A calibration code based on optical method for the JET Polarimeter
description
Transcript of A calibration code based on optical method for the JET Polarimeter
P. Gaudio 1 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
A calibration code based on optical method for the JET Polarimeter P. Gaudio1, M. Gelfusa1, A. Murari2, A. Boboc3, M. Brombin2, F.P. Orsitto4, E. Giovannozzi4 and
JET EFDA Contributors*
1 Associazione EURATOM-ENEA - University of Rome “Tor Vergata” , 2 Consorzio RFX Associazione EURATOM-ENEA per la Fusione3 EURATOM/CCFE Fusion Association, Culham Science Centre4 Associazione EURATOM-ENEA – CR. ENEA Frascati
*See the Appendix of F. Romanelli et al., Fusion Energy Conference 2008 (Proc. 22nd Int. FEC Geneva, 2008) IAEA, (2008)
Frascati – Italy - 26-28 March 2012Frascati – Italy - 26-28 March 2012
P. Gaudio 2 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Outline
• Polarimetry measurements– Description of measurements– Polarimeter setup
• Current calibration– Hardware Calibration procedure– Why a calibration is needed?– Why a new calibration procedure is needed?
• New Calibration optical method based– Ideas of use ray tracing method to reproduce laser
beam path– Optical scheme
• Some results and comparison
P. Gaudio 3 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Polarimetry measurements
• Measurements are based on polarization laser beam that crosses a magnetised plasma area
• Two effects are observed:– A change of polarization of the laser beam known
as Faraday effect described by follow equation
– A change of ellipticity of the laser beam know as Phase shift effet described by the following equation
dzBne 2
dzBne 23
P. Gaudio 4 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Polarimeter Set-up
Laser DCN
λ= 195 μm
Phase sensitiveanalog electronics
Gs
Gai
n co
ntro
lled
ampl
ifier
Gs
Gai
n co
ntro
lled
ampl
ifier
PLASMA
GratingWheel
Wire Grid(WG1)
HWP1
H - detector
V - detectorp(t)
100kHz beat signal
i(t)
100kHz beat signal
HWP2
Beam splitter
Recombinationplate
DieletricWaveguide
Mirror
Mirror
Freq
uenc
y of l
ight
incr
ease
d by
ω=1
00 k
Hz
Wire Grid(WG2)
BPF(80-120 kHz)
BPF(80-120 kHz)
RMSRMPPSDPSP
Wire Grid(WG3)
Pre-amplifier
Pre-amplifier
tEtEtp yy 00
0 cossincos
tEtEti xx 00
0 coscoscos
i’(t) ≈ Ex,0 sin (ωt) is generated by phase shifting i(t)
RMS = < i(t) x i(t) > PSD = < p(t) x i(t) >
RMP = < i’(t) x i’(t) > PSP = < p(t) x i’(t) >
RMSPSD
RRMPRMS
PSPR
'
RR
arctg'
'RRCarctg 2
P. Gaudio 5 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Hardware Calibration procedure
Faraday
Deg
rees
Time (s)D
egre
esTime (s)
Phase Shift
• Currently, the procedure of calibration is the following:– the half-wave plate, located at the entrance of the vacuum vessel, is
rotated (via a step-motor) of a well-known angle () and the phase shift () is recorded at each angle, while the Faraday rotation (2) is equal to twice the half-wave plate angle.
Current calibration code fit the phase shift data at the aim to determinate the “spurious ellipticity angle to use for to interpreter experimental data.
Laser DCN
λ= 195 μm
Phase sensitiveanalog electronics
Gs
Gai
n co
ntro
lled
ampl
ifier
Gs
Gai
n co
ntro
lled
ampl
ifier
PLASMA
GratingWheel
Wire Grid(WG1)
HWP1
H - detector
V - detectorp(t)
100kHz beat signal
i(t)
100kHz beat signal
HWP2
Beam splitter
Recombinationplate
DieletricWaveguide
Mirror
Mirror
Freq
uenc
y of l
ight
incr
ease
d by
ω=1
00 k
Hz
Wire Grid(WG2)
BPF(80-120 kHz)
BPF(80-120 kHz)
RMSRMPPSDPSP
Wire Grid(WG3)
Pre-amplifier
Pre-amplifier
P. Gaudio 6 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Current calibration
• Why a calibration is needed?– Polarimeter measurements are affected by:
• “Spurious phase shift” induced by not well identified optical component along laser path. Then a calibration procedure is needed at the aim to evaluate this effect and take it in account in final result of polarimetry measurements
• What are the problem?:– Current calibration is not able to determinate fit
parameter for every JET operation regime– Current calibration algorithm does not separate the
optical and the electronics effect• How to resolve the problem?
– To analyzed and check electronic components– To simulate the laser beam path through a series of
optical components which are represented with a matrix formalism.
P. Gaudio 7 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Electronics bench testThe tests to check the reliability of the electronic cards used on polarimetry have mainly consisted on acquiring the raw data after the detectors, process them via software (Simulink/Matlab) and then compare the obtained outputs with the ones given by from the polarimeter electronics.
Gaudio P.. et al., Modelling of the signal processing electronics of JET interferometer-polarimeter, NIMA 623, 660-663, 2010
P. Gaudio 8 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Laser DCN
λ= 195 μm
PLASMA
HWP1
H - detector
V - detector
Wire Grid
Retarder 1
Retarder 2
1000
0220
0220
0001
cossin
sincos
M
11
11
00
00
0010
0001
1
cossin
sincos
M
New Calibration code
22 22 RMRM'
1000
0220
0220
0001
11
111
cossin
sincos
R
yx
yx
yxyx
yxyx
xT
pp
pp
pppp
pppp
pM
2000
0200
00
002222
2222
2
yx
yx
yxyx
yxyx
yR
pp
pp
pppp
pppp
pM
2000
0200
00
002222
2222
2
WGxp cos WGyp sin
11 11 RMRM'
shiftphase1 retarderangle1
P. Gaudio 9 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
New calibration code
After the analyser, the laser beam is divided in two parts and the corresponding Stokes vectors are given by:
01 12SMMMMS TT
''
,
01 12SMMMMS RR
''
,
Therefore, it is possible to know the polarisation angle and the phase shift, given by:
2
3
SS
arctag
1
2
2
1
SS
arctag
Gaudio P.. et al., New calibration code for JET polarimeter, RSI, 81, 053507 (2010)
Overall the code depends on five adjustable parameters: .
To estimate these parameters an optimization routine has been written. The routine finds the values of
these five quantities which allow to best fit the calibration curves.
1 1 2 2 WGand
P. Gaudio 10 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
New calibration code: results
Calibration curveCalibration
Shot: 67677 chord #3
Using the better fit, the five adjustable parameters
are found!
Shot: 77650 chord #3
Deg
rees
Black line: HWP
Red line : New Cal
Time (s)
Faraday
Theta (Degrees)
Deg
rees
Black diamond: New cal
Red Asterisk : Raw data
Phase Shift
Time (s)
Faraday
Rad
ian
s
Time (s)
Phase Shift
Deg
rees
Legend:Blue line: New calibration
Red line: PPF signalGreen asterisk: Stokes Model
1 1 2 2 WGand
In the plot Green spots represent numerical
simulation of full propagation code based on Stokes model
P. Gaudio 11 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
New calibration code: results
Shot: 77650 chord #2
Shot: 77650 chord #4
Faraday Phase Shift
Faraday Phase Shift
Rad
ian
sR
adia
ns
Time (s) Time (s)
Time (s) Time (s)D
egre
esD
egre
es
Legend:Blue line: New calibration
Red line: PPF signalGreen asterisk: Stokes Model
P. Gaudio 12 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Alcoholλ= 119 μm
Laser DCN
λ= 195 μm
PLASMA
BS
BS
BS
RPBS
MM
MM
M
M
M
M
MM
M
WG2
M
WG1
HWP
HWP
HWP
GW
GW
5kHz
100kHz
M
V – detector
p(t)
H – detectori(t)
LEGEND
M : MirrorHWP: Half –Wave Plate
BS : Beam SplitterRP : Recombination Plate
GW : Grating Wheel
BS
Polarimeter scheme: lateral channels
1000
0220
0220
0001
cossin
sincos
M
180
P. Gaudio 13 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
New calibration code: lateral chords
Shot: 67777 chord #5
Shot: 67777 chord #6
Rad
ian
sR
adia
ns
Faraday
Faraday
Phase Shift
Phase Shift
Time (s)Time (s)
Time (s) Time (s)
Deg
rees
Deg
rees
Rad
ian
sR
adia
ns
Legend:Blue line: New calibration
Red line: PPF signalGreen asterisk: Stokes Model
P. Gaudio 14 (14) 7th Workshop on Fusion Data processing Validation and Analysis Frascati 26-28 March 2012
Conclusions
JET polarimeter has been analyzed to understand and to solve the problems posed by the spurious ellipticity induced by the instrument optical components.
A simulator has been developed to verify the proper operation of the signal processing electronics. The analysis shows a good agreement between the simulation outputs and the experimental data.
A new calibration code has been written and tested for many shots acquired in different campaigns. The experimental data, calibrated with this code, has been compared with the rigorous numerical solution of the Stokes equations.
The developed model for the calibration is valid for all configurations of the diagnostic (any operation regime at JET).