Theory and Modeling Support for Alcator C-Mod

Theory and Modeling Support for Alcator C-Mod Paul Bonoli PSFC, MIT Alcator C-Mod PAC Meeting February 2-4, 2005

Introduction Alcator C-Mod benefits from an extensive program of theory and modeling support in many areas: Core transport physics. Divertor and edge transport physics MHD phenomena energetic particles and macroscopic MHD Wave particle interactions Integrated scenario modeling

Introduction Theory and modeling support has two origins: Official collaborations such as PPPL, UT, IPP (Asdex-Upgrade) Individual initiatives between C-Mod personnel and theorists within MIT (PSFC Theory Group) and outside MIT. 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 will also been discussed in subsequent presentations more detail!

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 rotation) Carreras, Antar: SOL turbulence analysis, L-H dynamics Guzdar: L-H threshold theory Hallatschek, Scott, Rogers, Drake: Nonlinear turbulence models Diamond: Theory Mikkelsen, Dorland: Critical gradient nonlinear stability Redi, Ernst, Bravenec, Dorland: GS2 microturbulence modeling Batemann, Kritz: BALDUR transport simulations Chang, Chan, Coppi, Perkins, Rogister, Shaing: Transport, Plasma rotation Boswell, Sharapov, Zonca, Breizman, Berk: Alfven cascades Gorelenkov, Kramer: TAE modeling (NOVA-K) Huysmans, Wright: TAE modeling (CASTOR) Izzo, Brennan: 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 Catto, Helander, Fulop: Neutral effects on rotation Parks: Pellet ablation dynamics Fournier: Atomic physics modeling Chung, Strachan: screening simulations (EDGE2D)

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 McCune, C.K. Phillips, Okuda, 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: Launcher design and coupling simulations Integrated scenario development McCune, C.K. Phillips, J. Wright: Integration of TORIC4 into TRANSP McCune, Phillips: Integration of CQL3D into TRANSP C. Kessel: Time dependent modeling

Core Transport Physics D. Ernst, PSFC Implemented GS2 and GYRO on parallel computing cluster (MARSHALL) at PSFC. Codes are being used by doctoral candidates on C-Mod L. Lin (GS2) and B. Bose (GYRO) Gyrokinetic simulations of ITB modes with off-axis ICRH in Alcator C-Mod: PoP, 2004, IAEA, 2004, Sherwood Oral, 2004

Synthetic Diagnostics for Gyrokinetic Codes (Bravenec, Rowan) Developed a synthetic diagnostic [following Nevins, LLNL Rept. No. UCRL-TR-206016, August, 2004] to take gyrokinetic code output from GYRO [J. Candy, J. Comput. Phys. 186, 545 (2003)] and simulate beam-emission spectroscopy (BES) measurements of the top of the pedestal of a C-Mod EDA H-mode plasma. Simulation results indicate that the sample volume of the BES system on C-Mod was too large to detect the smallscale fluctuations.

Synthetic Diagnostics for Gyrokinetic Codes (Bravenec, Rowan) Example: BES signal from GYRO calculation at top of pedestal (R = 0.89 m, z = 0) of EDA H-mode n e fluctuation (desired measurement) H α emissivity fluctuation (what ideal BES measures) BES signal fluctuation (finite collection area) Factor ~ 2 reduction in amplitude Attenuation of high frequencies (large wave numbers)

Emissivity Fluctuations Emissivity rate ε from W. M. Mandl, et al., Plasma Phys. Control. Fusion 35 1373 (1993): E b 40 kev/amu 20 13.3 Z eff 1 3 6 ε depends on both n e and Z eff, both of which fluctuate. Backup Viewgraph

Approximate BES Collection Area (Four fibers per channel, integrated through beam) R 1.6 cm, z 1.0 cm Backup Viewgraph

Pfirsch-Schlüter Electric Field in C-Mod Pedestal Evaluate radial electric field for arbitrary cross-section (find Hazeltine drift kinetics incomplete for viscosities) For circular flux surfaces and T e T i we have from conservation of toroidal angular momentum (Claassen & Gerhauser): r dω Ω 0 3 dr 0.19q ρ 2 0 T e T e + T i d ln T i dr where ω = c[ Φ/ ψ + (en) 1 p/ ψ ] V = ω (ψ )R ˆ ζ + u(ψ ) B and, with u known. So ω = const if T = 0. P. Catto, A. Simakov (LANL) 2

Pfirsch-Schlüter Electric Field in C-Mod Pedestal Neoclassical momentum relaxation time for L ~ 1 cm: τ m 7.8(T e +T i )L 2 T e q 2 νρ 0 2 ~50ms in C Mod pedestal C-Mod global momentum relaxation time ~ 50 ms

Plans: Magnetic Topology Effects on Ion Flows Magnetic topology affects C-Mod SOL flows - LaBombard Evaluated effects of magnetic topology in pedestal for: 1. Reversing plasma current 2. Reversing toroidal magnetic field 3. Reversing both current & toroidal field 4. Change from lower to upper single null Up-down symmetric and asymmetric parts of the flow behave differently for (2) and (3). Expect same symmetries in P-S and banana regimes so plan to compare to C-Mod core measurements of Rice for (4). Hope to get more results from C-Mod and perhaps NSTX P. Catto, A. Simakov (LANL)

Disruption control studies using NIMROD Gas jet mitigation is simulated by temperature profile modification (V. Izzo, PSFC) Either, an initial condition with a modified T profile is used Or, a cold front is propagated inward as a function of time In the case on the right, the propagation speed of the cold front is 5000 m/s, or ~10 times faster than physical.

Instabilities produce stochasticity extending inside the imposed low temperature region, leading to additional heat transport away from the core (V. Izzo, PSFC) t=0.011 ms Results are from case with inward propagating cold front. Equilibrium reconstructed from C-MOD discharge 1040428011 at 800 ms.

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 (C-Mod) G. Kramer (PPPL) and E. Edlund & M. Porkolab (C-Mod)

Inboard RF Resonance Alfvén Cascades are More Stable inboard RF resonance R res /R = 0.9 central RF resonance R res /R = 1.0 outboard RF resonance R res /R = 1.1 Snipes, Gorelenkov, 2004

Theory Predicts RF Resonance Effect on AEs Theory predicts the AE growth rate to scale as γ where is the precession drift frequency, ω ω dh F(v)dv ω ω dh ω dh which slows down as the RF resonance is moved inboard An MHD code, Nova-K, including fast particles, finite orbit width and finite Larmor radius effects was used to model RF resonance changes The central RF resonance case was scanned over pitch angle keeping all other parameters fixed at t = 0.122 s at the top of a cascade Kinetic profiles were taken from TRANSP/FPPRF/TORIC which indicated a peak T H = 160 kev The q profile was assumed to have slightly reversed shear with q 0 = 2.11 and q min = 2.06 at r/a = 0.4 Snipes, Gorelenkov, PoP, 2005

AE Growth Rate is Lower for Inboard RF Resonance Snipes, Gorelenkov, PoP, 2005 Scanning the RF resonance radius in Nova-K indicates outboard growth rate is somewhat larger than inboard Qualitatively agrees with the experimental observation of weaker inboard modes Quantitative agreement would require measurements of the distribution function Toroidal precession drift frequency slowing on the inboard side may also explain the frequency downshift of AEs for the inboard resonance

Fast Ion Temperature Affects AE Growth Rate Maxwellian and pitch angle distribution in Nova-K: f exp E (p R res ) 2 /( dr ) 2 T H R axis R axis where E = mv 2 /2, T H is the fast ion temperature, p=µb axis /E, and µ is the magnetic moment µ = 1 2 mv 2 / B Snipes, Gorelenkov, PoP, 2005 AE growth rate peaks at 160 kev while finite Larmor radius effects reduce the growth rate at high tail temperatures

Wave Particle Studies ICRF & LHRF Implemented synthetic diagnostic on MARSHALL cluster to understand ICRF mode conversion experiments on C- Mod (J. Wright, Y. Lin, A. Parisot, M. Porkolab, S. Wukitch, M. Brambilla): Understanding fast wave conversion to ICW and IBW is crucial for optimizing mode conversion current drive and mode conversion flow drive (Jaeger et al., PRL, 2003) for plasma profile control. Through rf SciDac Project the ICRF solver (TORIC) can now be run for complete antenna spectra with sufficient resolution to provide realistic electric fields for the synthetic PCI diagnostic. Performed full-wave simulations in the LHRF regime, demonstrating that diffraction at wave caustics can lead to significant spectral broadening (J. Wright, M. Brambilla, P. Bonoli): Spectral broadening is sufficient to explain the spectral gap in LH current drive experiments.

A Synthetic PCI diagnostic for TORIC The PCI on Alcator C-Mod has 32 channels that measure the perturbed density due to mode converted ICRF waves along a cord, to produce a signal. Converged electric fields from TORIC are used to reconstruct the perturbed density detected by the PCI. The figures at the right show the 2D TORIC results above the simulated PCI signal using an algorithm originally implemented by E. Melby* (*) E. Nelson-Melby, et. al, Phys. Rev. Lett. 90(15), 155004 (2003).

15 10 5 Comparison Between Simulation (Synthetic) and Experiment is Remarkable S abs [MW/m 3 ] Experiment TORIC 0 0.2 0.4 0.6 0.8 1.0 r/a S. Wukitch, Y. Lin, A. Parisot, M. Porkolab, J. Wright, 2005 10 17 m -2 10 17 m -2 10 17 m -2 2 1 0-1 -2 2 1 0-1 -2 2.0 1.5 1.0 0.5 Re( n e dl) Im( n e dl) n e dl Experimental Synthetic MC layer 0.0 0.64 0.66 0.68 0.70 0.72 0.74 0.76 R (m) (a) (b) (c)

Field solvers employing different conductivity models give very similar results ICW IBW FW TORIC at 240N r x 255 N m J. Wright, PSFC, PoP, 2004 AORSA at 230N x x 230 N y E.F. Jaeger, PoP, 2002

Parallel Computing Has Made it Possible to do Full-Wave Simulations of Lower Hybrid Waves (λ < 1 mm) Eliminates need to do ray tracing eventually! Injected LH waves convert between fast and slow modes. Loci of edge reflections and mode conversions in the full wave field pattern forms a ring of accessible LH waves. Simulation required 8064 MPP s on Beowulf cluster (7 day utilizing 48 nodes) J. Wright, PSFC, IAEA, 2004

Caustic formation in full-wave fields follows the ray tracing prediction (J. Wright, P. Bonoli, PSFC)

Spectral shift is large at caustic because of diffraction In ACCOME, the local n evolves to 2.5 on the high field side from 1.5 at the antenna, purely from geometric effects. In TORIC, the distribution of n on flux surfaces shows a significant upshift from an averaged launched n of 2 to >4 in the middle of the annulus at r/a=0.75. Note, TORIC broadening near antenna, before caustic, is comparable to that seen in ray tracing (the fringes are from multiple wave reflections at the plasma surface). This rapid upshift at the caustic causes all the power to be absorbed in the narrow region bound by the caustic and the edge cutoff - an effect not predicted in geometrical optics!

10 8 LH Power deposition profiles are both localized, but at different radii TORIC Radial Power Deposition Profile 0.08 0.06 ACCOME Slh vs. r/a S(MW/m 3 /MW inc ) 6 4 3 Slh (MW/m ) 0.04 2 0.02 0 0.0 0.2 0.4 r/a 0.6 0.8 1.0 0.00 0.0 0.2 0.4 0.6 0.8 1.0 r/a Differences in the absorption may be related to the downshifting of v φ by diffraction, which is high at the caustic - evidence for full wave enhancement in k filling the spectral gap.

Future Wave Particle Studies Implementation of nonthermal ion and electron distribution functions in TORIC solver (J. Wright, C.K. Phillips, P. Bonoli rf SciDac): Closed loop computation with Fokker Planck and TORIC solver can then be performed. Self-consistent minority ion distributions (H and 3 He) Parallel implementation of 2D (v,v // ) Fokker Planck solver CQL3D on MARSHALL cluster (P. Bonoli, R. Harvey, C.K. Phillips, J. Wright rf SciDac): Provide accurate calculation of driven LH current for C-Mod Establish expertise for CQL3D implementation in TRANSP

Kinetic description of the electron distribution function (A. Ram, J. Decker, PSFC) A Fokker Planck code (DKE) has developed to solve the bounce averaged drift kinetic equation for electrons in the banana regime: Solves kinetically for the neoclassical bootstrap current. Includes a quasilinear operator for studying rf driven plasma current. Treats the interplay between the rf driven and bootstrap currents. Calculates the hard X-ray emission for comparison with LH current drive diagnostics.

Studies planned for Alcator C-Mod (A. Ram, J. Decker, 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, and LH waves (including any synergism with the bootstrap current). Using DKE to understand observed hard X-ray emission during LH current drive.

Electric fields from a full-wave solver (TORIC) have been coupled to a finite orbit width code (ORBIT-RF) to study minority ion heating in C-Mod (M. Choi, GA, APS, 2004 rf SciDac) TORIC Simulation for N r = 200 N m = 31 Shot 1040415006 P RF : 1.0MW Frequency : 78 MHz B axis =5.5 T 4% (H)

ORBIT-RF Simulation of minority (H) distribution in C-Mod TORIC ORBIT-RF simulation results At ~30000 transit time ORBIT-RF

TOPICA3: ICRF Antenna Modeling Collaboration R. Maggiora (Torino); A. Parisot, S. Wukitch, J. Wright (MIT) - TOPICA3: - Fully 3D solid antenna structure model (including FS, box, ) - FELICE: - 1D full-wave ICRF solver - Non-homogeneous, FLR, absorption (fitted to curved boundary (1.5D) - Coax, voltage and current excitation of strap ports - Multi-port circuit parameters (Z, Y, S matrices) calculation; Computes currents, fields, and voltages everywhere around antenna and housing - TOPICA3 - FELICE model implemented on MARSHALL cluster.

Meshing for C-Mod E-Antenna Faraday shield and backplane removed from mesh figure

Reflection Coefficient DC4 Computed 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Measured 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 Plasma shot

Reflection Coefficient DC2 Computed 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Measured 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 20 Plasma shot

Conclusions and Next Steps - Good agreement obtained both in vacuo and with real plasma. - 1.5D plasma model is suitable for antenna analysis. - TOPICA3 is capable of predicting reliable behaviour for strap (IC) antennas. - TOPICA3 can be well adapted to analyze waveguide (LH) antennas. - Coupling with 3D plasma model (TORIC) is underway through rf SciDac Initiative.

The PSFC Theory Cluster has been a valuable resource for C-Mod experimentalists

Summary Theory and Computation Group at the PSFC has provided valuable theory and modeling support for the C-Mod Project leading to advances in the areas of: Transport Gyrokinetic studies of ITB formation and control Wave particle interactions in the ICRF and LHRF regimes Synthetic PCI diagnostic Predictive capability for mode conversion current drive and flow drive Full-wave LHRF studies Disruption mitigation Computing cluster support

Summary Significant external collaborations have been initiated by the C-Mod Group to provide modeling support for: Understanding TAE mode and Alfven cascade observations in C- Mod (PPPL) 3D ICRF antenna modeling (Torino) Synthetic diagnostics for gyrokinetic codes Integrated scenario development using TRANSP and CQL3D Minority ion distribution evolution using TORIC in TRANSP