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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Kenneth Teh-Yong Liao
University of Texas at Austin
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Helium Charge Exchange Recombination Spectroscopy
on Alcator C-Mod Tokamak
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Overview
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IntroductionCharge Exchange Recombination Spectroscopy (CXRS)Helium TransportRole of Minority in ICRF HeatingConclusion
OverviewIntroduction
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Fusion Energy
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Tokamak (magnetic confinement)
Fusion EnergyIntroduction
TransportParticlesEnergyMomentum
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Alcator C-Mod Tokamak
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Alto Campo Torus (high field torus)
Fusion EnergyIntroduction
Compact
High Field
Density
Pulse Duration
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Alcator C-Mod
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Fusion EnergyIntroduction
DNBI
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Interactions (partial list):
1. DNB charge exchange
2. Halo charge exchange
3. Spontaneous emission
4. Ionization
Charge Exchange Recombination Spectroscopy
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Physics of CXRSCXRS
Neutral Beam
1,23
4
B
Ip
Beam Halo
Gyro orbit
collection optics
chord
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
CXRS Spectrum
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Physics of CXRSCXRS
Most of signal is background and must be subtracted
Chord-integrated signal at detector
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
Spectral emissivity per volume per solid angle
This quantity is integrated along a viewing chord to give spectral radiance
synthetic spectra
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
Beam Distribution Function
Beam density modeled using beampropagation code (ALCBEAM*)
I. Bespamyatnov, W. Rowan, and K. Liao. Computer Physics Communications, 183(3):669-676, 2012
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
He2+ Ion Distribution Function
If Maxwell-Boltzmann shape is assumed, can fit for
During ICRF, may not be Maxwellian
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
Effective photon emission rate coefficient
Many possible branches:
radiative branching factors
4686 Å
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
Effective emission rate coefficient
Calculate using ADAS 309CR modelall branching factorsn=4…20
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Emission Model
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Physics of CXRSCXRS
Atomic line emission model
Doppler shift
Zeeman/Fine structure cluster
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
CXRS Apparatus
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ApparatusCXRS
C-Mod “Cell” Diagnostics lab
F-port
Poloidalview
Toroidalview
Detector
DNBI
F-Top
Optical Fibers
PC
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Beam is modulated to allow background subtraction
Analysis
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AnalysisCXRS
Analysis WidgetScreenshot
beam modulation60 ms on20 ms off
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Line fitting
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AnalysisCXRS
Fit Gaussians using MPFIT:
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
CXRS Profiles
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ResultsCXRS
Database with55 3He shots (473 time points)123 4He shots (1179 time points)
Random errors estimated using Monte Carlo technique
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Transport Introduction
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Transport IntroductionTransport
1D transport ansatz
For Equilibrium Plasma
Continuity equation
Steady state density measurements give us the ratio v/D
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Turbulent Transport
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Turbulent TransportTransport
Drift wave turbulence
(assume electrostatic)
Expansion into Fourier modes
Driven unstable by thermodynamic gradients and bad curvature
motion
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Turbulence Classification
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Turbulent TransportTransport
Mode abbrev. Free energy λ, ω scale Driver
Trapped Ion Mode TIM
trapped ion precession resonance
Trapped Electron Mode
TEMtrapped electron precession resonance
Ion Temperature Gradient
ITGtemperature gradient and bad curvature
Electron Temperature Gradient
ETGtemperature gradient and bad curvature
Dominant mode typically ITG, sometimes TEM
TEM and ITG transport impurities in opposite directions
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Shot Database
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Turbulent TransportTransport
1179 time points from 123 shots
473 time points from 55 shots
D(3He) plasma D+4He impurity plasma
all radii all radii
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Gyrokinetic Transport
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Turbulent TransportTransport
Diffusion
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Gyrokinetic Transport
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Turbulent TransportTransport
Curvature pinch
Estimate Cc using 5 similar shots varying Ip
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Gyrokinetic Transport
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Turbulent TransportTransport
28 shots with 3He
Thermodiffusion pinch
Poor fit statistics
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Gyrokinetic Transport
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Turbulent TransportTransport
Parallel compression pinch
Scales with
*N. Dubuit, et al. Physics of plasmas, 14:042301, 2007
Negligible* for realistic
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Gyrokinetic Transport
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Turbulent TransportTransport
rotodiffusion pinch
Inward (outward) for TEM (ITG) dominated turbulence
Not yet studied on Alcator C-Mod
F. Casson, et al. Nucl. Fusion, 53(6):063026, 2013.
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Helium Puff Experiment
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Cannot separate and using equilibrium profilesUse time dependent profiles to measure and separatelyAssume and are independent of time!
Helium Puff ExperimentTransport
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Time Resolution
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Helium Puff ExperimentTransport
Require high time resolution
Too fast for standard time-slice subtraction method
Combine three “identical” shots to improve time resolution
Beam timing is shifted by different amounts per shot
10 ms frame time
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
STRAHL fitting
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Run STRAHL with initial guess for ,Iterate:
Compute Goodness of Fit
Generate new , by adding random value to current best fitIf a better (lower) fit is found, reduce random variance
Helium Puff ExperimentTransport
STRAHL is a 1D transport code which solves
for a numerical flux geometry
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Best-Fit Transport Parameters
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Helium Puff ExperimentTransport
outside CXRS window
outside CXRS window
Smoothed results after finding best STRAHL fit
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Machine Comparison
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Helium Puff ExperimentTransport
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
GENE Gyrokinetic Simulations
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Gyrokinetic SimulationsTransport
“Gyrokinetic Electromagnetic Numerical Experiment”
F. Jenko, et al. Physics of plasmas, 7:1904 (2000)
Solves linear or nonlinear gyrokinetic Vlasov equation as an initial value problem on a flux tube geometry
State variables:
Run on “Stampede” 102400 core cluster at Texas Advanced Computing Center
~100 CPU-hours for a linear run (scan over ky modes)~10000 CPU-hours for a nonlinear run
deviations from equilibrium
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Linear/Nonlinear
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Gyrokinetic SimulationsTransport
Linear run:obtain growth rate and frequency for fastest growing modeturbulence grows without boundobtain flux ratios (e.g. or )
Nonlinear run:obtain particle/heat fluxes and saturated power spectrum
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Quasilinear Analysis
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Gyrokinetic SimulationsTransport
Used to estimate absolute fluxes from linear runs
Scaling/Correction factor
Heuristic estimate of amplitude of saturated turbulence
Flux ratio (linear run)
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Nonlinear Power Spectrum
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Gyrokinetic SimulationsTransport
*M. Barnes, F.I. Parra, A.A. Schekochihin. PRL 107, 115003 (2011)
Spectra show power law decay which agrees with critical balance scaling*:
Turbulence has typical ITG wavelength scale
Nonlinear correction factorTurbulence Power Spectrum
quasilinear heuristic
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Quasilinear and Nonlinear Fluxes
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Gyrokinetic SimulationsTransport
Nonlinear simulation for single point used to obtain
Same value of extrapolated to all radial points to compute quasilinear flux
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Simulated Transport Coefficients
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Gyrokinetic SimulationsTransport
1120822020, ρtor=0.5
propagateduncertainty
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Experimental vs Quasilinear v/D
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Gyrokinetic SimulationsTransport
Rather poor agreement
Comparison of 9 shots from run 1121001
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
AORSA-CQL3D
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AORSA-CQL3D SimulationICRF
CQL3D provides distribution functions via quasilinear Fokker-Planck
3He midplane distribution function from CQL3Dshot 1121001003, Rmid=0.7439m
ln f(v)
E||α from AORSAshot 1121001003, J-port RF: 1.0MW
R (m)
Z (m)
AORSA provides solutions for mode conversion and high harmonic fast wave heating
Coupled solver† used to solve power deposition and fast ion distribution †E.F. Jaeger, R.W. Harvey, et al. Nucl. Fusion 46 (2006) S397-S408
Fast magnetosonic wave
Ion Bernstein mode converted wave
minority 3He resonance
Ion-ion hybrid resonance
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Kenneth T. Liao Helium CXRS on Alcator C-Mod Tokamak
Summary
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Measured Helium Density, Temperature, Velocity profiles for 3He and 4He on Alcator C-ModObtained transport parameters D, v, Cc, CT
Compared transport with gyrokinetic simulationsSimulated effects of minority density profiles on ICRF heating
ConclusionConclusion