Performance of Spectral MSE diagnostic on C-Mod and ITER · Performance of Spectral MSE diagnostic...
Transcript of Performance of Spectral MSE diagnostic on C-Mod and ITER · Performance of Spectral MSE diagnostic...
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