Page 1 - Development of Spatial Heterodyne Spectroscopy Measurements for the C-2W Plasma Expansion Divertor

1.0
0.8
0.6
0.4
0.2
DC magnets
• Assumed • s/photon
Ionization in Outflow Jet Plasma
0.0
3.0 ne(r,z=2.1)=nel/(a π)exp−(r/a)2 0.17 Gaussian model 50
+Z
35◦ FOV
+Y
tunable parameters:
• λ: speed vs. stability
• FHP(x): high-pass filter shape, cut-o
frequency
residual errors typically ± ∼25% due to non-axis-symmetry
Degas2 interpretive modeling does not have this limitation
0.7 0.6 0.5 0.4 0.3 0.2 0.1
0.07 0.6 0.5 0.4 0.3 0.2 0.1
1e19
+Z
(192 px, 0.52)
0.5 0.0 0.7
0.4 0.6 0.5 0.3 0.4
160
48 5000
18 μs 23 μs 27μs
S divertor
equilibrium vessel
biased electrode
N formation
N divertor
6–12 ionization-
1000
800
600
400
200
3.5 1200 400
Jet camera
Bias B-field coils
Quadrupole RMF Antenna
pulsed magnets
1.5 1.0 0.5 0.0
012345678 Time [ms]
0.13
0.12
see poster BP11.00045 (Erik Trask) for description of quadrupole
Instrument Design Viewed of both sides of the plasma jet
+Y side view +X
3,4 Algebraic Reconstruction Technique
• Apply Gaussian smoothing to image • Back-projection: ε = PT · b
Iterate back-projected error to conver-
0.11 10
0.10 0 0.00
0.05 0.10
0.15 0.20 0.25 R [m]
0.30
axial camera
◦ FOV
jet camera
60
•
Vz,i(z=2.1)=Φtot/(2nel(z=2.1)a π)
0 1 2 3 4 5 6 7 8
Compact jet imager operated in 2.5 kG magnetic field
Sputtering and re-deposition led to coating buildup on jet camera viewport
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.25 0.20 0.15 0.10 0.05 0.00 0.25 0.20 0.15 0.10 0.05 0.00 0.25 0.20 0.15 0.10 0.05 0.00
6.5 6.0
0.30 0.25 0.20
ART emissivity shot:45728
S formation
A er ∼ 2 ms ionization ≲ half core particle loss rate to each side
2.5 Φtot =
2.0
1.5
1.0 100
5
FRC 5
Optics calibration
Photometric calibration
40 0.14 30
Fast imaging measurements and modeling of the C-2U outflow jet and pre-ionization plasmas
C-2U1 machine layout
E.M. Granstedt, E. Trask, S. Krause, R. Smith, D. She man, the TAE Team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 Jet Imaging
Degas25 interpretive modeling CV measurements initialize jet
Pre-ionization (PI) study Test stand constructed to improve RMF PI
R [cm]
R [cm]
R [cm]
R [cm]
px
Bz [T]
Vz,i(z=2.1) [km/s]
1019m−2 or m−3
1019
−SE,D+ [W/m−3]
−SE,e [W/m−3]
Sioniz [m−3 s−1] R [cm]
nHeff [m−3] R [cm]
Brightness [W/m2-sr] R [cm] px
O4+ emissionradius[m] Te [eV]
A electrons Ti [eV]
1467855532
1467855316
NUC: Relative illumination
1467855550
1467855327
1467855613
1467855349
t: 4.01 ms, m
t: 1.73 ms, m t: 0.15 ms, m
t: 7.79 ms, m
t: 4.43 ms, m
t: 2.85 ms, m
t: 1.07 ms, m
Jet Camera t: 0.649 ms
1467855639
1467855398
1467855658 W/m2-sr
1467855515 W/m2-sr
Axial Camera t: 5.785 ms
bCVaxial
R [m]
px
px
PCVaxial
Pjet
bjet
−SE,D+ [W/m−3]
−SE,e [W/m−3]
Error [W/m2-sr] nHeff [m−3]
Ti [eV]
Te [eV]
ne [m−3]
W/m2-sr
W/m2-sr
W/m2-sr
W/m2-sr
W/m2-sr
datum index
R [cm]
R [m]
R [m]
R [m]
Sioniz [m−3 s−1]
728.1 nm 706.5 nm 667.8 nm
Time [μs]
668nm / 707 nm ratio
668nm / 728 nm ratio
728nm / 707 nm ratio
W/m2-sr
Jet o set axial view
CV axial view
Radius (meters)
Transmission or QE
far (z: -1.7 m) center (z: 0.0 m)
near (z: 1.3 m)
O1+ 3p 3s
Ar1 + 4p(2 F) 4s
C2+ 3p 3s
Ar1 + 4p(2 D) 4s
O5+ 8 7
O4+ 4p 4s H/D-α
He0+ 3d 2p
He0 + Ar0 + He0 +
3s(3 S) 2p 4p(2 F) 4s 3s(1 S) 2p
Jet Camera t: 1.593 ms
Jet Camera t: 5.792 ms
shot: 45728
jet plasma
plasma gun
2.5 a(z= −2.0m) 0.16 Flat model 2.0 0.15 Triple probe
3.7 m
0
Cylindrical axis (meters)
•
• black annodized “light-blind” reduced reflections from flange
• mapped nonlinear detector re- • sponse
Relative response
Optics nonuniformity
BP
Simple ``Trial'' model for jet plasma
• T a flux function e
t: 20μs t: 25μs t: 30μs t: 55μs t: 60μs t: 65μs
100
10-1
10-2
•
Jet Camera Viewport Transmission
clean viewport 2016-Feb-29 Post-Run
2015-Nov-13 Post-Run 2016-Jun-10 Post-Run 2016-Jan-14 Post-Run
separate neutral sources along each wall Initial estimated n , T from He0+ imaging •ee
absolute photon e iciency measuredforeachfilter
gence: k+1 k

• n = n , T , v : ions undergo isentropic compression/expansion e iiz
1.0 0.8 0.6 0.4 0.2 0.0
1.0 0.8 0.6 0.4 0.2
(64 px, 0.97) (96 px, 0.95)
(128 px, 0.91)
0
300
400
Wavelength [nm]
Shot 45728 Formation Camera Best Fit, t: 2643us Timin Temin
QE and transmission
relay optics (theoretical transmission)
Edgertronic QE
Phantom v5.2 QE
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
22.5 20.0 17.5 15.0 12.5 10.0 7.5 5.0
t: 70μs
t: 75μs
t: 80μs
t: 95μs
t: 105μs
t: 125μs
350 400 450 500 550 600 650 700 750 800 0.00 50 100 150 200 250
•
0.3 0.1
Wavelength [nm]
Radial distance [px]
6 0
500 600
e
T
•ε =ε +λ P ·FHP b−P·ε
k
along flux tubes
8 7 6 5 4 3 2
Inferred from particle balance 1
D emission
42 140
36 37μs
30 120 4000 47μs
24 57μs
18 72μs 12 100 3000 102μs
α
• reconstruction artifacts due to emission at edges of field-of-view
0.2
0.1 0.2
54 48 42 36 30 24 18 12 6 0
32 28 24 20 16 12 8 4 0
24
21
18
15
12 50 9
Synthetic images constrain unknown source magnitudes
Radial px
Radial px
axial camera est. ioniz. rate [A] jet camera est. ioniz. rate [A] core electron loss rate [A]
−dN /dt
e 350
R: 0.56 m R: 0.47 m R: 0.52 m R: 0.38 m
1.0 1.5 2.0 Time [ms]
R: 0.44 m R: 0.32 m R: 0.34 m
2.5 3.0
0.35 0.40
0
0 2 4 6 8 10
ms
200 50 0
3.0 1000 ΦNB
0.5
0.0 0 0.0 0.5
Ne
3.5 0.18 nel(z= −2.1m)
60
1.0
0.8
0.6
0.4
0.2
0.0
0.7
0.6
R center [m]
0.0 0.2 0.4 0.6 0.8 1.1 1.4 1.8 2.3 0.0 0.2 0.4 0.6 0.8 1.1 1.4 1.8 2.3
Bz
M (t=2.6 ms)
6000
Time [ms]
300 −dN/dt + ΦNB 800 250
600
150
400
0.0 0.0
0 2 4 6 8 10 0 2 4 6 8
80
2000 40 1000
20
020406080100120140160 020406080100120140
Fit
100 50 0 50 100 px
Error
Z [m]
Z [m]
60
200
20
antenna, operating parameters
Dα movies indicate discharge transition
•
• •
synthetic camera to compare with measurements
NNLS used to adjust source magnitudes to best
experimentalimages
match
• 667.8, 706.5, 728.1 wavelengths measured over 3 shots
19 −
⇒ 1/9 He, 8/9 D atoms, 4 × 10 e injected
1.0 105 16 0.8
20% He, 80% D
n toohigh.Improvewithsimultaneous2λimaging?
t: 65 μs
12 0.6 8 0.4
18 μs 22 μs
0.2
0.1
26 μs 42 μs
50 μs 58 μs
70 μs 82 μs
0.8 1.0 1.2
0.4 0.5 0.6
2
R center [m]
27 cm
Model View Sensor Typ. Frame
150
100
50
O4+ 3d → 3p (650 nm) ART emissivity shot:48787
0.9 0.8 0.7 0.6 0.5
0
Neutral e ects on ``trial'' plasma jet model 10
50
100
←0.6
1.5 1.0 0.5 0.0 0.5 1.0 1.5 Z [m]
40
100 50 0 50 100 150 px
10 1
Camera Specifications
6 3 0
13.5 12.0 10.5 9.0 7.5 6.0 4.5 3.0 1.5 0.0
f camera, 2643us_Timin_Temin
Vision Research Phantom v5.2
CV Axial 10.3x13.2 mm, 12 bit 256x256 @ 15,564 fps
Sanstreak Edgertronic
Jet Axial 17.92x14.34 mm, 10 bit 240x160 @ 10,114 fps
Axial Camera Coordinate Mapping, method: ext+int+2rad
0
17
Simulated forward projection
50 0.00 50
0.25 2.25 60
21 50 40 1020 30 20 10 0
0.2
70
0 0 20
152.00 1.75 101.050 1.25 51.00 0.75 0.50 0
canned Te, Ti over factor of 2, n 5x
0.0 0.2 0.4
→
40
60
80 100
50
10
10
3
22 •
erences for CV axial view
0.20 1.75 40 1.50
3 102
(r −rpk)
50
150 100 50 0 50
50
150 100 50 0 50
50
150 100 50 0 50
50
10050 0 50100
150 100 50 0 50
4.5 4.0
m10050 0 50100
1.25 30 50
1.00 20
10
, ψ(r,z) = Hill(r,z;rpk,l), e(r,z) = e(ψ)
0.6 60
0.4 40
e(r) = sech2
(rpk, α, l) = (0.20 m, 0.21 m 1.00 m)
0.15
100.1500 0 50100
0.05 0.00 0.25 0.20 0.15 0.10 0.05 0.00
2
α
19
80
checkerboard pattern used as • references for jet view
pixel sightlines integrated to form • projection matrix P
measured b = P · ε (emissivity)
10
20
600 800
60 4
50 0 50 100 px
30
102
Spatial calibration used checkerboard and machine references
90
75
60
45
30
15 0
generic camera model2
datums mapping
20000
15000
10000
5000 x
y
r
8 4 0 4 80
Residual [px]
mean: 1.078 σ: 1.190
15 22 10 20
R max [m] 0.4 0.6
R center [m] 0.2 0.3
aperture position x ••0
50 0
120
200 400 600 800 16 18
extrinsic parameters:
0
Z [cm]
100 50 0 50 100 10 14
• orientation: pitch, yaw, roll • polynomial radial function
19
4 3 2 1
105 104
6
0.0 5
4 3 2 1
••
• 2 focal lengths, skew, center 0.5
Z [cm]
2-5 params
intrinsic camera parameters:
70 10 60
pixel o set
• CAD geometry (ports) used as ref-
0.0
0100 1
50
2
3 4 1005 r-residual [px]
50
6
7
100 0.05 100
0
10.01 0 200
0 70
200
200
400
Z [cm]
400
Z [cm]
600
600
800
800
0.7 0.6
DCA07BCoordinate Ma0.1p5ping, method: ext-int-2rad
5.5 5.0
4.5
4.0
3.5
3.0
px
1021 12 10 1020 8
m
2.00 50 00000
10 10
10050 0 50100
10050 0 50100
10050 0 50100
10050 0 50100
10050 0 50100
10050 0 50100
60 50 40 30 20 10
10
6.5
10050 0 50100
6.0
3.5
3.0
5 104 103 102
5.5
5.0
2.5
2.0
1
59th Annual Meeting of the APS Division of Plasma Physics
Milwaukee, Wisconsin
0
50
70 60 50 40 30 20 10
0.0
50 70
600 50 40 30 20
10 0.2
10 0.0 4
1016 0.0 8 24
0.4
0.3 150 150
0.2
0.1 0.2 0 0
150 150 0.10
150.04 0.3
15
0.75
0.50
0.25 0
0.00 0 200
0.25 0.00 50
0
10
x-residual y-residual r-residual
400
Z [cm]
600
800
•3 70
00 200
f camera, 2643us_Timin_Temin
0 200 400 600 800
400
Z [cm]
• s
• 900–1300 A particle source 20
400
Z [cm]
0
[1] [2]
[3] [4]
[5]
0–50 kW electron power loss
0 200 400
600 800
Z [cm]
0–100 kW ion power loss
600 800
17 1016
50 40 30 20 10
10
18
10 10 10
10
1022 60
10
0 10 20 30 40 50 60 Radial px
References
M.W. Binderbauer et al. Physics of Plasmas 22 (2015), p. 056110.
J. Kannala and S.S. Brandt. IEEE Transactions on Pattern Analysis and Machine Intelligence 28.8 (Aug. 2006), pp. 1335–1340.
A. H. Andersen and A. C. Kak. en. Ultrasonic Imaging 6.1 (Jan. 1984), pp. 81–94.
W.H. Meyer, M.E. Fenstermacher, and M. Groth. 56TH Annual Meeting of the APS Division of Plasma Physics. Vol. 59. Bulletin of the American Physical Society 15. 2014.
Daren Stotler and Charles Karney. en. Contributions to Plasma Physics 34.2-3 (1994), pp. 392–397.
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70 60 50 40 30 20 10
22
16