Theory and Modeling Support for Alcator C-Mod

Theory and Modeling Support for Alcator C-Mod Paul Bonoli Alcator C-Mod PAC Meeting January 24-26, 2007

Introduction Alcator C-Mod benefits from an extensive program of theory and modeling support in many areas: Plasma boundary Core transport physics. MHD phenomena energetic particles and MHD stability Wave plasma interactions Integrated scenario modeling Theory and modeling support has two origins: Formal collaborations such as PPPL, UT, IPP (Asdex-Upgrade), ITPA & BPO, and SciDAC Initiatives Individual initiatives between C-Mod personnel and theorists within MIT (PSFC Theory Group) and outside MIT. Recent C-Mod Ideas Forum included active participation from theorists and computational physicists.

Theory and Modeling Collaborations Transport, Turbulence, and MHD Xu, Nevins, Rognlien, Ryutov, Umansky, R. Cohen: (EDA H-mode, QCM, Edge Fluctuations (BOUT simulations) Catto, Simakov (Edge flows and rotation) Guzdar: L-H threshold theory Halletschek, Scott, Rogers, Drake: Nonlinear turbulence models Diamond: Theory Mikkelsen, Dorland: Critical gradient nonlinear stability Ernst, Bravenec, Dorland: Gyrokinetic microinstability analysis / nonlinear turbulence simulations (GS2, GYRO) Chang, Chan, Coppi, Perkins, Gurcan, Shaing: Transport, Plasma rotation Sharapov, Zonca, Breizman, Berk: Alfven cascades T. Hender: Locked modes Gorelenkov, Kramer: TAE modeling (NOVA-K) Huysmans, Wright: TAE modeling (CASTOR) Izzo, Brennan: Disruption mitigation modeling (NIMROD) Angioni, Ernst: Particle transport theory Impurity and Particle Dynamics Stangeby, Lisgo, Elder: OSM-EIRENE divertor plasma and neutral modeling Stotler: DEGAS II neutral transport modeling Pigarov, Krasheninnikov: edge atomic processes, 2D edge transport modeling (UEDGE), edge turbulence/structures Parks: Pellet ablation dynamics Fournier: Atomic physics modeling Strachan: screening simulations (EDGE2D)

Theory and Modeling Collaborations (continued) ICRF Jaeger, Myra, D Ippolito: ICRF flow drive, RF sheath studies Ram, Brambilla, Jaeger, D Azevedo, Batchelor, J. Wright: Fast wave and mode converted waves in toroidal geometry Choi, McCune, C.K. Phillips, E. Valeo, Brambilla, J. Wright: Full-wave / Fokker Planck minority heating simulations R. Maggiora (Torino): TOPICA modeling of antenna plasma system D. Smithe: PIC simulations of RF sheaths using VORPAL Lower Hybrid C.K. Phillips, M. Brambilla, J. Wright: 2D full-wave simulations Peysson, Decker: 2D Fokker Planck code development Harvey: 2D LHCD Fokker Planck simulations / synthetic diagnostics Ekedahl, Maggioria: Coupling simulations with swan & TOPLH Integrated scenario development McCune, Brambilla, C.K. Phillips, J. Wright: Integration of TORIC5 into TRANSP Harvey, McCune, Phillips: Integration of CQL3D into TRANSP C. Kessel: Time dependent modeling

SOL Flows Change in Alcator C-Mod Upon LSN USN (and B -B) [B.LaBombard] Inner Probe Outer Probe V, km/s 20 15 10 LSN DN Low field side parallel flows 5-5 USN 2 4 6 8 ρ, mm Inner Probe Outer Probe Inner Div. "Nose" V, km/s 40 20-20 -40 High field side parallel flows LSN DN ρ, mm 2 4 6 8 USN

Effects of Magnetic Topology on SOL Flow [A. Simakov, P. Catto, B. LaBombard] (nv) = 0 Flow V = (ω s + ω a )R 2 ζ +(u s +u a )B Asymmetric portions of flow change sign going from LSN to USN (symmetric part is unchanged). Note that B -B corresponds to LSN USN and reversal of all flows.

TAE and Energetic Particle Studies Studies of Alfven cascades and TAE modes in Alcator C-Mod: N. Gorelenkov (PPPL), H. Berk, B. Breizman (UT) & J. Snipes (MIT) APS (2006) M. Porkolab, E. Edlund (MIT), N. Gorelenkov, B. Breizman, G. Kramer IAEA (2006)

NOVA-K Finds Spatially Broad n=10 TAE in H-mode Weak continuum interaction both in the core and near the edge NOVA-K finds a spatially broad n=10 mode at 478.3 khz This broad radial structure may couple core TAEs to the edge QC mode Snipes (APS, 2006)

Core Transport Physics D. Ernst, PSFC Developed interface and analysis software to enable simulations of experiments: Guides C-Mod thesis research involving turbulence simulation: Kirill Zhurovich MIT graduate student, nonlinear GS2 simulations of ITB onset. Liang Lin MIT graduate student, PCI fluctuations and comparison with gyrokinetic simulations Brock Bose MIT graduate student, GYRO simulations of lithium pellet striations Undergraduate participation David Ely, Eric Grebing MIT undergraduates, development/release of fits profile fitter Viraj Navkal NUF, collisional energy diffusion in GS2 Basic Theory: New nonlinear upshift of TEM critical density gradient, relevant to C-Mod ITB, increases with collisionality (IAEA '06)

Trapped Electron Mode Turbulence Identified PCI shows strong density fluctuations during on-axis heating of ITB Relative increase in fluctuation level reproduced by nonlinear GS2 simulations Linear stability analysis shows TEM dominates PCI spectrum during onaxis heating (ITG in barrier prior to on-axis ICRH) Ernst et al., IAEA oral TH/1-3 (2006)

Spectrum of Density Fluctuations due to TEM Turbulence Reproduced by Gyrokinetic Simulation Synthetic PCI diagnostic in nonlinear GS2 enables first of kind comparison of wavelength spectra QC mode filtered; spectrum is dominated by TEM in the ITB PCI spectrum is linear combination of radial and poloidal wavelength spectra Ernst et al., IAEA oral TH/1-3 (2006)

fits Automated Profile Fitting Software Released Automatically fits all available density and temperature profile data with spline/poly/tanhfit Graphical interface to previous command line utilities developed by Ernst/Zhurovich/Ely Versatile and customizable smoothing and fitting options D. Ely, K. Zhurovich, D. Ernst

E B Shear Reduction has been Estimated in Pedestal Region on C -Mod Using E r Inferred from CXRS Diagnostic (Bravenec, Rowan) Top of H-mode pedestal Stabilization when γ max (k θ ρ s < 1) α E γ HB γ HB γ WM α E γ ExB γ max, where α E κ/(r 0 /a) 0.6 if γ ExB = γ WM * or 0.73/[κ 0.25 (R 0 /a) 0.6 ] if γ ExB = γ HB (Kinsey, et al., 2006 Sherwood) α E γ WM *Waltz and Miller, Phys. Plasmas 6, 4265 (1999) Hahm and Burrell, Phys. Plasmas 2, 1648 (1995) Low-k modes reduced but not quenched. Perhaps quenched in pedestal?

NIMROD Simulations of Gas-Jet Mitigation Experiments on Alcator C-Mod show that equilibrium edge is rapidly cooled (V. Izzo) 2/1 mode appears first and stochastic fields form at the edge, eventually destroying all field lines outside q=1 1/1 mode levels core temperature by swapping cold island with hot magnetic axis

NIMROD: Simulated thermal quench resembles experimental Thomson scattering profiles on C-Mod Thermal quench occurs in 3 stages: 1) Outer few cm are cooled directly by impurities 2) Stochastic fields outside of q=1 lead to cooling of outer ~40% 3) 1/1 modes convects heat from core, collapsing central temperature All times are in units of (S/2 10 7 ) 0.6 τ A t=0 defined by edge temperature collapse

NIMROD combined with KPRAD (NIMRAD) successfully captures density differences observed between helium vs. argon jet penetration C-Mod Thomson profiles NIMRAD profiles Simulation at experimental parameters (S~10 7 )

Theoretical Studies of ICW-IBW Mode Conversion in Alcator C-Mod (A. Ram, A. Parisot) TORIC simulation of ICW mode conversion in Alcator C-Mod at 240N r x 255 N m J. Wright, PSFC, PoP, 2004 ICW IBW FW Trying to understand up-down asymmetry in IBW-ICW mode conversion in Alcator C-Mod: Using toroidal ray tracing to study k // evolution of mode converted IBW-ICW wave fields. Will compare k // evolution from full-wave solvers (TORIC and AORSA) with ray tracing.

AORSA/CQL3D can reproduce the fast ion tail evolution during minority ICRH in Alcator C-Mod (V. Tang & RF SciDAC) Relatively low energetic tail energies render finite ion orbit effects less important in which case zero banana width approx. in CQL3D should be OK. Fundamental minority ion absorption is well-understood. Good experimental measurements of the energetic ion tail have been made using a compact neutral particle analyzer (CNPA) V. Tang Using a Maxwellian fit to data gives T ion 70 kev. H+ ~0.1% B Vincent Tang, MIT (PhD Thesis, 2006)

Calculation for C-Mod minority H, N R = 128, N Z = 128, [256 processors for 3 hrs on Cray XT3 ORNL] (a) (r/a = 0.46) (r/a = 0.46) (r/a = 0.46) (r/a = 0.46) (r/a = 0.46) u_parallel u_parallel u_parallel u_parallel u_parallel at const. pitch angle at const. pitch angle at const. pitch angle at const. pitch angle at const. pitch angle 3 kev r/a = 0.46 87 kev 52 kev 72 kev 72 kev (b) u / u_norm u / u_norm u / u_norm u / u_norm u / u_norm Power absorbed Power absorbed Power absorbed Power absorbed Power absorbed H H H H H D D D D D r r r r r P(H) = 0.459 MW = 76 % P(H) = 0.499 MW = 83% P(H) = 0.518 MW = 86% P(H) = 0.526 MW = 87% P(H) = 0.522 MW = 87%

AORSA-CQL3D: Contours of converged power deposition exhibit off-axis feature needed to reproduce CNPA tail measurements (V. Tang) Wave fields Heating (H)

Assessing the validity of QL Theory to describe ICRH in C-Mod Monte Carlo ORBIT-RF code has been used to show that large RF electric field can destroy superadiabaticity via phase stochasticity M. Choi, V. Chan, J. Wright, D. Smithe Mechanism works even in the absence of collisions Δφ = 1 ( ω Ω // v // ) ds ci k 2π v // Using parameters from the C-Mod minority heating case: P RF = 0.6 MW E RF 1 kv/m -> ε=0.428 (Mapping parameter) Δμ μ Δφ Y/a X/a Green = 0.1 kv/m Red = 1 kv/m θ θ

Analysis of LHCD Experiments in Alcator C-Mod Using the 3-D(p, p //, r) Fokker Planck Ray Tracing Model CQL3D-GENRAY [Schmidt, Bonoli, Harvey, Parker, Wright] Codes compute the steady state solution of FPE, neglecting the radial diffusion operator: p // D rf ( p // f ) p + Γ δ ( p s e // + C( fe, p, p ) + // // 1 fe ) + rχ F r r r ee = // f p f t e e // Ray tracing and FP solver iterate until a self-consistent D rf and f e are obtained. Self-consistent nonthermal f e is used in synthetic diagnostics for hard X-ray and EC emission.

Distribution Function Computed by CQL3D Exhibits a Nonthermal Tail Shot 1060728014 Contour plot of distribution function 10 19 10 18 10 17 10 16 Cuts of f(v) at Constant Pitch Angle θ=0 θ=π/4 θ=π/2 θ=3π/4 θ=π γ v perp /c 1 0.8 0.6 0.4 0.2 0 1 0.5 0 0.5 1 1.5 2 γ v /c f 10 15 10 14 10 13 10 12 10 11 10 10 10 9 0 1 2 3 4 5 6 7 γ v/c

Comparison Between Experimental Hard X-rays and Synthetic Diagnostic (CQL3D) for Shot 1060728104 Count Rate (s 1 kev 1 ) 16 x 104 Modeled and Measured HXR Spectra 14 12 10 8 6 4 2 0 5 10 15 20 25 30 Channel Number 24 kev (cql3d) 34 kev (cql3d) 44 kev (cql3d) 24 kev (experiment) 34 kev (experiment) 44 kev (experiment) HXR Spectra from Synthetic Code are narrower than measured profiles. This suggests that radial diffusion effects on fast electrons could be important. Next step is to include a model radial diffusion operator in the CQL3D simulations.

Full-wave solver TORIC is now being coupled to the CQL3D Fokker Planck solver Electron and ion plasma response in TORIC can now be evaluated using the nonthermal f e, from CQL3D (E. Valeo, C.K. Phillips, J. Wright). Final step is to reconstruct D QL from TORIC and pass it to CQL3D. Full-wave LH Simulation first performed on the MARSHALL cluster at MIT(6 days @ 32 processors). Now simulation can be done on CRAY XT3 JAGUAR at ORNL (1 hour @ 4096 processors). This work is part of the 2008 DoE High Level Theory Milestone

ICRF Antenna Modeling Collaboration: TOPICA TORIC Code Integration R. Maggiora (Torino); A. Parisot, S. Wukitch, J. Wright TOPICA: Fully 3D solid antenna structure model (including FS, box, ) Code runs on MARSHALL cluster (parallel version can model the ITER ICRF antenna). TORIC: Toroidal full-wave solver provides the plasma response through an admittance matrix that includes effects due to curvature of the antenna and poloidal mode coupling. This activity is a main thrust of the RF SciDAC Project. Alcator C-Mod: E antenna

Surface Admittance from TORIC Shown is the perpendicular response to a perpendicular drive electric field at the surface. The 2D response appears to be stiff, varying only in magnitude but not shape for different driven poloidal modes. Shown on the right is a slice of the 2D admittance with the self admittance versus parallel wavenumber for comparison with the 1D FELICE code. Y m,m' 1D response for m=[-16,16] plotted versus k

Integrated Scenario Modeling of LHCD Profile Control in C-Mod Using TSC-LSC [Kessel, Hubbard, Bonoli, Harvey, Wright] Simulations presently use TSC LSC: TSC performs discharge evolution using 1.5D transport equations, free boundary MHD solver, and LSC code for the LHCD. Active efforts through ITPA SSO and RF SciDAC projects to improve the LHCD model used in TSC and TRANSP. Need to incorporate 2D Fokker Planck results for LHCD from the CQL3D code into scenario modeling. Treatment of LHCD in LSC using adjoint method combined with 1D (v // ) damping of LH waves is only approximate [Bonoli, IAEA, 2006]. Eventual solution will be to include CQL3D in TRANSP and perform combined simulations with TRANSP and TSC: TRANSP computes source terms for the LHCD using CQL3D and for the ICRH using TORIC. Plasma is evolved using these source terms in TSC.

TSC-LSC Simulation: LHCD with H-mode Plasmas Can Produce High f NI and Drive q(0) > 1 ICRF on LH on I LH = 145 ka I LH = 75 ka

Basic Theory Work With High Impact for C-Mod Application of alternate basis functions to solve the wave equation [H. Kohno (GS), J. Freidberg, P. Bonoli, J. Wright, C.K. Phillips]: Use Gabor Element Method to solve the wave equation. Can be a big computational gain over standard FEM s when there are multiple spatial scales (mode conversion). Thesis project will be to use this new basis set to solve the 1D integral wave equation (all orders conductivity relation). Develop kinetic closure relation for coupling RF and MHD codes (J. Ramos, CSWIM Project) Application to NTM stabilization via ECCD and LHCD. Spatial regions exist near rational flux surfaces within which RF, the kinetic evolution of the velocity distribution, and extended MHD phenomena are all tightly coupled. Need to couple the RF-driven evolution of the plasma distribution function into the dynamical equations of the extended MHD model [e.g. through a drive term like Γ rf / v].

Marshall Computing Cluster

Upgrades to Hardware & Physics Capabilities on MARSHALL Cluster Marshall Marshall II Marshall II Present State Phase 1 (Funded) Phase 2 (Not funded) Processor AMD Athlon 2000 + 32 bit 1.67 GHz Single core per chip AMD Opteron 64 bit 2.2 GHz Two cores per chip Four cores per chip Memory PC 2100 DDR DDR - 667 (Access two cells per cycle) Compute node configuration 2 processors 2 Gbyte memory 80 Gbyte disk 2 processors/ 4 cores 4 Gbyte memory 200 Gbyte disk 2 processors/ 8 cores 8 Gbyte memory Number of nodes 24 64 64 Total Capability Processor cores Memory Processor cycles Network 48 48 Gbyte 80 GHz @ 32 bit Myrinet 256 256 Gbyte 563 GHz @ 64 bit Infiniband 512 512 Gbyte 1126 GHz @ 64 bit Infiniband Physics Capability LOW resolution nonlinear turbulence simulations (many days) Full-wave LH in 6-7 days HIGH resolution nonlinear turbulence simulations (many days) Full-wave LH in 2 days ICRF QL simulations 1 day High resolution nonlinear turbulence simulations (1-2 days) Full-wave LH in a day ICRF QL simulations with full spectra -2 days

Summary Theory Group at the PSFC has provided valuable theory and simulation support for the C-Mod Project leading to advances in the areas of: Transport Gyrokinetic studies of ITB formation and control Synthetic PCI diagnostic for TEM turbulence Wave particle interactions in the ICRF and LHRF regimes Synthetic diagnostics for hard X-ray emission and CNPA. Predictive capability for minority heating and quasilinear tail formation. Full-wave LHRF studies Disruption mitigation Computing cluster support Many PSFC theory activities were not covered in this talk!!

Summary Significant external collaborations have been initiated by the C-Mod Group to provide simulation support for: Understanding TAE mode and Alfven cascade observations in C-Mod (PPPL & UT) 3D ICRF antenna modeling (Torino) Integrated scenario development using TSC & TRANSP (PPPL) Predictive LHCD capability using CQL3D (CompX) Predictive nonthermal ion evolution using CQL3D/AORSA (ORNL & RF SCiDAC)