An Interesting Poster to look at from the Tri Alpha Energy Team in California

Spectral and Intensity Calibration of a Thomson Scattering Diagnostic for the C-2W Field- Reversed Configuration Plasma Experiment
Abstract
The C-2W Thomson Scattering diagnostic consists of two individual systems for monitoring electron temperature and density; one system in the central region is operational and the second system, currently under design, will monitor the open field line jet region1. The laser and collection optics for this diagnostic will be described separately2. A broadband source and a scanning monochromator have been setup for the spectral calibration of the polychromators. The system intensity calibration is performed using Rayleigh scattering with the vessel filled with argon gas at different pressures. This paper will detail the design principles and results of the spectral channel configurations, signal conditioning of the polychromators and their spectral calibrations, and the Rayleigh scattering calibration for the whole system response.
Motivation & System Design
T.M. Schindler, K. Zhai, A.Ottaviano, M.C. Thompson and the TAE Team
TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
Polychromator Design & Calibration
Calibration with Rayleigh Scattering
2
Pr dΩnLc
7Δλ
3
2 cΔλ
2
=
𝑠𝑖𝑛2𝜙
Ngas
𝑑𝜎
𝜋2𝛼2
S
R
ts−ch Ray−ch 0
dσray dΩ ∗
2 cΔλ
2 πa sin 2 λi 4a λi sin2 2
λ
P R, λ dλ dΩ = S λ n P L = i 0 e 1 − +
scss TSsei θ 2λi 23 θ
exp −
dλ
𝑑Ω 𝜀2𝜆4 0𝑖
𝑛 =
22 θs 4a λi sin2 2
Differential Rayleigh scattering cross section6 with polarizability α as p = α E
𝛼 = 3є0 𝑛2 − 1 𝑁 𝑛2+2
 Index of refraction n relation by the Lorentz-Lorenz eq’n7
𝑒 σ𝑆𝜆𝑅𝜆ΔλSray 𝑖 𝑡𝑠 𝑖 𝑐h 𝑖 s
 Electron density in terms of Rayleigh scattering signal
 Thomson scattering theoretical power spectrum3
 Polychromator optical

Light Striking Position
CW (nm)
FWHM (nm)
Cut-on (nm)
Cut-off (nm)
1
928.0
154
851.0 ±3
1005.0 ±3
2
1022.0
34
1005.0 ±2
1039.0 ±2
3
1046.0
16
1039.0 ±1
1055.0 ±1
4
1058.0
6
1055.0 ±1
1061.0 ±1
5
1064.3
6
1061.3 +0/-1
1067.3 +1/-0
filter configurations
 Average T for each passing wavelength band is >80%
 Average R out of band is >95% from 850 – 1070 nm
 Spectral calibration setup

n − 1 x 108 = 6432.135 + 286.06021 x 1012 14.4 x 109 − νΤcm−1 2
Argon gas refractive index7 where 𝝂 is the wavenumber in cm-1
𝑆 =෍𝑆𝜆𝑅𝜆Δ𝜆ΔΩEL𝑛𝐹
𝑖
 Expected Thomson scattering spectrum for various Te
Jet Region Thomson scattering measurement locations
Central Thomson scattering measurement locations
The electron temperature expected to span from ~100 eV to ~2 keV
Thomson scattering is one of the primary diagnostics for the C-2W machine (now also called “Norman”).
The electron density range is expected to be from 0.5 – 10 x1013 cm-3.
In-house designed collection optics systems1,2 Two Te & ne measurement regions:
 Central region (r = -8, -4, 0, 4, ... 36, 41, 49, 57, 65 cm) and Jet region (r = -10, -5, 0, 5, 10 cm))
Optically filtered polychromators procured through GA6
 System parameters for the central and jet region Thomson systems
𝑑𝜎
𝑡𝑠−𝑐h
𝑡𝑠 𝑖 𝑐h 𝑖 𝑠 𝑒 𝑠𝑦𝑠𝑡𝑒𝑚
 Thomson scattering signal per channel
𝑆 = 𝑟𝑎𝑦𝑁 𝐿ΔΩ𝑅
𝑟𝑎𝑦 𝑔𝑎𝑠 𝑅𝑎𝑦−𝑐h
𝜆 𝐸𝐹
0 𝑠𝑦𝑠𝑡𝑒𝑚
 

 

𝑑Ω )  Rayleigh scattering signal
 Rayleigh Scattering Calibration performed with Argon gas
 Expected signal per polychromator channel for varying Te
 Spectral calibration detector ratio
System Status & Future Work
Central Thomson system is commissioned and operational on C-2W
Rayleigh Scattering Calibration has been performed on Central Thomson System
Spectral calibration system operational, perform polychromator spectral calibrations at TAE
REFERENCES
3J.Sheffield “The incoherent scattering of radiation from a high temperature plasma, Plasma Physics Vol. 14, pp783 (1972)
4
T.M.Deterly et al., IEEE Trans. Plasma Sci. 38 7 (2010). This paper includes a complete description of the pre-amplifier.
5 General Atomics Polychromator Systems User Manual Polychromator Model GAPB-1064-1K-I, Document 4-3248-3MAN, Rev.A, 2017
6
Born and Wolf 1980
7Journal of Quantitative Spectroscopy & Radiative Transfer 92,293(2005). formula 2, and 9
Sts−ch = ෍ 𝑆𝑡𝑠 𝜆𝑖 𝑅𝑐h 𝜆𝑖 𝑖
𝑛e Δλs 𝐑𝐫𝐚𝐲
dσray 𝑅Ray−ch λ0 dΩ
 Where Rray = Sray / Ngas is the Rayleigh scattering coefficient
 C-2W Thomson systems
Parameter
Central Region
Jet Region
Laser Wavelength λ (nm)
1064
1064
Number of Radial Locations
16
5
Radial Location Span (cm)
-8 to +65
-10 to +10
Scattering Region Length L (cm)
2.5
1.5
Laser Energy per pulse Ei (J)
2
2
Collection Optics Diameter Φ (cm)
10
10
Collection solid angle dΩ
1.25 x 10-4
2.77 x 10-4
Distance to Scattering Region (cm)
100
52
Scattering Angle θ
90°
90°


Polychromator spectral calibration results and expected Thomson scattering spectrum for various Te
(polychromator spectral calibration data courtesy of GA6)
  
Polychromator optical filter housing and pre-amplifiers6
APDs (Avalanche photodiode) are Excelitas C30956EH
Low noise, high bandwidth transimpedance APD amplifier based on the LMH6624 op-amp
 Te uncertainty as a function of Te due to the spectral calibration error
   
Build and commission jet Thomson system
θ 4 λ˳ sin 2
 AC / DC calibrations 2A. Ottaviano Characterization of system components for Thomson scattering diagnostics on C-2W HTPD 2018
2k Te ln2 mec2
1K. Zhai Thomson scattering systems on C-2W field-reversed configuration plasma experiment HTPD 2018
∆λ =
= 4.957
Te