Theory and Simulation in the Alcator C-Mod Program

Paul Bonoli

Alcator C-Mod Five Year Proposal ReviewMay 7-9, 2008

Plasma Science and Fusion Center

Research Goals on C-Mod in Theory and Simulation address many of the Topical Scientific Questions in the 2005 FESAC

Priorities Report

• Core transport physics:– Activity:

• Gyrokinetic simulations of ITB’s with ICRF and LHCD.• Synthetic diagnostic comparisons from simulation with experiment to elucidate the role

of ITG vs TEM turbulence.– Contributes to:

• T4. How does turbulence cause heat, particles, and momentum to escape from plasmas?

• T5. How are electromagnetic fields and mass flows generated in plasmas?• MHD phenomena – energetic particles and MHD stability

– Activity:• Application of kinetic MHD codes (NOVA-K) to understand intermediate-n AE’s and

energetic particle modes.• Simulation of gas-jet mitigation experiments to develop predictive capability for

disruptions.• Simulation of sawtooth modification via ICRF-generated ion tails and MCCD.

– Contributes to:• T1. How does magnetic field structure impact fusion plasma confinement?• T2. What limits the maximum pressure that can be achieved in laboratory plasmas?• T12. How do high-energy particles interact with plasma?

Research Goals on C-Mod in Theory and Simulation address many of the Topical Scientific Questions in the

2005 FESAC Priorities Report

• Pedestal and Plasma boundary– Activity:

• Testing of simulation codes (e.g., BOUT, ESEL, GEM) and integrated models (XGC0, ELITE – CPES) using data from well-diagnosed C-Mod pedestal and edge.

– Contributes to:• T10. How can a 100-million-degree-C burning plasma be interfaced to its room temperature

surroundings?• Wave – plasma interactions

– Activity:• Comparison between synthetic diagnostic codes for CNPA, PCI, hard x-rays, MSE, and ECE

with measurements made during ICRF and LHRF experiments.– Contributes to:

• T11. How do electromagnetic waves interact with plasma?• T12. How do high-energy particles interact with plasma?

• Integrated scenario modeling– Activity:

• Simulations of ramp-up, hybrid, and steady state discharges in C-Mod using TSC with realistic ICRH and LHCD source models.

– Contributes to:• T3. How can external control and plasma self-organization be used to improve fusion

performance?

• A2. Integration of high-performance, steady-state, burning plasmas:– Simulations of ramp-up, hybrid, and operating scenarios in C-Mod using TSC with

realistic ICRH and LHCD models.• A3. Validated Theory and Predictive Modeling:

A6. Plasma Modification by Auxiliary Systems: – Gyrokinetic simulations of ITB's with ICRH & LHCD and synthetic diagnostic

comparisons from simulations with experiment to elucidate the role of ITG vs. TEM turbulence.

– Simulations of gas jet disruption mitigation experiments using NIMROD / KPRAD.– Comparison between synthetic diagnostic codes for CNPA, PCI, hard x-rays, MSE,

and nonthermal ECE with measurements made during ICRF and LHRF experiments.– Benchmarking TAE codes (NOVA-K) against experiment.– Validation of simulation models for mode conversion current drive (MCCD) and flow

drive using synthetic diagnostic comparisons for PCI and HIREX-Sr.– Validation of simulation codes (e.g., BOUT, ESEL, GEM) and integrated models

(XGC0, ELITE - CPES) using data from C-Mod pedestal and edge.– Simulations of linear ICRF antenna coupling and nonlinear RF sheath formation and

comparisons with experiment.

Research Goals on C-Mod in Theory and Simulation contribute toward addressing issues identified in the

2007 FESAC Planning Panel Report:

Collaborations

• Theory and simulation research consists of active collaborations through:– ITPA and BPO (ITER and Burning Plasmas).– PPPL, UT, IPP (Asdex-Upgrade), – Individual initiatives between C-Mod personnel and theorists within

MIT (PSFC Theory Group) and outside MIT.– SciDAC Centers:

• Center for Simulation of Wave-Plasma Interactions – (CSWPI)• Center for the Study of Plasma Microturbulence• Center for Gyrokinetic Simulation of Energetic Particle Turbulence and

Transport (GSEP)• Prototype FSP – Simulation of Waves in MHD (SWIM)• Prototype FSP – Center for Plasma and Edge Studies (CPES)

• Theory and simulation research on C-Mod provides support for interpretation and guidance of experiment as well as for program / experimental planning.

Core Transport Physics - StatusC-Mod Benefits from Extensive Gyrokinetic Simulation

Program• Basic Theory:

– New nonlinear upshift of TEM critical density gradient, relevant to C-Mod ITB, increases with collisionality (Ernst, IAEA '06)

• Developed interface and analysis software to enable simulations of experiments – GS2_PREP – (Ernst)– fiTS – (Ernst and Zhurovich)

• Thesis research involving turbulence simulation:– Nonlinear GS2 simulations of ITB onset (Zhurovich, Ernst, Fiore)– PCI fluctuations and GS2 linear code studies (Lin, Porkolab, Ernst)– PCI fluctuations and comparison with GYRO linear and nonlinear

simulations (Lin, Porkolab, Rost, Candy (GA), Mikkelson (PPPL))– GYRO simulations of lithium pellet striations (Bose, Ernst)

• Gyrokinetic simulations of C-Mod H-mode plasmas– GS2 (Mikkelson – PPPL and Dorland – U. Md.)

• Studied collisionality dependence of Dimits shift in C-Mod

Spectrum of Density Fluctuations due to TEM Turbulence Reproduced by Gyrokinetic Simulation and

Correlated to ITB Control by ICRH

• Synthetic PCI diagnostic in nonlinear GS2 enables first of kind comparison of wavelength spectra.

• TEM turbulence observed to increase in simulation with on-axis ICRH (1.22 sec) realtiveto off-axis ICRH only (1.05 sec).

• New PSFC cluster will allow these nonlinear studies to continue “in-house”

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Gyrokinetic Simulation (TEM)

ρ=0.35, 1.22 s

1.05 +/- 0.03 s

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kR [ cm-1]Wavenumber

D. Ernst, PoP, 2004

Plans for Understanding Core Transport Physics on C-Mod

• Determine role of ITG, TEM and ETG on turbulent transport in L and H mode plasmas with equilibrated Ti, Te:

– Use GS2, GYRO, including comparisons with synthetic diagnostics.• Understand ITB formation and control:

– Use GYRO and GS2 simulations to distinguish ITG vs. TEM turbulent roles.

• Modify GYRO and GS2 to simulate momentum fluxes and compare withnew profile measurements from HIREX-Sr.

• Assess role of LHCD in:– ITB formation via magnetic shear modification.– Modification of core plasma rotation.– Modification of pedestal density and temperature.

• Assess viability of using mode converted ICRF waves for shear flow generation.

• Study particle and impurity transport– Determine relationship to drift wave turbulence (ITG, TEM).

Macroscopic MHD Research – StatusC-Mod has a Strong Interaction Between Theory,

Simulation, and Measurements

• Studies of Alfven cascades and TAE modes in Alcator C-Mod:– NOVA simulations of frequency spectra of Alfven cascades under

reverse shear conditions:• Edlund, Porkolab (MIT), Breizman (UT), Gorelenkov, Kramer (PPPL) –

IAEA (2006)– Synthetic PCI diagnostic code to interpret mode structure of Alfven

cascades:• Edlund, Porkolab, IAEA (2006)

– Effect of fast ion β on TAE mode frequency • Snipes, Jaeger, APS (2006)

• Simulations of gas-jet mitigation experiments on C-Mod:– Simulations with NIMROD and KPRAD

• (Izzo 2004, Granetz, 2006)

Importance of Pressure (and Gradient) Gradient Terms on TAE Mode Frequency has Recently Been Elucidated on C-Mod

• Comparison of NOVA data and a theoretical form (Breizman et al, Physics of Plasmas 2005, Gorolenkov 2006) also show generally good agreement when realistic temperature gradients are included.

• Minimum frequency measurements of RSAEs from PCI data shows a strong correlation between fmin

2 and Te.– Edlund (Graduate

student), Porkolab(2008)

•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 Simulations of Gas-Jet Mitigation Experiments on AlcatorC-Mod show that equilibrium edge is rapidly cooled (V. Izzo)

Plans for Macroscopic MHD

• Understand the role of realistic ICRF-generated fast ion distributions in excitation of unstable AE and Alfven Cascades:– Better implementation of fast ion distributions from AORSA-CQL3D and

TORIC-CQL3D in NOVA-K: (Gorelenkov, RF SciDAC Center)• Compare these synthetic NOVA-K predictions for mode stability with data.

– Use SparSpec code to interpret magnetic data on C-Mod to determine toroidal mode number spectrum of TAE’s (JET)

• Continue gas-jet simulations with NIMROD+KPRAD• Assess viability of ICRF for sawtooth modification via:

– ICRF-generated minority tail (energetic particle stabilization).– Local shear modification via mode conversion current drive (MCCD).– Work with SWIM FSP Project.

Pedestal and Edge – StatusWell-diagnosed SOL and edge of C-Mod Plasmas

Provide an Excellent Test of Theoretical and Simulation Predictions

• Detailed profile measurements are especially useful for testing simulation predictions.

• Theoretical predictions (Guzdar) are midway between measurements with gradB drift in favorable and unfavorable directions.

– Theory doesn't include the equilibrium flow effects that we think are important to explain the topology dependence.

Edge Te/Ln1/2 at L-H Threshold

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PredictedExpt, LSNExpt, USN

Long Term Plans for Pedestal and Edge will Emphasize Theory and Simulation

• Test predictions of Er for pedestal by comparing with recent C-Mod data: – Er from density, temperature, flow measurements of Boron impurties:

• Compare Pfirsh-Sclüter prediction for the shape of Er• Compare neoclassical flow predictions with measurements.• Examine effects of magnetic topolgy on flow inside the separatrix• Examine role of E × B shear reduction in L-H transition.

– Work to be done with PSFC Theory Group (Catto)• Application of advanced simulation codes to C-Mod edge:

– Use ELITE and M3D to study edge stability.– Validate 5D neoclassical edge transport codes (XGC0, XGC1 -CPES)

and TEMPEST code (LLNL) against pedestal structure and scalings from C-Mod data.

– Simulate L-H transitions and complete ELM cycle using integrated codes developed through on-going CPES Fusion Simulation Project, as they become available.

ICRF Wave-Particle Interactions in the ICRF Regime - StatusProgress has been made in Developing a Predictive Capability for

Nonthermal Ion Tail Evolution

Using a Maxwellian fit to the CNPA data gives Tion ∼ 70 keV.

H+ ~0.1% B

Vincent Tang, MIT (PhD Thesis, 2006)

r/a = 0.46

72 keV

E. F. Jaeger, R. Harvey, L. Berry, ORNL

AORSA/CQL3D Simulation –103 processor hours

3D (r, V⊥ , V//) distribution function from CQL3D – AORSA reproduces CNPA measurements using

a synthetic code diagnostic

Synthetic diagnostic code developed through a close collaboration between theory and experiment (V. Tang and R. Harvey)

100 150 200 250 300

1012

1013

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V. Tang, PhD Thesis, MIT (2006); also PPCF, 49, 873 (2007).

Plans: Accurate Computation of ICRF-Generated Energetic Ions Will be a High Priority in 2008-2013

• Accurate calculation of 3D ion tail distributions is important for several key physics areas on C-Mod:– MHD studies of Alfven cascades.– Sawtooth modification experiments using ICRF.– Transport analysis of standard and improved confinement

(ITB) regimes.– Analysis of ICRF heated plasmas with significant toroidal

rotation.• Continue CNPA synthetic diagnostic analysis with:

– Combined CQL3D and AORSA/TORIC:• Analyze where FLR approximation breaks down.

– Combined ORBIT RF with AORSA/TORIC:• Assess importance of finite ion drift orbit effects.

– Research activities to be carried out through RF SciDACCenter

Plans: ICRF Current and Pressure Profile Control Emphasis will be to apply simulation capability to mode

conversion current drive (MCCD) and flow drive applications.

• Improve synthetic PCI diagnostic code calculations:

– Resolve scale differences between predicted and measured signals:

– Construct and compare PCI signals from AORSA and TORIC fields.

• Mode Conversion Current Drive:– Compute MCCD using TORIC and

AORSA fields in CQL3D (with appropriate quasilinear diffusion coefficient).

• Identify scenarios in C-Mod that maximize ion damping of mode converted ICRF wave (IBW or ICW):

– Compute associated flow drive.

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Work to be performed in collaboration with RF SciDAC Center

Wave-Particle Interactions in the LHRF Regime - StatusAbility to predict 3-D(p⊥, p//, r) electron distribution and LH

current density has been tested on C-Mod

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Measured and Predicted Current Densities

(φtor-Norm)1/2 ~ (r/a)

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Channel #

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J. Ko, A. E. Schmidt (Graduate students)Bonoli, Harvey, Parker, Scott, Wright

• Self-consistent nonthermal fe from GENRAY-CQL3D is used in synthetic diagnostics for hard X-ray and EC emission.

• HXR Spectra from synthetic code agree with measured profiles in magnitude (no renormalization !) –but are narrower.

nebar = 7 × 1019 m-3 Te(0) = 2.6 keVn// = 1.95 PLH = 685 kW

• Full-wave effects are being currently being investigated as a possible reason for discrepancy in hard x-ray predictions:

– Converged LH full-wave simulations have now been performed on the Loki cluster at MIT (30 hours @ 256 processors).

– This work is part of the 2008 DoE JOULE Theory Milestone

• Electron and ion plasma response in TORIC can now be evaluated using the nonthermal fe, from CQL3D (E. Valeo, C.K. Phillips, J. Wright).

• Final step is to reconstruct DQL from TORIC and pass to CQL3D and then iterate codes:

– Evaluate hard x-ray emission and nonthermal ECE using synthetic diagnostic codes.

• Collaboration with PSFC Theory and RF SciDAC

Plans: Combined LH Full-wave – Fokker Planck Simulation is major goal for 2008-2013

Plans: Linear ICRF Antenna Coupling will be achieved through TOPICA – TORIC Code Integration

• TOPICA: (Torino)– Fully 3D solid antenna structure

model (including FS, box,…)– Code runs on Marshall cluster

(parallel version can model the ITER ICRF antenna).

Alcator C-Mod: “E” – antenna

• TORIC: (MIT)– 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.

Plans: Nonlinear ICRF Antenna Sheath Simulations

• Implement a metal wall (or general sheath) boundary condition (BC) in TORIC that accounts for misalignment between metal wall and B.

– Compute the linear ICRF fields from TOPICA-TORIC.– Evaluate a sheath BC for TORIC using the linear fields.– Re-compute the TORIC fields with the new sheath BC.– Repeat process above to convergence. – Get sheath dissipation from converged fields.– Collaboration with Lodestar Research and RF SciDAC Center

• Investigate sheath dissipation for minority heating schemes in C-Mod:– Strong single pass damping – D (H)– Weak single pass damping – D (3He)

• Time domain simulations using 3D EM field solver – VORPAL– Fully implicit time domain dielectric response module has been implemented

for electrons and ions.– Use PIC-treatment for ion response (fully nonlinear).– Collaboration with Tech-X and RF SciDAC Center

Time Dependent Integrated Scenario Modeling - Status Simulations began in 2003-2008 using TSC

• Simulations presently use TSC – LSC:– TSC performs discharge evolution using 1.5D transport equations, free

boundary MHD solver, and LSC code for the LHCD. – Model profiles for ICRF heating.– Tang-Coppi micro-instability based χe– Collaboration with PPPL.

• TSC – LSC Simulation with H-mode Plasmas Can Produce High fNIand Drive q(0) > 1 (C. Kessel, PPPL):

ICRF on LH on

Plans for 2008-2013 will be to Improve the Physics Components in Time Dependent Integrated Scenario

Modeling• Active efforts through PPPL, ITPA-SSO, RF SciDAC Project, and

SWIM/FACETS FSP Projects to improve the ICRH, LHCD, and transport models used in time dependent TSC simulations:

– Incorporate 3D Fokker Planck simulations for LHCD from CQL3D-GENRAY:

– Include self-consistent ICRF tail formation from AORSA/TORIC –CQL3D:

– Include predictive transport capability through TGLF:– Partial solution is to perform combined simulations with TRANSP and

TSC:• TRANSP computes LHCD using LSC, ICRH using TORIC, and transport using

GLF23.• Plasma is evolved using these source terms in TSC.

• Need to develop kinetic closure relations for coupling RF and MHD codes (J. Ramos, PSFC Theory and SWIM Project)

– Application to NTM stabilization via ECCD and LHCD.– Application to sawtooth stabilization via energetic particles (ICRF).– 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.

Plan to ultimately employ parallel frameworks being developed under existing Fusion Simulation Projects

Python Driver Script

TSCDriver

CQL3DGENRAY

AORSA TORIC

Ideal MHDStability

Plasma State (equilibrium/geometry, profiles, scalars)

… ExperimentData

“Integrated Plasma Simulator -IPS”developed through SWIM Project.

Collaboration with D. B. Batchelor and SWIM

New PSFC Parallel Computing Cluster - Loki

T. Baker, D. Ernst, J. Wright

• Status:– 256 Opteron processors in 64 nodes.– Infinipath and Gigabit network

connectivity.– Nonlinear GK simulations can be

done in-house.– Full-wave LH field simulations

can be done in 4.6 hours (required six days on old Marshall cluster).

• Plans:– Upgrade to 512 cores with quad

core processors.

Summary• Alcator C-Mod benefits from advances in theory and

simulations and promotes 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• Predictive LHCD capability using CQL3D• Synthetic diagnostic codes for hard x-ray emission, CNPA, and

nonthermal ECE• Predictive capability for minority heating and quasilinear tail formation.• Full-wave LHRF studies using TORIC LH• 3D ICRF antenna modeling using TOPICA (Torino)

– Understanding TAE mode and Alfven cascade observations in C-Mod using NOVA-K

– Integrated scenario development using TSC & TRANSP – Disruption mitigation using NIMROD, KPRAD– Pedestal and edge modeling with ELITE, BOUT, ESEL, GEM– Graduate student training a key part of the program

Summary

• During the next five years we plan to continue to develop a predictive capability in these areas by:– Taking advantage of theoretical advances.– Employing advanced simulation codes and integrated models

(when available).– Validating predictive capability using synthetic diagnostic codes

and developing metrics for these comparisins.– Applying predictive capability to ITER.

• Targeting key problem areas:– Radial electric field in the edge– ICRF – antenna edge interactions– Full-wave effects in LH wave propagation– Simulation of the ELM cycle.– Prediction of pedestal characteristics– Transport of energetic particles due to Alfven wave activity

Strong Relationship Between Theory / Simulation Research on C-Mod and ITER / ITPA

ITER / ITPA Topical Area

Contributing Activity in Theory and Simulation

Scrape Off Layer and Divertor

- Improve understanding of plasma transport to targets and walls through validation of simulation codes (ESEL, BOUT, and GEM).

MHD - Application of NIMROD + KPRAD simulation model to simulate gas jet injection mitigation experiments on C-Mod helps to develop reliable disruption prediction methods.

- Application of NOVA-K with realistic fast ion distributions and SparSpeccodes to AE and Alfven cascade experiments in C-Mod contributes to the understanding of intermediate-n AE’s and energetic particle modes.

Steady State Operation - Comparison of synthetic diagnostic codes for CNPA, PCI, hard x-rays, and ECE contribute to ICRF and LHRF code benchmarking activities.

- TSC simulations of ramp-up, hybrid, and steady state scenarios in C-Mod with ICRH and LHCD contribute to the focused modeling-benchmark activities for ITER hybrid and steady state scenarios.

Transport Physics - ICRF flow drive and LHCD simulations for C-Mod contribute to the development of turbulence stabilization mechanisms compatible with reactor conditions.

- GS2 and GYRO simulations of ITB’s with ICRH and LHCD in C-Mod contribute to the understanding of improved core transport physics in reactor relevant plasmas with Te ≈ Ti and low momentum input.

Strong Relationship Between Theory / Simulation Research on C-Mod and ITER / ITPA

ITER / ITPA Topical Area Contributing Activity in Theory and Simulation

Confinement Database and Modeling -Simulation of C-Mod integrated scenarios using the Integrated Plasma Simulator (IPS) and Plasma State frameworks contribute to the development of common technologies for integrated modeling.

Pedestal and Edge Physics -Simulating edge turbulence data in C-Mod using the ESEL, BOUT, and GEM non-linear fluid codes will contribute to the testing of non-linear MHD and turbulence models of ELM evolution and will improve the capability for small ELM regimes.-Using the XGC0 and XGC1 codes to simulate the pedestal structure and scalings measured in C-Mod will contribute to improving the predictive capability of pedestal structure.