Edge pedestal formation • ELM effects • Plasma/material interactions • Plasma heating • Externally driven current or plasma flow • Wave processes – mode conversion, absorption, reflection • Non-Maxwellian particle distributions DBB

11. Integrated Simulation – even when the time scales are separated they can interact • Unlike climate model components (atmosphere, land-mass, ocean, sea ice) which have a separating boundary, coupled fusion process can occur at the same time, in the same place, in the same chunk of plasma • Our ultimate goal is to couple all of the relevant processes on all relevant time scales –this is unrealistic at this time • We are taking a realistic approach – continued improvement in individual models, incremental coupling of separate phenomena as it makes sense • Made possible by access to super-computers, computer science and mathematics expertise  SciDAC Turbulent transport RF Codes: wave-heating and current-drive Gyrokinetics Codes: micro-turbulence Extended MHD Codes: device scale stability Transport Codes: discharge time-scale RF induced plasma modifications: “quasilinear” time-scale DBB

12. We have begun three pilot projects of restricted scope for Fusion Simulation Project (FSP)  Focused integration initiatives Partnership of OFES and OASCR under the aegis of SciDAC • Center for Simulation of Wave Interactions with MHD (SWIM) • Center for Plasma Edge Simulation (CPES) • Fusion Application for Core-Edge Transport Simulation (FACETS) We have a significant comparative advantage to succeed in such an undertaking • World leading fusion theory and simulation capability • Established, working partnerships with Mathematics and Computer Science • Accessibility to supercomputing resources DBB

13. Center for Edge Plasma Studies – simulation of edge transport barrier formation and pedestal growth using XGC code 5D particle in cell gyrokinetics code Objectives: • Understand how the thin edge plasma exerts such a strong influence on core confinement • Develop methods to protect the hot, core plasma and the plasma facing material components from each other • Full f electrons, ions, and neutrals • Transition closed  open flux surfaces • Collisions and neoclassical effects • Electrostatic turbulence • Realistic magnetic geometry including X point • Neutral ionization particle source DBB

14. Points to come away with • Developing an improved simulation capability is a cost effective way to increase the productivity of the worldwide fusion research effort. • Making the next steps in integrated simulation is a significant scientific challenge and not, as some might say, an exercise in computer programming • There are key issues of basic theory that must be resolved in order to successfully advance in simulation • Building on the base theory program, the SciDAC projects, and other OFES sponsored projects we are making progress on codes and on integration. DBB

15. One more Point to come away with • Developing an improved simulation capability is a cost effective way to increase the productivity of the worldwide fusion research effort. • Making the next steps in integrated simulation is a significant scientific challenge and not, as some might say, an exercise in computer programming • There are key issues of basic theory that must be resolved in order to successfully advance in simulation • Building on the base theory program, the SciDAC projects, and other OFES sponsored projects we are making progress on codes and on integration. But: This has come at the expense of ability to support this development with theory With powerful simulations you need more theory, not less. And you need more manpower to apply the codes to experiments with increasingly sophisticated diagnostics DBB

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