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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?

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Simulation in fusion and its foundation on basic theory l.jpg
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


A constellation of recent events has resulted in a re emphasis on simulation in fusion research l.jpg
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


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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?

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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

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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


Slide6 l.jpg
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


Slide7 l.jpg
Understanding the basic theory requires simulation to formulate experiments, rests on a foundation of basic theoryUnderstanding 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

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Simulation in fusion is scientifically challenging there are a number of fundamental issues l.jpg
Simulation in fusion is scientifically challenging to formulate experiments, rests on a foundation of basic theoryThere 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

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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


Slide10 l.jpg
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


Integrated simulation even when the time scales are separated they can interact l.jpg
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


Slide12 l.jpg
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

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Slide13 l.jpg
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

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Points to come away with l.jpg
Points to come away with transport barrier formation and pedestal growth using XGC code

  • 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


One more point to come away with l.jpg
One more Point to come away with transport barrier formation and pedestal growth using XGC code

  • 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


For further reading see l.jpg
For further reading see transport barrier formation and pedestal growth using XGC code

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