kenneth t. liao kenneth teh-yong liao university of texas at austin helium cxrs on alcator c-mod...

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


Overview

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IntroductionCharge Exchange Recombination Spectroscopy (CXRS)Helium TransportRole of Minority in ICRF HeatingConclusion

OverviewIntroduction


Fusion Energy

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Tokamak (magnetic confinement)

Fusion EnergyIntroduction

TransportParticlesEnergyMomentum


Alcator C-Mod Tokamak

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Alto Campo Torus (high field torus)


Compact

High Field

Density

Pulse Duration


Alcator C-Mod

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DNBI


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


CXRS Spectrum

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Physics of CXRSCXRS

Most of signal is background and must be subtracted

Chord-integrated signal at detector


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


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


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


Emission Model

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Physics of CXRSCXRS

Effective photon emission rate coefficient

Many possible branches:

radiative branching factors

4686 Å


Emission Model

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Physics of CXRSCXRS

Effective emission rate coefficient

Calculate using ADAS 309CR modelall branching factorsn=4…20


Emission Model

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Physics of CXRSCXRS

Atomic line emission model

Doppler shift

Zeeman/Fine structure cluster


CXRS Apparatus

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ApparatusCXRS

C-Mod “Cell” Diagnostics lab

F-port

Poloidalview

Toroidalview

Detector

DNBI

F-Top

Optical Fibers

PC


Beam is modulated to allow background subtraction

Analysis

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AnalysisCXRS

Analysis WidgetScreenshot

beam modulation60 ms on20 ms off


Line fitting

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AnalysisCXRS

Fit Gaussians using MPFIT:


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


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


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


Turbulence Classification

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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


Shot Database

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1179 time points from 123 shots

473 time points from 55 shots

D(3He) plasma D+4He impurity plasma

all radii all radii


Gyrokinetic Transport

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Diffusion



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Curvature pinch

Estimate Cc using 5 similar shots varying Ip



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28 shots with 3He

Thermodiffusion pinch

Poor fit statistics



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Parallel compression pinch

Scales with

*N. Dubuit, et al. Physics of plasmas, 14:042301, 2007

Negligible* for realistic



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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.


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


Time Resolution

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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


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


STRAHL is a 1D transport code which solves

for a numerical flux geometry


Best-Fit Transport Parameters

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outside CXRS window

outside CXRS window

Smoothed results after finding best STRAHL fit


Machine Comparison

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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


Linear/Nonlinear

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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


Quasilinear Analysis

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Used to estimate absolute fluxes from linear runs

Scaling/Correction factor

Heuristic estimate of amplitude of saturated turbulence

Flux ratio (linear run)


Nonlinear Power Spectrum

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*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


Quasilinear and Nonlinear Fluxes

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Nonlinear simulation for single point used to obtain

Same value of extrapolated to all radial points to compute quasilinear flux


Simulated Transport Coefficients

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1120822020, ρtor=0.5

propagateduncertainty


Experimental vs Quasilinear v/D

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Rather poor agreement

Comparison of 9 shots from run 1121001


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


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

kenneth t. liao kenneth teh-yong liao university of texas at austin helium cxrs on alcator c-mod...

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