Performance of Spectral MSE diagnostic on C-Mod

and ITER

K.T. Liao1, W.L. Rowan1, R.T. Mumgaard2,

Bob Granetz2, Marchuk3, Y. Ralchenko4

1The University of Texas at Austin, Institute for Fusion Studies, 2MIT, Plasma Sciences and Fusion Center,

3Forschungszentrum Jülich , 4National Institute for Standards and Technology

57th Annual Meeting of the APS Division of Plasma Physics

November 16-20, 2015; Savannah, Georgia

Introduction

We have created a detailed synthetic diagnostic for the Spectral

Motional Stark Effect and applied it to Alcator C-Mod, ITER,

and EAST.

Several features of the code are presented, including a newly

identified source of broadening called spot broadening.

Performance of magnetic field |B| measurements has been

predicted for each device under various plasma scenarios.

Experimental results for Alcator C-Mod at 5.6T show similar

error to prediction by synthetic diagnostic.

A proposal has been approved to make measurements on Alcator

C-Mod at 8T, which will give a much-needed comparison at

ITER-equivalent magnitude of Stark splitting

at ITER field of 5.3T

What is Spot Broadening?

zero spot size finite spot size

Previous BES models [Bracco (1981), Marquet (1967)] assume zero spot (pre-image) size

and do not include spot broadening

A realistic optical system has a finite spot size, necessary for finite étendue

The calculations for spot broadening are the same as for aperture broadening, replacing

the aperture radius with the spot radius

Combined aperture and spot broadening is a convolution of two semicircular distributions

λ

I

Sample lineshape: equal

aperture and spot sizes

D

2r

Physics of MSE Spectrum

Fast beam atoms moving through a B field experience a Lorentz E field EL

Stark Effect:

EL field splits energy levels

Emission is polarized:

π—parallel projection of EL

σ—perpendicular proj. of EL

In nkm parabolic basis: (atomic units)†

weak

†Condon and Shortley. The Theory of Atomic Spectra. (1959)

Synthetic Spectrum Model

Synthetic spectral model includes

– Stark+Zeeman eigenfunctions + quadratic Stark perturbation

– non-statistical beam excited population

– plasma variation along viewing chord

– beam grid pattern broadening

– finite beam width broadening

– aperture broadening

– spot focus broadening

– beam energy ripple broadening

– instrumental broadening

– photon shot noise

– fractional energy beam components

– bremsstrahlung

– CXRS of thermal D

– neutral halo

– relativistic Doppler effects

Reduced Fitting Model

Fitting model includes

– Stark+Zeeman eigenfunctions + quadratic Stark perturbation

– non-statistical beam excited population

– simplified line broadening

– fractional energy beam components

– simplified CXRS background

Fit parameters (for 1 beam component case):

– A0: wavelength shift

– A1:

– A2: intensity scaling for MSE spectrum

– A3: width of MSE lines (assumed to be equal and Gaussian)

– A4: intensity scaling for CXRS component

– A5: center of CXRS component

– A6: width of CXRS component (assumed to be Gaussian)

– A7:

Calculation Flow Chart

ALCBEAM

neutral beam model

BES spectrum

Dα CXRS

Bremsstrahlung

+

+

Calculate

geometry

emission

spectrum

detector

model

For each chord point

Edge

spectrum + =

synthetic

spectrum

Spectral

MSE fitting

Magnetic field

measurement

Spectral MSE

performance

ALCBEAM

ALCBEAM simulation of EAST heating beams viewed from above

a) full energy component. b) neutral halo

a) b)

ALCBEAM† provides 3D neutral beam density and velocity distribution simulation

Recent update provides a new halo calculation based on a diffusion model

†I.O. Bespamyatnov, W.L. Rowan, K.T. Liao. Computer Physics Comm. 183 (2012) 669

Halo calculation

diffusion ionization CX source

Halo transport dramatically decreases

the central halo density

(by a factor of 20 on EAST)

EAST HNBI simulation with and

without transport, which is modeled

as a random walk diffusion process

cf. Stratton et al. Nucl. Fusion 30 4 (1990);

Tendler and Heifetz. Fusion Techno. 11 1987

Finite Grid Effects

Each beam grid aperture accelerates some atoms toward the view spot

Each beam ray intersects the viewing chord spot at a different angle

Each angle is weighted according to Gaussian beamlet divergence

Repeat for each spot along (discretized) viewing chord

grid apertures

Analysis of line shifts requires an accurate model of energy levels

Quadratic corrections in Stark Effect are important on C-Mod and ITER

(up to 1.5% on C-Mod, 1.5-5% on ITER)

Zeeman effect is also included as additional 1.5% correction for C-Mod, but

may be neglected for ITER (0.15-0.75% effect)

Stark+Zeeman eigenvalues [R.C. Isler. Phys Rev A. 14, 3 (1976)]

Quadratic corrections added as a perturbation

Fine structure corrections have been tested but have negligible effect on the

splitting (~0.02Å) and complicate the analysis (from 15 lines to 144)

Hα atomic model

C-Mod 5.6T Measurements

0

3

4

1

Blocking

bar on Dα

We performed MSE Line Shift and Line Ratio fitting on measured spectra

model

DNB was modulated 50ms on, 25ms off to subtract background bremsstrahlung

and impurity lines

An opaque blocking bar was used to filter the bright Dα signal to reduce blooming

since passive Dα is much brighter than beam emission on Alcator C-mod.

Results are compared with Kinetic EFIT

C-Mod 5.6T MSE-LS Fitting

Fitting was performed on 15 spectra from shot 1120621026

Lines are poorly resolved. 4 spectra failed to fit

Fitting is very difficult when lines are not resolved because Levenberg-

Marquardt algorithm will often converge in local minima

Error is roughly 0.1T

8T Experiment Planned For 2016

8T test on C-Mod will allow better line resolution and produce equivalent

line splitting as ITER DNB

Line resolution will be increased further by decreasing the aperture size

Simulations show that when line resolution is improved, fitting robustness

is greatly improved

Optics are reconditioned for improved throughput

C-Mod DNB ITER DNB

Eb 50 keV 100 keV

B0 8 T 5.3 T

EL =γvbB┴ 24.8 MV/m 23.2 MV/m

Simulation of 2012 configuration

|B| = 5.04T (weighted average)

Fit 1000 synthetic spectra:

|B|fit = 5.04T ± 0.11T (1σ)

Alcator C-Mod Synthetic Diagnostic

Simulation of 2016 optimized

configuration

|B| = 7.21T (weighted average)

Fit 1000 synthetic spectra:

|B|fit = 7.189T ± 0.005T (1σ)

Standard deviation is similar to

uncertainty inferred from

experiment

ITER Spectral MSE Performance

We assume the following parameters

Etendue 1mm2/sr

quantum efficiency 90%

optical transmission 0.5%

dispersion 0.2 Å/pixel, 3 Å/mm

instrument function 0.3 Å

slit width 0.1 mm

aperture width 3.4 cm

spot width 3.4 cm

periscope position U-2, U-3, E-2, E-3

beam energy 100 keV

beam current 35.4 A (after neutralizer)

beam position E-4, 6° tilt

Spectral fitting

periscope R LS std-dev |B| LR std-dev θpitch

U-3 7.48m 0.0016T 0.086°

U-2 7.48m 0.0008T 0.051°

E-3 7.48m 0.0006T 0.12°

E-2 7.48m 0.0003T 0.10°

Upper periscope positions are better for Line Ratio measurements

Equatorial periscopes are better for Line Shift measurements

ITER Synthetic Spectra (Equatorial)

Periscope pos: E-port2

View: R=6.88m

The equatorial ports have higher Stark-π line intensity and are better for line shift

measurements for |B|.

E-2 has better performance due to lower bremsstrahlung background

Periscope pos: E-port3

View: R=6.88m

ITER Synthetic Spectra (Upper)

Periscope pos: U-port3

View: R=6.89m

Periscope pos: U-port2

View: R=6.88m

U ports have better sensitivity for π/σ ratio measurements because the angle

between the view and electric field is closer to the optimal angle of 62.1°†

†N.A. Pablant. Ph.D. Thesis. University of California, San Diego (2010)

ne Sensitivity

Performance degrades very quickly at higher electron densities due to poor beam

penetration in the core.

High density H-mode

ne0 = 2.32 ×1020 m-3

using Te, ne profiles from

Casper et al. Nucl. Fusion 54

(2014)

Low density H-mode

using parabolic Te, ne profiles

from Kappatou et al. Nucl.

Fusion 52 (2012)

ITER MSE-LS Performance vs. Radius

Raxis Raxis

Performance drops rapidly toward inner radii

Nevertheless MSE-LS can provide a useful constraint for EFIT reconstructions

ne0 = 2.32 ×1020 m-3

ne0 = 1×1020 m-3

EAST Synthetic Spectra

We use our code to test the performance of MSE-LS on EAST

High blending at EAST parameters (BT = 3.5T; Ebeam = 30keV/amu)

Somewhat compensated by improved beam penetration and very low

bremsstrahlung

full

1/2

1/3

std-dev |B| = 0.01T

std-dev pitch = 1°

Raxis

Performance Drivers (C-Mod DNB)

The synthetic diagnostic can provide insight into factors affecting performance

Complex B dependence due to “interference” between beam components.

Conclusions

Spectral MSE can provide accurate measurements of |B|, but

performance varies greatly with experimental parameters

Error decreases with square root in signal intensity and increases

roughly linearly with line broadening and slowly with background

intensity

This diagnostic can provide direct measurements of |B| and pitch angle

for ITER or be used to constrain EFIT reconstructions

(cf. Foley et al. RSI 79, 10F521 (2008))

Equitorial ports on ITER provide better |B| measurements, while upper

ports provide better pitch angle measurements