Calibration of the Joint European Torus energetic ion and alpha particle collectiveThomson scattering diagnostic receiverJan Egedal, John S. Machuzak, John S. Fessey, Henrik Bindslev, A. J. Hoekzema, Thomas P. Hughes, PoulDavies, Christopher Gatcombe, and Paul P. Woskov Citation: Review of Scientific Instruments 70, 1167 (1999); doi: 10.1063/1.1149475 View online: http://dx.doi.org/10.1063/1.1149475 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/70/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Correction of the spectral calibration of the Joint European Torus core light detecting and ranging Thomsonscattering diagnostic using ray tracing Rev. Sci. Instrum. 84, 103507 (2013); 10.1063/1.4824074 Initial results from the lost alpha diagnostics on Joint European Torus Rev. Sci. Instrum. 77, 10E701 (2006); 10.1063/1.2217928 Electron cyclotron emission radiometer upgrade on the Joint European Torus (JET) tokamak Rev. Sci. Instrum. 75, 3831 (2004); 10.1063/1.1781376 Collective Thomson scattering based on CO 2 laser for ion energy spectrum measurements in JT-60U Rev. Sci. Instrum. 74, 1642 (2003); 10.1063/1.1532760 Linewidth measurements of the JET energetic ion and alpha particle collective Thomson scattering diagnosticgyrotron Rev. Sci. Instrum. 70, 1154 (1999); 10.1063/1.1149580

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

129.105.215.146 On: Sun, 21 Dec 2014 11:42:08

Calibration of the Joint European Torus energetic ion and alpha particlecollective Thomson scattering diagnostic receiver

Jan Egedal, John S. Machuzak,a) John S. Fessey, Henrik Bindslev, A. J. Hoekzema,Thomas P. Hughes, Poul Davies, Christopher Gatcombe,b) and Paul P. Woskova)

JET Joint Undertaking, Abingdon, Oxfordshire OX14 3EA, United Kingdom

~Presented on 11 June 1998!

The receiver of the Joint European Torus~JET! energetic ion and alpha particle collective Thomsonscattering diagnostic is calibrated assuming blackbody emission from the torus vacuum vessel~VV !and using electron cyclotron emission~ECE!. The 32 receiver channels are absolutely calibratedwith a mechanical chopper in the quasioptical arm of the receiver, alternating the receiver viewbetween the torus vacuum at 320 °C and room temperature. This calibration is noisy due to the smalldifference between torus and room temperatures. A more accurate relative calibration is achievedwith the ECE during plasma shots. The intensity of the ECE is found to be a smooth function offrequency, which enables the combination of the ECE calibration with the VV calibration. Theaccuracy of the absolute VV calibration is hereby improved to nearly the same standard as therelative ECE calibration. ECE signals measured by the calibrated receiver agree well with standardJET ECE diagnostics. Based on mathematical considerations presented here, noise is injected intothe receiver final intermediate frequency stage during VV calibrations to provide more bittransitions for accurate analog-to-digital~AD! conversion of the low level calibration signals. Thisyields a resolution which is better than 1% of an~AD! step. © 1999 American Institute of Physics.@S0034-6748~99!75701-1#

I. VACUUM VESSEL „VV… CALIBRATION

An absolute calibration of the receiver system of thecollective Thomson scattering~CTS! diagnostic at Joint Eu-ropean Torus~JET! is obtained by utilizing the signal differ-ence between the 320 °C vacuum vessel and room tempera-ture ‘‘Ecco-sorb.’’1 By means of a mechanical chopper inthe quasioptical arm of the receiver the two signal sourcesare viewed alternatingly.2 Even though the vessel wall re-flects about 50% of all incoming radiation the assumption ofthe vessel being a blackbody is reasonable, since only a tinyfraction of the radiation leaving the antenna and entering thevessel is reflected back to the antenna.

Ideally the room temperature noise source~the Ecco-sorb! should be placed inside the vessel in direct view of thereceiver antenna. However, assuming that the absorbingparts of the transmission line from the vessel to the detectoralso emit radiation at room temperature, the signal recordedwhen placing the Ecco-sorb in the quasioptical arm is iden-tical to the radiation recorded from a piece of in-vessel roomtemperature Ecco-sorb. Hence, with the assumption of roomtemperature waveguide, the losses in the transmission lineare correctly include in the calibration.

Let S1n and S2

n be measured signals in channeln corre-sponding to the two different temperaturesT1 and T2 , re-spectively. The calibration factors,Gn, for the individualchannels are then simply given by

Gn5Sn

Dt5

S1n2S2

n

T12T2. ~1!

When applying the calibration the signal in a given channelshould be divided by the respective calibration factor:

Tn5Sn

Gn2Toffsetn . ~2!

HereToffsetn correct for the different offsets of the zero points

for the various channels. These offsets may be found usingthe equation

Toffsetn 5

S1n

Gn2T1 . ~3!

In scattering experiments interest is limited to differences inthe signal levels measured at different times. The offsets,which are unchanged, are then of no importance.

The plots in Fig. 1 show raw signals,SVVn 5S1,VV

n

2S2,VVn , recorded using a chopper switching between the

two sources with temperatures 583 and 293 K, respectively~the subscripts VV stands for vacuum vessel!. The data ac-quisition time was 2 h. We may note how the relative uncer-taintiessn5AVar(Sn)/Sn are very significant for the centralchannels. This is due to their narrow frequency bandwidthand the presence of notch filters for eliminating 140.260.05 GHz gyrotron stray light.

a!Also at MIT Plasma Science and Fusion Center, 167 Albany St., Cam-bridge, MA 01239.

b!Presently at Eaton Corporation, Beverly, MA.

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 70, NUMBER 1 JANUARY 1999

11670034-6748/99/70(1)/1167/4/$15.00 © 1999 American Institute of Physics

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

129.105.215.146 On: Sun, 21 Dec 2014 11:42:08

II. ECE CALIBRATION

Using ECE recorded during plasma pulses a strong cali-bration signal,S1,ECE

n , is obtained. The background level re-corded with a empty vacuum vessel~again 583 K! is used asthe second set of signals,S2,ECE

n .An example of an ECE signal,SECE

n 5S1,ECEn 2S2,ECE

n , isgiven in Fig. 2. By comparing the relative uncertainties ofSECE

n and SVVn , it is clear that the quality of a calibration

based on ECE is much higher than the quality of a VV cali-bration.

The problem in obtaining an absolute ECE calibration byusing Eq.~1! is that the temperatureT1,ECE( f ) of the signalS1,ECE

n , is an unknown function of frequency. Standard ECEdiagnostics at JET do provide information onT1,ECE, butbecause of differences in the line of sight between the CTSdiagnostic and standard ECE diagnosticsT1,ECE( f ) cannotbe accurately estimated.

Selecting ECE data for which most of the radiation at140 GHz comes from the central part of the plasma the ra-diation temperature,T1,ECE, is a smooth function of fre-quency. It does not vary significantly over frequency inter-vals comparable to the sum of bandwidths of the narrowfrequency channels.

III. THE COMBINATION OF VV AND ECECALIBRATIONS

The ECE calibration signalSECEn can be used to reduce

the noise on the vacuum vessel signalSVV . Consider theratio of signals:

SVV

SECE.

T1,VV2T2,VV

T1,ECE2T2,ECE. ~4!

In this equation the equalty holds in the limit of perfect mea-surement with no noise. The quantities on the right-hand sideof Eq. ~4! do not depend on frequency apart fromT1,ECE

which is smooth function off. Consequently, the ratio(T1,VV2T2,VV)/(T1,ECE2T2,ECE) is a smooth function.

The purpose of Eq.~4! is to show that the ratioSVV /SECE is a smooth function of frequency except for fluc-tuation introduced by the noise onSECE and especially onSVV . These fluctuation are eliminated by least-squares fittingof a polynomium toSVV /SECE giving ^SVV /SECE&. The orderof the polynomium used in the fit should be high enough togive an accurate representation of (T1,VV2T2,VV)/(T1,ECE

2T2,ECE) but so low that the fit is not affected by the noiseon SVV . The optimal choice of the polynomial order,N,depends on the quality of the measured data.

Figure 3 shows the ratioSVV /SECE of the data presentedin Figs. 1 and 2. The smooth ratio^SVV /SECE& also shown inFig. 3 was obtained by fitting a sixth-order (N56) polyno-mium. Fit withNP$4,...,8% all gave similar results indicatingthat (T1,VV2T2,VV)/(T1,ECE2T2,ECE) is accurately repre-sented by the fit, and that the noise onSVV /SECE is nearlyorthogonal to the set of functions used in the fit.

Systematically, we find in Fig. 3 thatSVV /SECE

,^SVV /SECE& for the central channels. In the last section ofthis paper, we derive a condition for the noise on signals.This condition need to be fulfilled to ensure subbit resolutionafter analog-to-digital conversion. The noise in the centralchannels do not meet the requirement which explain the sys-tematic errors observed in Fig. 3.

We may now create an improved vacuum vessel spec-trum

FIG. 1. Signal differences measured by alternating observation of vacuumvessel at 320 °C and ‘‘Ecco-sorb’’ at 20 °C.

FIG. 2. ECE signal recorded in JET pulse No. 41776 during the time inter-val t563– 64 s.

FIG. 3. Ratio ofSVV andSECE before and after smoothing.

1168 Rev. Sci. Instrum., Vol. 70, No. 1, January 1999 Egedal et al.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

129.105.215.146 On: Sun, 21 Dec 2014 11:42:08

^SVV&ECE5 K SVV

SECEL SECE, ~5!

where the noise on all channels is reduced to the noise levelof the ECE calibration.

The final expression for the combined VV and ECE cali-bration is given by

Gn5^SVV

n &ECE

T1,VV2T2,VV. ~6!

The first plot in Fig. 4 shows an ECE signal, recorded inJET pulse No. 41776 in the time intervalt568– 69 s, whilethe second plot shows the same signal calibrated.

The calibrated signal is seen to be smooth and a slowlydecreasing function of frequency, which is in agreement withthe measurements by other ECE diagnostics. For the centralfrequency channels, some none physical fluctuations arefound but these are clearly small compared to the noise onthe VV calibration eliminated in the process:SVV /SECE

→^SVV /SECE& ~see Fig. 3!.The information from the noisySVV is only used in the

fit of (T1,VV2T2,VV)/(T1,ECE2T2,ECE). The combined infor-mation from the many data channels is adequate for accuratedetermination of this smooth function. The information onthe fine details~channel to channel! of the calibration factorsis provided solely by the relative ECE calibration which hasgood signal-to-noise figures in all channels.

IV. MATHEMATICAL MODEL FOR ANALOG-TO-DIGITAL „AD… CONVERTOR

The signal differences between the hot vacuum vesseland room temperature,SVV , in Fig. 1 are given in units ofthe step size in the AD convertor. It is seen that the signal isonly a few percent of the step size. Measurement of sub-bitlevel signals is done by calculating the average value of adata time series. For this to provide the correct value, we relyon the presence of noise. If there is no noise, the time aver-age of the data is equal to the AD step nearest to the signallevel and there will be no sub-bit resolution.

Measurements on the receiver and mathematical consid-erations given below indicate that there is too little noise inthe receiver for correct detection of the VV signals. The

necessary noise on the signal could be obtained by increasingthe gain in the system. The noise compared to the AD-stepsize would then be increased and so would the signal whichwe try to measure. However, for the JET CTS receiver, theupper limit on the gain in the detection system is fixed by therequirement that the dynamic range cover signals up to atleast 1 keV. With 1000 steps in the AD convertor, each stephas to cover 1 eV. This is about 50 times the size of thevacuum vessel signal. The require noise for the AD conver-sion was achieved by injecting noise into the receiver at theintermediate frequency stage.

The stocastic input signalS is represented by the distri-bution function f (S) which is assumed to have a Gaussiandistribution, f (S), with mean,m, and variances2:

f ~S!51

sA2pe2~1/2s2!~S2m!2

. ~7!

Data samplesSn are created by the AD converter by evalu-ating S(t) at timest5t0 ,t1 ,..., androunding off the signallevel to the nearest discrete step. Let the signals be measuredin units corresponding to the steps in the AD convertor. Wenumber the steps in the AD convertor such that 0<m,1,and we consider a range of steps:$2K,2K11,...,K21,K%. Under the conditionK@s all data samples are in-cluded in this ranges.

Let pk represent the probability of a given sample havingthe valuek. We find thatpk is given by

pk5Ek2

12

k112 f ~S!dS5F~zk!2F~zk21!, zk5

122m1k

s,

~8!

where

F~z!51

A2pE

2`

z

e2x2/2dx.

An estimate for the mean,m, of S is found by taking theaverage of a large number of samples. We denote the expec-tation value for the mean ofN samples,Sn , by m̄. As indi-cated belowm̄ is a function ofm ands:

m̄~m,s!5EH 1

N (n50

N

SnJ ~9!

5 (k52K

K

kpk . ~10!

Even if we have take the average of an infinite number ofsamplesm̄ does not in general provide an accurate estimateof m. In Fig. 5~A! a surface plot of the differencem̄2m isgiven as a function of (m,s2) and we see that

m̄50 for s50, mP@0,0.5@ ,

m̄51 for s50, mP]0.5,1@ ,

m̄.m for s50.5.

As expected fors.0 the error onm̄ can be as much as halfan AD step.

FIG. 4. ECE signal before and after calibration.

1169Rev. Sci. Instrum., Vol. 70, No. 1, January 1999 Egedal et al.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

129.105.215.146 On: Sun, 21 Dec 2014 11:42:08

Vacuum vessel calibrations are obtained by measuring asmall difference signal with a mean,d, which is typically afew percent of an AD step. Since an estimate,d̄, for d can beexpressed by

d̄5m̄~m1d,s!2m̄~m,s!>ddm̄

dm, ~11!

it follows that we must requireudm̄/dm21u!1 for all m toensure an accurate estimate of the difference signal.

From Eqs.~8! and~10! we find after a few manipulationsthat

dm̄

dm5 (

k52K

K1

sA2pe2zk

2/2, zk5

122m1k

s. ~12!

In Fig. 5~B! dm̄/dm is shown as a function of~m,s!.The interval between consecutive arguments

(zk21 ,zk ,...) decrease ass is increased and forK@s@1,the sum in Eq.~12! is equal to the integral

E2`

` 1

sA2pe2t2/~2s2!dt51.

We therefore find that a high value ofs will secure that theexpectation value of

1

N (n51

N

Sn

is identical to the mean of the signal before AD conversion.However, if the value ofs is too high~too much noise! thesum above does not convert when only a finite number ofsamples is available.

The quantity L52 log10(udm̄/dm21u) provides thenumber of accurate digits on the expectation valuem̄. Theplot in Fig. 6~A! showsL as a function of~m,s!. The lowestvalues of L for constant s are generally found form

P$0,1%. In Fig. 6~B! the surface plot from previous figure isprojected on to the~L,s! plane. For s50.6, we findL(m,s)>3 which ensures that no more that 0.1% error isintroduced under the AD conversion.

Experimentally, it was found that back wall calibrationswere reproducible withs>1. This noise level was achievedby injecting noise into the intermediate frequency stage ofthe receiver.

V. CONCLUSION

A reliable method has been developed for calibrating thedetection system of the collective Thompson scattering diag-nostic at JET. The method combines a noisy absolutevacuum vessel calibration with a relative ECE calibrationproviding an overall absolute calibration with accuracy com-parable to that of the relative ECE calibration.

Mathematically, we investigated the amount of noisenecessary to ensure that a sub-bit level signal is recoverableafter analog-to-digital conversion. Based on these consider-ations additional noise was injected into the receiver finalintermediate frequency stage, enabling measurement with aresolution better than 1% of the AD steps. The dynamicrange necessary for combining the vacuum vessel calibrationwith that of the 104– 105 times stronger ECE signal washereby obtained.

ACKNOWLEDGMENT

This work was supported by the JET Joint Undertakingand U.S. DOE

1J. S. Machuzak, P. P. Woskov, H. Bindslev, M. Comiskey, J. Fessey, J. A.Hoekzema, T. P. Hughes, and F. Orsitto, Rev. Sci. Instrum.63, 4648~1992!.

2M. McCarthy, G. Taylor, P. Efthimion, E. Fredd, M. Goldman, F.Stauffer, and D. Boyd,Eighth International Conference on Infrared andMillimeter Waves, Conference Digest~IEEE, New York, NY, 1984!, pp.M4.5/1–2.

FIG. 5. ~A! Transfer function,m, for the AD-convertor as a function of~m,s!. ~B! Derivative of transfer function,dm̄/dm, as a function of~m,s!. FIG. 6. Number of accurate digits in the AD conversion:L

52 log10udm̄/dm21u as a function of~m,s!.

1170 Rev. Sci. Instrum., Vol. 70, No. 1, January 1999 Egedal et al.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

129.105.215.146 On: Sun, 21 Dec 2014 11:42:08