# Presentation: 555769

## 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

**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

**Notes:**
DOE investing far more in supercomputers than in ITER
DOE (OASCR) sponsoring Computer Science/Mathematics resources to work with applications
OASCR resources (even $) are coming into fusion

## 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

## Simulation is essential in designing new experimental facilities   ITER auxiliary systems, diagnostics now  operation

**Compact systems with transport and ******** limits competitive to tokamaks**
**Stable to neoclassical tearing modes**
**Reduced current drive requirements for steady state**

**Plasma optimizations using extensive simulations have allowed unprecedented stellarator design improvements – NCSX, QPS**

- Quasi Poloidal Stellarator (QPS)
- Naturally developing poloidal shear flowPotential for turbulence suppression

**Validated simulation is critical to determine what follows ITER**

- DBB

## 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

## 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

## Understanding the basic theory requires simulationUnderstanding the simulation requires basic theory

**Understanding the basic theory requires simulation****Understanding 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

## 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

**Basic description of plasma is 7D  ********* f*****(x, v, t)**
**Extreme range of time scales **
**wall equilibration/electron cyclotron O(10****14****)**
**Extreme range of spatial scales **
**machine radius/electron gyroradius O(10****4****)**
**Extreme anisotropy **
**mean free path in magnetic field parallel/perp O(10****8****)**
**Many non-linearly coupled phenomena**
**Sensitivity to geometric details**
** **
**     **
**   **

**Simulation in fusion is scientifically challenging *****There are a number of fundamental issues:***

**Developing computable formulations dealing with these fundamental issues depends on basic theory**

- DBB

**Notes:**
The physics is complicated, the mathematics is hard, the computations are extremely demanding

## We have been able to make progress by separating out the different phenomena and time scales into separate disciplines

**10****-10**

**10****-2**

**10****4**

**10****0**

**SEC.**

**CURRENT DIFFUSION**

**10****-8**

**10****-6**

**10****-4**

**10****2**

**CYCLOTRON PERIOD**** **ce-1 	                   ci-1

**SLOW MHD INSTABILITY, ISLAND GROWTH**

**ENERGY CONFINEMENT, ********E**** **

**FAST MHD INSTABILITY,****SAWTOOTH CRASH**

**MICRO- TURBULENCE**

**ELECTRON TRANSIT, ********T**** **

**GAS EQUILIBRATION WITH VESSEL WALL**

**PARTICLE COLLSIONS, ********C**** **

- Transport Codes:
- discharge time-scale

- RF Codes:
- wave-heating and current-drive

- Gyrokinetics Codes:
- micro-turbulence

- Extended MHD Codes:
- device scale stability

- DBB

**Notes:**
In each we face the difficulties of high dimensionality, multi-scales, non-linearity – we have made great progress in each discipline but there is a lot to do

## We have a portfolio of SciDAC and other computational projects addressing the separated phenomena and time scales

**Nonlicar dynamics of:**
**Sawteeth**
**Neoclassical tearing modes**
**Edge localized modes**
**Energetic particle modes**

**Center for Extended MHD Modeling **

**Gyrokinetic Particle Simulation Center**

**Micro-stability**
**Turbulence and turbulent transport**
**Long mean-free-path collisional transport**

**Center for Simulation of Wave-Plasma Interactions**

**Plasma heating**
**Externally driven current or plasma flow**
**Wave processes – mode conversion, absorption, reflection**
**Non-Maxwellian particle distributions**

**Edge Simulation Laboratory**

**Divertor performance**
**Heat and particle loads**
**Edge pedestal formation**
**ELM effects**
**Plasma/material interactions**

- DBB

## 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**

- RF induced plasma modifications: “quasilinear” time-scale

- Turbulent transport

- Transport Codes:
- discharge time-scale

- RF Codes:
- wave-heating and current-drive

- Gyrokinetics Codes:
- micro-turbulence

- Extended MHD Codes:
- device scale stability

- DBB

## We have begun three pilot projects of restricted scope for Fusion Simulation Project (FSP)  Focused integration initiatives

**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**

**Partnership of OFES and OASCR under the aegis of SciDAC**

- DBB

## Center for Edge Plasma Studies – simulation of edge transport barrier formation and pedestal growth using XGC code 

**5D particle in cell gyrokinetics code**

**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**

**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**

- DBB

## 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

## 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

## For further reading see

- DBB