1. Modeling of ELM Dynamics for ITER A.Y. PANKIN 1, G. BATEMAN 1, D.P. BRENNAN 2, A.H. KRITZ 1, S. KRUGER 3, P.B. SNYDER 4, and the NIMROD team 1 Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015 2 University of Tulsa, Tulsa, Oklahoma 3 Tech-X, Boulder, CO 80303 4 General Atomics, San Diego, CA 92186 Workshop on Edge Transport in Fusion Plasmas 11-13 September, Kraków, Poland

2. 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, f low 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

3. 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

4. Numerical Constraints Requirements: Required problem time: at least 1 sec, at least 500 runs per year Conclusions: 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 sec Mesh points in each dimensions=100 500 cases/year Q=1.4 10 -4 TFlop/meshpoint/timestep

5. 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 and free 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

6. 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, B 0 = 5.3 T, I = 15.0 MA, n 0 = 1.1  10 20 m -3, n ped = 7.1  10 19 m -3, T 0 = 20.0 keV, T ped = 4.0 keV DIII-D High Triangularity Peeling Ballooning Stable 2 4 6 0 50 100 0  j ║ (A/cm 2 ) ITER 0 100 50 0 2 4 6  j ║ (A/cm 2 ) Peeling Stable Ballooning

7. Integrated Approach to Edge Modeling Vision 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:

8. 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 form spontaneously after auxiliary heating power turned on Integration of Ideal MHD Stability Analysis Within ASTRA Simulations A C B

9. ELM Modeling with NIMROD Code The NIMROD code numerically advances the resistive MHD equations in 3D geometry High-order finite element representation of the poloidal plane: Accuracy for MHD and transport anisotropy at realistic parameters: S>10 6,  || /  perp >10 9 Flexible spatial representation Temporal advance with semi-implicit and implicit methods Multiple time-scale physics from ideal MHD (ms) to transport (ms) time scales

10. 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

11. 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

12. 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=7NIMROD n=7

13. Nonlinear ELM Modeling for ITER with NIMROD Code Time dynamics of kinetic energies for different mode numbers for ITER This NIMROD simulation includes 2-fluid effects There are stages of explosive growth after 200 steps due to nonlinear mode coupling (limited by 21 modes in this simulation) (~20  s)

14. 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)

15. Velocity field Electron temperature Nonlinear ELM Modeling with NIMROD Code

16. NIMROD Results: Nonlinear ELM Dynamics Filament-like structures are observed at the plasma edge

17. 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

18. 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 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 Single Fluid Hall and Gyroviscous Effects Included

19. 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

20. Without flow shearWith flow shear TeTe

21. 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 TeTe 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

22. 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>10 6 ), viscosity, particle transport, parallel and perpendicular thermal transport (  || /   >10 9 ) 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