Theory and Modeling Support for Alcator C-Mod

Transcription

1 Theory and Modeling Support for Alcator C-Mod Paul Bonoli PSFC, MIT Alcator C-Mod PAC Meeting January 25-27, 2006

2 Introduction Alcator C-Mod benefits from an extensive program of theory and modeling support in many areas: Core transport physics. Plasma boundary MHD phenomena energetic particles and MHD stability Wave plasma interactions Integrated scenario modeling

3 Introduction Theory and modeling support has several origins: Formal collaborations such as PPPL, UT, IPP (Asdex-Upgrade) Individual initiatives between C-Mod personnel and theorists within MIT (PSFC Theory Group) and outside MIT. Collaborations with on-going research initiatives such as SciDAC, ITPA, BPO, etc Purpose of this talk is to review several areas where theory and modeling support have impacted the physics program on C-Mod: Contributions of collaborators in theory and modeling have also been discussed in previous presentations more detail!

4 Theory and Modeling Collaborations Transport, Turbulence, and MHD Xu, Nevins, Rognlien, Umansky, R. Cohen: (EDA H-mode, QCM, Edge Fluctuations (BOUT simulations) Catto, Simakov (Edge flows and rotation) Carreras, Antar: SOL turbulence analysis Guzdar: L-H threshold theory Hallatschek, Scott, Rogers, Drake: Nonlinear turbulence models Diamond: Theory Mikkelsen, Dorland: Critical gradient nonlinear stability Ernst, Bravenec, Dorland: GS2 microturbulence modeling Chang, Chan, Coppi, Perkins, Rogister, Shaing: Transport, Plasma rotation Boswell, Sharapov, Zonca, Breizman, Berk: Alfven cascades T. Hender: Locked modes Gorelenkov, Kramer: TAE modeling (NOVA-K) Huysmans, Wright: TAE modeling (CASTOR) Izzo, Brennan, Whyte: Disruption mitigation modeling (NIMROD) Impurity and Particle Dynamics Stangeby, Lisgo, Elder: OSM-EIRENE divertor plasma and neutral modeling Stotler: DEGAS II neutral transport modeling Bonnin, 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)

5 Theory and Modeling Collaborations (continued) ICRF Jaeger, Myra, D Ippolito: ICRF flow drive Ram, Brambilla, Jaeger, D Azevedo, Batchelor, J. Wright: Fast wave and mode converted waves in toroidal geometry Choi, McCune, C.K. Phillips, Brambilla, J. Wright: Full-wave / Fokker Planck minority heating simulations R. Maggiora (Torino): TOPICA modeling of antenna plasma system Lower Hybrid C.K. Phillips, M. Brambilla, J. Wright: 2D full-wave simulations Peysson, Decker, Ram: 2D Fokker Planck code development Harvey: 2D LHCD Fokker Planck simulations Bernabei: Coupling simulations Integrated scenario development McCune, Brambilla, C.K. Phillips, J. Wright: Integration of TORIC5 into TRANSP McCune, Phillips: Integration of CQL3D into TRANSP C. Kessel: Time dependent modeling

6 D. Ernst, PSFC Core Transport Physics Implemented GS2 and GYRO on parallel computing cluster (MARSHALL) at PSFC. Codes are being used by doctoral candidates on C- Mod L. Lin (GS2), K. Zhurovich (GS2), B. Bose (GYRO) Developed synthetic PCI diagnostic for GS2 Coordinate transformation from field-line-following system to cartesian, appropriate integrations PCI 32 vertical chords Provides direct comparison of gyrokinetic simulation spectra with measured density fluctuation spectra D. Mikkelsen GS2 simulations of C-Mod discharges

7 Synthetic PCI Diagnostic for GS2 shows good Agreement with Measurement (Long, Ernst, PSFC) Result for C-Mod ITB, dominated by TEM: Synthetic diagnostic brings simulation into agreement with measured spectra Electron density Spectra (A.U.) A. Long, D.R. Ernst (APS, 2005) New GS 2 k R spectrum Wavenumber [ cm -1 ] Original GS 2 k y spectrum Measured P CI k R spectrum

8 Future Synthetic Diagnostic Development (R. Bravenec, W. Rowan, FRC) Core: Reflectometer (planning) ECE (in progress) Edge: T e fluctuations n e fluctuations near cutoff Gas-puff imaging (GPI) Langmuir probes

9 Critical Role of MHD in disruption mitigation by high pressure gas jet where penetration is shallow (V. Izzo, PSFC) NIMROD simulations show dominant 1/1 and 2/1 modes Very simple gas jet model reproduces qualitative features of experimental thermal quench

10 Coupling of NIMROD and KPRAD codes to move toward quantitative predictability V. Izzo, (PSFC) D. Whyte, U. Wisc. Ionization and recombination are computed for each charge state to produce electron source/sink Impurity mass density and contribution to plasma pressure are accounted for Thermal losses from ionization, recombination, line radiation and bremsstrahlung are computed dn r e + ne V r = D ne + Sion - Srec, dt r dv r r r r r r ρ = p + J B + µρ V, dt r r r r E + V B = ηj, dt r r r e r ne = (γ -1)[neTe V + qe - Qloss]. dt Z eff dependence of resistivity is included Impurity change state populations tracked Accurate radiation rates and density evolution obtained. Preliminary results from the combined code have been obtained.

11 TAE and Energetic Particle Studies Growth rate studies of TAE modes in C-Mod using NOVA-K: N. Gorelenkov (PPPL), F. Zonca (Frascati), B. Breizman (UT) & J. Snipes (MIT) G. Kramer (PPPL) and E. Edlund & M. Porkolab (MIT) Use full-wave EM field solver (TORIC) to compute global Alfven eigenmodes: Leverage work off Wave-Plasma SciDAC Initiative (C.K. Phillips, J. Wright. M. Brambilla)

12 Progress In the Theory and Simulation of Extended-MHD (J. Ramos, PSFC) Recent new results have advanced the fluid theory of low-collisionality magnetized plasmas [Pop, 2005; PoP, 2005]: Finite-Larmor-radius equations for stress and stress-flux tensors. Most general gyroviscous force in coordinate-free form. Arbitrary magnetic geometry and plasma beta. Electromagnetic and fully non-linear Large anisotropy and far from Maxwellian distribution functions. These results are being used by the Center for Extended MHD SciDAC project and the RF-MHD Fusion Simulation Project: Final computational models will be useful in C-Mod for understanding RF- MHD interactions (sawtooth and NTM stabilization). Reduced version of theory with large aspect ratio and small parallel gradient orderings now implemented in simulation code at NIFS: Multi-scale simulation of coupled MHD and drift-mode turbulence (IAEA, 2006)

13 Wave Plasma Studies ICRF & LHRF Implemented CQL3D-GENRAY codes on MARSHALL cluster to interpret ICRF and LHRF experiments on C- Mod: Synthetic diagnostics for ECE and hard X-ray emission in CQL3D- GENRAY have been adapted to LHCD experiments in C-Mod. Synthetic diagnostic for CNPA measurements during ICRF minority heating has also been written for CQL3D. Modeling of ICRF mode conversion current drive (MCCD) in sawtooth modification experiments on C-Mod. Coupling of realistic antenna code to ICRF full-wave field solver.

14 ICRF Field Solver TORIC is coupled to a Package for Mode Conversion Current Drive (MCCD) Parallel TORIC solver can now be used to resolve ICW and IBW using 240N r 255N m J. Wright, PSFC (PoP, 2004) J n rf φ 2π ( ρ) = dθ Grf ( ρ, θ, ω / k// 0 m m S ELD rf m ) ( ρ, θ, m, m ). G rf is a parameterization of the current Drive efficiency due to Ehst-Karney (1991). ICW IBW ICW Strong up-down asymmetry in mode converted ICW wave fields. IBW fields excited at midplane are more symmetric.

15 Modeling results indicate localized counter-mccd near q=1 may be reducing shear and stabilizing sawteeth in C-Mod (A. Parisot, APS, 2005) Up-down asymmetry in ICW wavefields leads to net driven current. Symmetry in IBW fields results in a small ambipolar current.

16 CQL3D GENRAY Codes have been installed on the MARSHALL Computing Cluster at the PSFC fe fe fe = Drf ( p C fe p p ee sδ p 1 // ) + (, //, ) + // + Γ ( // ) + rχ F t p p p r r // // // fe r Collaboration between R.W. Harvey (CompX), C-Mod, and PSFC Theory Group (P. Bonoli, J. Wright, A. Schmidt, J. Liptac, V. Tang) Code installation was serial but parallel implementation is now underway (R. W. Harvey). Code has been used to assess LHCD for actual C-Mod target plasmas: Confirmed earlier work (Bonoli & Harvey, APS, 2003) that LHCD is 30-35% higher than adjoint code predictions when 2-D damping of LH wave is properly included. Calculations neglect radial diffusion operator since fast LHRF electrons are expected to thermalize rapidly.

17 LH Current Drive Computed with CQL3D GENRAY Codes for C-Mod Target Plasma J_lh (A/cm 2 ) I LH = 185 ka rho S_lh (W/cm 3 ) P LH = 2 MW [n // (0)=2.33]

18 Synthetic Diagnostic in CQL3D GENRAY (HORACE Code) has been used to study the effect of energetic LHRF tails on ECE emission (A.E. Schmidt, APS, 2005) Equivalent Radiation Temperature (kev) ECE Spectra for varying LH Power 2 MW 800 kw 600 kw 400 kw No Power ω/ω ce0 Synthetic diagnostic suggests that the effect of fast tail electrons on the ECE spectra should be apparent with 400 kw of LH power.

19 Synthetic Diagnostic for Hard X-ray emission in CQL3D may be used to Study Spectral Control in LHCD Discharges (J. Liptac, APS, 2005) n F //(0) = 2.33 n F //(0) = 2.75 Ray color changes from blue to red as power in the ray decreases.

20 Synthetic Diagnostic for Hard X-ray emission in CQL3D has been used to Study Spectral Control in LHCD Discharges (J. Liptac, APS, 2005) The low initial value of n for 90 0 means that the wave is resonant with higher phase velocity electrons, increasing the bremsstrahlung emission in the higher energy channels relative to

21 Parallel Computing Has Made it Possible to do Full-Wave Simulations of Lower Hybrid Waves (λ < 1 mm) Full-wave solver TORICLH is now being coupled to electron Fokker Planck solver (CQL3D): Electron plasma response is reevaluated using nonthermal f e First ever combined full-wave Fokker Planck calculation of LHCD. Collaboration through Wave- Plasma SciDAC Group (J. Wright, C.K. Phillips, P. Bonoli) J. Wright, PSFC, IAEA, 2004

22 For typical C-Mod parameters, the electron distribution function will have a modest plateau region C-Mod parameters: T e ~ 2 kev n e ~ cm -3 f LH = 4.6 GHz B = 5 T n // = 2 (launch) plateau : v 1 ~ 2.5 v Te v 2 ~ 4 v Te Log(f(v // )) Maxwellian plateau v 1 v 2 C.K. Phillips, APS, v // vte

23 Modifications to the wave damping and absorption are seen in the plateau region of phase space plateau Max χ zz,e for model distributions plateau P e ~ χ e,a,zz (T = T e ) -300 Max plateau χ e,real,zz C.K. Phillips, APS, n // = ck // ω = 1 ζ c v Te

24 Extensive Modeling Effort to interpret ICRF Minority Heating Experiments in C-Mod Use of Monte Code (ORBIT-RF) to assess effects of finite orbit width on minority ion tail formation and transport (M. Choi, GA; V. Tang, MIT). Synthetic diagnostic for compact neutral particle analyzer (CNPA) has been implemented in CQL3D (V. Tang, MIT; R. Harvey, CompX). In 2006, the Wave-Plasma SciDAC Group will be using a C-Mod minority heated discharge with CNPA measurements to benchmark and validate their codes.

25 ORBIT-RF Coupled with TORIC Field Solution Agrees with Measured Minority Ion Spectrum from NPA (M. Choi, APS, 2005) Alcator C-Mod minority fundamental heating Counts (a.u.) Fundamental harmonic heating result agrees with Stix formula as 5 expected Stix Formula C-Mod 78 MHz P RF = 1.0 MW B(0) = 5.4 T, H(5%) n e (0) = cm 3 T e (0) = T i (0) = 3 kev ORBIT-RF Time (msec) 1 0 Exp Energy(keV)

26 ORBIT-RF Predicts Broad Power Deposition Profiles due to Finite Orbit Width and Pitch-Angle Scattering (M. Choi, APS, 2005) Normalized Power Deposition ORBIT-RF indicates the importance of radial diffusion TORIC4 ORBIT-RF at early RF time ORBIT-RF at late RF time Normalized ψ p Spatial diffusion due to RF perpendicular heating and pitch angle scattering Initial position

27 Studies planned for Alcator C-Mod (A. Ram, PSFC) Modeling the coupling of ICRF waves in the edge plasma. Modeling the mode conversion of fast wave power to ICW and IBW. Using DKE to solve for the current drive due to ICW, IBW, FW, and LH waves (including any synergism with the bootstrap current). Using DKE to understand observed hard X-ray emission during LH current drive.

28 TOPICA3: ICRF Antenna Modeling Collaboration R. Maggiora (Torino); A. Parisot, S. Wukitch, J. Wright, P. Bonoli (MIT) C-Mod E-Antenna Faraday shield and backplane removed from mesh figure

29 TORIC and TOPICA Coupling is Near Completion TORIC finds the impedance weighted wave solution and surface fields on the antenna. Full-wave solver is run with a single (m, n) excitation of a component of E η,e ζ at the plasma surface and the reactive magnetic field components are measured. The admittance, Y, is defined as B = YE for the surface components of B and E where, Y = Y Y ηη ζη Y Y ηζ ζζ

30 Modal response of TORIC system E η driven at plasma edge m= B η response at surface m Next step: m Compute admittance matrix for entire (m,n) spectrum excited by antenna straps.

31 Summary Theory and Computation Group at the PSFC continues to provide valuable theory and modeling support for the C- Mod Project leading to advances in the areas of: Transport: Gyrokinetic studies C-Mod ITB s with first ever synthetic PCI diagnostic for GS2 Wave particle interactions in the ICRF and LHRF regimes Synthetic diagnostics for PCI, ECE, hard X-ray, and CNPA (with R.W. Harvey and M. Choi). Interpretive capability for mode conversion current drive (with M. Brambilla). Full-wave LHRF studies and self-consistent electron tail evolution (with C.K. Phillips and M. Brambilla). Disruption mitigation Computing cluster support

32 Summary Significant external collaborations are on-going to provide modeling support for: Understanding TAE mode and Alfven cascade observations in C-Mod (PPPL) Synthetic diagnostics for core and edge plasma (UT- FRC) 3D ICRF antenna modeling (Torino) Minority ion distribution evolution using full-wave and Fokker Planck / Monte Carlo codes (GA, CompX, PPPL, RF SciDAC) Benchmarking of ICRF and LHCD codes used in C- Mod: Carried out through the Steady State ITPA Group

33 Summary Integrated scenario development using TRANSP and TSC will be initiated in the coming year with PPPL: Approach of Kessel (ITPA, 2005) will be adopted. TRANSP will provide source modules for ICRF heating (FPPRF) and LH current drive (LSC). TSC will solve for time evolution of plasma. Codes will iterate.