Modeling of ELM Dynamics for ITER

A.Y. PANKIN1, G. BATEMAN1, D.P. BRENNAN2,A.H. KRITZ1, S. KRUGER3, P.B. SNYDER4, and the NIMROD team

1Lehigh University, 16 Memorial Drive East, Bethlehem, PA 180152University of Tulsa, Tulsa, Oklahoma3Tech-X, Boulder, CO 803034General Atomics, San Diego, CA 92186

Workshop on Edge Transport in Fusion Plasmas

11-13 September, Kraków, Poland

Outline• Goal: Integrated modeling of pedestal and ELMs

– Constrains of numerical modeling

– Elements of model for ELMs

• Triggering conditions for ELMs

– Equlibria generated with TOQ and TEQ codes

– Ideal MHD stability analysis with ELITE, DCON, and BALOO codes

• Ballooning/peeling marginal stability condition parameterized for use as ELM trigger within integrated simulations

• Integrated modeling simulation of ELMy H-mode plasma with ASTRA code

• Simulation of ELM crash with the NIMROD MHD code

– Non-ideal effects in NIMROD code

• Resistivity, viscosity, anisotropic thermal transport, flow shear, two-fluid and FLR effects

– Linear results obtained using NIMROD code

• Compared with corresponding results from other MHD codes

– Nonlinear ELM evolution computed using NIMROD code

• Mode coupling, filaments and explosive growth observed

• Effect of flow shear on ELM evolution

ELM Model for Integrated Simulations

A long range goal is to develop a model for ELMs for use in predictive whole device modeling code

–To simulate ITER plasmas on macro time scales

• Elements needed for integrated model for ELMs–Model for triggering conditions for ELM crashes–Model for ELM width–Model for particle, current and heat losses

• Important effects to include–Flow shear effect–Effect of neutrals –Effect of dust particles–Effect of NTMs and sawteeth on pedestal and ELMs–Effect of X-point and vertical asymmetry–FLR and two-fluid effects–Effect of scrape-off layer

Numerical Constraints

# of dimensions

7Mesh points in each dimension3 10

time step < > # of runs per year Problem time < >

Q - code-algorithm requirements

Q P

sec sec

Tfl

Algorithms Constraints

P - peak hardware performance sec

- hardware efficiency

op

meshpoint timestep

Tflop

Requirements:Required problem time: at least 1 sec,

at least 500 runs per yearConclusions:• 3-D (i.e., fluid) calculations for times of

~ 10 msec (single ELM cycle) within reach

• Longer times require next generation computers (or better algorithms)

• Higher dimensional (kinetic) long time calculations unrealistic

• Integrated effects must come through low dimensionality closures (transport modeling)

Algorithm performance and problem requirements with available cycles

Assumption:time step=10-7-10-2 secMesh points in each dimensions=100500 cases/yearQ=1.4 10-4 TFlop/meshpoint/timestep

ITER Equilibrium for MHD Studies

• TOQ code — inverse equilibrium solver

– Fast and can be used in a batch mode with the ideal MHD stability codes to generate ELM stability diagram.

– Equilibrium extended into scrape-off region with supplementary code VACUUM, called from MHD stability code DCON

– Non-ideal MHD NIMROD code requires an even more robust equilibrium that includes the scrape-off region

• TEQ code — direct equilibrium solver

– Extracted from CORSICA code as NTCC module

– Can be used both for prescribed boundary andfree boundary equilibria

– Parameterized pressure and current density profiles generated in a similar manner as with TOQ code

– Free-boundary TEQ equilibrium solver applied to generate new equilibria, including scrape-off region, for use with non-ideal MHD NIMROD code

ITER Peeling-Ballooning Stability Map• Ideal MHD stability codes, DCON, ELITE, and BALOO, used to

produce peeling/ballooning stability map in the pedestal region– Stability boundary parameterized for ELM threshold condition

• Stability boundaries for the ITER normalized pressure gradient and bootstrap current are comparable to the values obtained for the DIII-D high triangularity case described by M. Murakami et al., Nucl. Fusion 40, 1257 (2000)

– Parameters for the ITER reference case: a = 2.0 m, R = 6.2 m, = 0.49, = 1.85, B0 = 5.3 T, I = 15.0 MA, n0 = 1.11020 m-3, nped = 7.11019 m-3, T0 = 20.0 keV, Tped = 4.0 keV

DIII-D High Triangularity

Peeling

Ballooning

Stable

2 4 60

50

100

0

j ║(A

/cm

2 )

ITER

0

100

50

02 4 6

j ║(A

/cm

2 )

PeelingStable

Ballooning02 22 2

p V V

R

Integrated Approach to Edge ModelingVision for integrated (whole device) modeling with edge

1. Transport modules are called directly from code:• GLF23 and MMM models for anomalous transport• NCLASS for neoclassical transport

2. Ideal MHD stability codes used to parameterize peeling-ballooning triggering conditions for ELM crashes• BALOO, DCON, ELITE, and MISHKA

3. Nonlinear NIMROD MHD code results for ELM crash• Including effects of resistively, viscosity,

anisotropic heat flux, FLR and two-fluid effects

4. SOLPS (B2/EIRINE) code results for effects of neutrals

In the future, integrated modeling codes will include:

Currently, integrated modeling codes include:

• Results of ASTRA simulations of DIII-D using the new parameterized ideal MHD stability model– ELM frequency increases with

heating power and triangularity

– Pedestal and ELMs formspontaneously after auxiliaryheating power turned on

Integration of Ideal MHD Stability Analysis Within ASTRA Simulations

A C

B

ELM Modeling with NIMROD Code• The NIMROD code numerically advances the resistive

MHD equations in 3D geometry

divbt

B

E B

BJ 0

nn D

tn

V

viscpt

VV V J B

||ˆ

1ˆn T

T p n T Qt

bb IV V

• High-order finite element representation of the poloidal plane:

• Accuracy for MHD and transport anisotropy at realistic parameters: S>106, ||/perp>109

• Flexible spatial representation

• Temporal advance with semi-implicit and implicit methods

• Multiple time-scale physics from ideal MHD (ms) to transport (ms) time scales

E V B J

• Sequence of DIII-D-like equilibria• Mode structure changes with pedestal height

DIII-D Equilibria for Stability Analysis

The linear growth rates as a function of mode number for different equilibria as computed by NIMROD

Ideal Growth Rates Bracketed by NIMROD Depending on Dissipation

NIMROD can approach the ideal MHD limit by using high resistivity in vacuum and small resistivity and viscosity in the plasma region

NIMROD Linear Mode Structure Agrees with ELITE

Good agreement between NIMROD and ELITE DIII-D results for poloidal and radial mode structure

NIMROD n=21

ELITE n=7 NIMROD n=7

Nonlinear ELM Modeling for ITERwith NIMROD Code

Time dynamics of kinetic energies for different mode numbers for ITERThis NIMROD simulation includes 2-fluid effects

There are stages of explosive growthafter 200 steps due to nonlinear mode coupling(limited by 21 modes in this simulation)

(~20s)

ELM Modeling for ITER with NIMROD Code

Contour plots of vector and scalar fields computed with nonlinear NIMROD simulation of an ELM crash for ITER (at 400 time steps)

Velocity fieldElectron temperature

Nonlinear ELM Modeling with NIMROD Code

NIMROD Results: Nonlinear ELM Dynamics

Filament-like structures are observed at the plasma edge

NIMROD Code: Two-fluid and FLR terms• In addition to previously added non-ideal effects,

recent advances have enabled two-fluid treatment – Hall and diamagnetic terms in Ohm’s law– More complete stress tensor in momentum equation

transpose34

bbIb Wpgv

W V VT 2

3IV

||

||Ideal MHD Resistive MHD

Two-fluid effects(Hall + diamagnetic)

1

Equations for and , + closures

gvvisc i

e e

i e

pt

pne

p p

VV V J B

E V B J B J

The drift velocity in the poloidal direction, which can be stabilizing to the edge mode, especially nonlinearly, is a critically important effect

Extended MHD Effects Important Linearly

*e,i c

qe,inB2k (Bpe,i)

Computationally, the two-fluid model with drift effects requires more temporal resolution than the MHD model.

Poloidal Drift Frequency

*

B

Complete picture should include both toroidal and poloidal flows.

Linear Growth Rate

Stable

SingleFluid

Hall andGyroviscousEffects Included

Effect of Flow Shear on ELM Evolution

Flow destabilizes linear spectrum especially at high n in case shown which can possibly change qualitative linear picture

Ideal MHD high n modes stabilized

Nonlinear energy spectrum similar to that without flow although nonlinear evolution strongly affected by flow

Linear

Flow

resonance

No Flow

Toroidal Flow Shear Only

B

V

Without flow shear With flow shear

Te

Without flow, the high temperature filaments propagate to the wall

With flow, the perturbation is dragged by the fluid, significant localization in long term evolution

Te

With Flow Shear the Mode Structure is Limited in Radial Propagation

Lower amplitude poloidal fluctuation and reduced radial gradients with flow shear. Possible healing?

With flow

Without flow Filaments

Sheared

Toroidal Flow Shear Only

B

V

Summary• Progress in development of reduced model for ELM for

integrated modeling transport simulation is reported• Triggering conditions for ELMs in ITER and DIII-D studied

with ideal MHD stability codes BALOO, DCON and ELITE• ELM crash studied with non-ideal MHD code NIMROD

– Linear and nonlinear stages of ELM crash investigated – Non-ideal MHD effects included in NIMROD

• Additional effects include resistivity (S>106), viscosity , particle transport, parallel and perpendicular thermal transport (||/>109)

• Hall and diamagnetic terms added to Ohm’s law• Stress tensor in momentum equation

– Linear growth rate is enhanced by flow shear • Growth rate strongly affected by resistive SOL region

– Filaments, explosive growth and non-explosive growth are observed during nonlinear evolution of ELM crash• Filaments are dragged and twisted by flow shear

before they extend all the way to the wall

• Results being used to construct reduced models for whole device for integrated modeling simulations