Modeling of ELM Dynamics for ITER

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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 University of Tulsa, Tulsa, Oklahoma 3 Tech-X, Boulder, CO General Atomics, San Diego, CA ITPA meeting October, Chengdu, China

2 Outline Goal: Integrated modeling of pedestal and ELMs Constrains of numerical modeling Elements of reduced 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 MHD code NIMROD 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

3 Numerical Constraints [ ] [ # of dimensions Mesh points in each dimension ] Q 7 εp = 3 10 [ time step < sec> ] [# of runs per year][ Problem time < sec> ] Algorithms Constraints Q - code-algorithm requirements P - peak hardware performance ε - hardware efficiency Tflop meshpoint timestep Tflop sec Algorithm performance and problem requirements with available cycles 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) Assumption: time step= sec Mesh points in each dimensions= cases/year Q= TFlop/meshpoint/timestep

4 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-of-layer

5 ITER Equilibrium TOQ code inverse equilibrium solver Fast and can be used in a batch mode with the ideal MHD stability codes to generate of 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, δ = 0.49, κ = 1.85, B 0 = 5.3 T, I = 15.0 MA, n 0 = m -3, n ped = m -3, T 0 = 20.0 kev, T ped = 4.0 kev 100 j (A/cm 2 ) 50 ITER Peeling Stable 100 j (A/cm 2 ) 50 DIII-D High Triangularity Peeling Stable 0 0 Ballooning 2 α Ballooning μ0 p V V α= π ψ ψ 2 π R α 2 4 6

7 Integrated Approach to Edge Modeling Vision for integrated (whole device) modeling with edge Currently, integrated modeling codes include: 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 parametrize peelingballooning triggering conditions for ELM crashes BALOO, DCON, ELITE, and MISHKA In the future, integrated modeling codes will include: 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

8 Integration of Ideal MHD Stability Analysis Within Transport Simulations 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 A C B

9 ELM Modeling with NIMROD Code The NIMROD code numerically advances the resistive MHD equations in 3D geometry B = E + κ divb B t E= V B+ηJ μ 0 J = B n + ( nv) = D n t V ρ + V V = J B p Π t High-order finite element representation of the poloidal plane: Accuracy for MHD and transport anisotropy at realistic parameters: S>10 6, χ /χ perp >10 9 n T T p n ( ) ˆ ˆ + V = V + χ χ + χ T + Q γ 1 t bb I visc 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 Nonlinear ELM Modeling with NIMROD Code Electron temperature Velocity field

11 DIII-D Equilibria for Stability Analysis Sequence of DIII-D-like equilibria Mode structure changes with pedestal height The linear growth rates as a function of mode number for different equilibria as computed by NIMROD

12 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)

13 Nonlinear ELM Modeling for ITER with NIMROD Code Time dynamics of kinetic energies for different mode numbers for ITER This nonlinear NIMROD simulation is limited to 21 toroidal modes The n=21 mode is being driven by the unstable modes with lower mode number More modes will have to be included in the computation to demonstrate convergence of the nonlinear mode coupling effects Accurate account for two-fluid and FLR effects might also stabilize modes with high mode numbers

14 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 V ρ + V V = p + J B Πvisc Π Π i t 1 E= V{ B + ( J B p ) e Π e + η { J Ideal MHD ne Resistive MHD Two-fluid effects (Hall + diamagnetic) + Equations for p and p, + closures i e gv Π gv = p 4Ω [( b W) ( I + 3bb) + transpose] W = V + V T 2 3 I V

15 Extended MHD Effects Important Linearly The drift velocity is in the poloidal direction, which can be stabilizing to the edge mode, especially nonlinearly, is a critically important effect Linear Growth Rate B ω * ψ Hall and Gyroviscous Effects Included Single Fluid Stable Poloidal Drift Frequency c ω *e,i = q e,i nb k (B p ) 2 θ e,i θ Computationally, the two-fluid model with drift effects requires more temporal resolution than the MHD model. Nonlinear effect on ELMs not yet explored. Complete picture includes both toroidal and poloidal flows nonlinearly

16 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 Toroidal Flow Shear Only B V No Flow resonance Flow ψ Linear

17 With Flow Shear the Mode Structure is Limited in Radial Propagation 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 Toroidal Flow Shear Only B V T e ψ Without flow With flow Filaments Sheared Lower amplitude poloidal fluctuation and reduced radial gradients with flow shear. Possible healing. Toroidal flow shear must now be combined with drift effects for completeness

18 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 (χ /χ >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 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

19 Extra Slides

20 Transport model for ELMs in ASTRA code Theory-based model for pedestal and ELMs at the edge of H-mode plasmas Flow and magnetic shear stabilization of anomalous transport χ = χ F ( s, ω ) +χ F ( s, ω ) +χ +χ i i i i i ITG ITG ExB RB RB ExB KB i,neo χ = χ F ( s, ω ) +χ F ( s, ω ) +χ e e e e e TEM TEM ExB RB RB ExB KB ETG e,neo j where are shear suppression functions F F l () 1 αlj j s l ( s, ω ExB) = (2) 2 1+ αlj ( ωexbτlj) () 1 ( 2 ) ( j ) lj lj l, where +χ + χ ( ITG / TEM, RB) l = j = ( ions, electrons) α and α are adjustable constants, χ is anomalous thermal diffusivity caused by () l -mode turbulence, ωexb is flow shear ExB rate, and τlj are 2 ( j ) turbulence correlation times, which are estimated as τ = L χ. lj l l Pedestal width and critical pressure gradients are parameters that responsible for the pressure at the top of the pedestal Pedestal width is result from the model of shear suppression of anomalous transport Critical pressure gradient can be computed with ideal MHS stability codes

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