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Electron density diagnostics by Fe XXII line intensity ratio
Volume 123,number 8
PHYSICSLETTERSA
31 August 1987
ELECTRON DENSITY DIAGNOSTICS BY Fe XXII LINE INTENSITY RATIO Kuniaki MASAI and Takako KATO Institute of Plasma Physics, Nagoya University,Nagoya 464, Japan Received 51January1987; revisedmanuscriptreceived 15 May 1987;acceptedfor publication9 June 1987 CommuniCatedby F. Troyon The electrondensityof a tokamakplasmais obtainedfrom the 114.41 and 117.17J~line intensitiesof Fe XXII. This measurement is fouhd to be usefulfor electrondensitiesin the range 10t2-1015 cm-3, on accountof its weakdependenceon temperature and of the proximityof these spectrallines.
1. Introduction On many tokamaks, the electron density is often measured by the Thomson scattering technique. This measurement is often used in the analysis of spectroscopic data, !for example, to obtain the impurity concentrations. Such an analysis is not free from the spatial distribution of the ion of interest, and is often complicated by a rapidly changing plasma. Conversely, the electron density derived from the line intensity ratio provides a continuous measurement. Therefore, diagnostics using line intensity ratios are of great interest i for impurity studies in tokamaks as well as in astrophysical plasmas. The intensityi ratio of energetically close lines of the same ion may be used to obtain density information, if one Of the lines is excited from a rectastable state. In a previous paper we investigated the electron densityidependence of the line intensities of oxygen III-V ions for use in the peripheral region of a tokamak plasma [ 1 ]. In the higher temperature regime, highly ionized iron with mulfiplet ground configurations may be similarly used. Measurements for solar flares [2] and tokamaks [3-5] have been reported as well! as theoretical calculations [6-10] and empirical formulae [ 11 ]. In the present! paper, we demonstrate that a pair o f F e XXII lineslprovides a useful means of the density diagnostics, ihTe lines under consideration are associated witll the transitions 2s22p(2p3/2-
2s2p2(2p3/2) 114.41 Jt and 2s22p(2p l/2)-2s2p2(2Sl/2 ) 117.17 J~. Our goal is to observe the time variation of the line intensities particularly when the density changes'rapidly. In the next section, we outline the line intensity ratio dependence on the electron density. The experimental results and the theoretical calculation including proton/deuteron excitation are described in sections 3 and 4, respectively.
2. Electron density dependence In this section, we consider a four-level atom excited only by electron impact and give a theoretical account of the proposed density diagnostics. The rate coefficients for collisional excitation as well as the level configurations of the transitions concerned and the wavelengths are shown in fig. 1. The energy levels are designated by indices, for instance 2s22p(2Pl/2 ) as level 1, and the collisional rate coefficients are distinguished thereby with subscripts as Cjk for the transition from levelj to k; Cik (Ckfl means excitation (de-excitation) for j < k . The rate coefficients by proton and deuteron impacts are distinguished from those by electron impact by the additional subscripts p and d, respectively. We denote by n,, nj and Aj~ the electron density, the population of level j and the radiative transition probability from level j to k, respectively. The relation between the intensity ratio and the
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
405
Volume 123, number 8 I
10-9!
PHYSICSLETTERSA
I I Ill]
I
I
I
I i'll
i
is the branching ratio for the transition from level 4 to k. (I) For ne< 1012 cm -3, n2 is negligible compared to nl because neCjkS~.A21 in eq. (2). Then eq. (1) reduces to
i
C26
10-~o -
i
II 14 b42 C14
_
i
1117 ~b31 C13~0.17 .
& zp~
C23 I I Illl
i
i
,
, ,,,I]
o.1 1.o Temperature ( keV )
Fig. 1. Temperature dependences of the rate coefficients for collisional excitation processesand the schematicenergy diagram. electron density depends on the domain in which lies the density n~. Three regimes, labeled (I), (II) and (III), respectively, can be identified. The essential parameter which differentiates the regimes is the population of the ground level 2. The intensity ratio of 114 to 117 A can be written approximately, 1114 ~ b42
['CI4 C24 n2 )
1117 ~
~,~--13+ ~
~-~-t ,
(1)
where
represents the branching ratio of the radiative transition from levelj to k. The relative population of the ground states can be expressed as n2 n¢( C12 "~C14842) nl ~ ne( C21 + C24B41) +A2t where A21 = 1.39X 104 s - t [8], and
B4k=(A4k+neC4k)(~,i A4i+ne x?i C4i) -1 406
(3)
Hence, as the electron density decreases, the population distributions approaches that of the so-called corona regime, which is fully realized at ne< 1011 cm -3. (II) With an increase in the electron density, level 2 becomes populated. In the region of n~ ~ 1013-1014 c m - s, eq. (1) can be approximated by keeping only terms proportional to n~ and the value of s varies little when n~ is near the value neo for which s is at its maximum, Smax: S m a x = ( 1 - - q ) / ( l + q ) at ne=n~o ~-"qa 21/(C21 -~-C24B41), where q is defined as
10 -u
I
31 August 1987
(2)
C24 C12-.~t-C14B42~-1/2 q-= 14 C1~ C21 +C24B41]
(4)
Then eq. (1) can be approximated by,
1114
I11-'--7~'q-
1 b42 b31
C14(ne~ (l-q)/(l+q) Ct3\neo/
(5)
The value ofn~o lies in the range (6-10) × 1013 c m -3 when Te ranges from 0.5 to 2 keV, while q remains nearly constant around 0.33. Thus the ratio (5) is nearly proportional to n~/2. (III) For n¢> 10 Is cm -3, neCjks dominates over A21 in eq. (2), and the ground levels 1 and 2 are marginally boltzmannian. As the electron density increases, B4k approaches C4k/Y~iC4,. Then eq. (2) reduces to n2/nt ~ C~2/C2~ -~ 2, according to their statistical weights, because the excitation energy is much smaller than T~ assumed to be of the order of 1 keV. Hence, eq. (1) can be approximated by
1114 b42 C24 C12 +C14B42 I117m[9--'-31C13 C21+C24841
b42 C24
~2b-~-3~~3 "~2"3' (6)
where the last two expressions are valid for n~> A41/C41, A42/C42 ~ 1020 cm -3. It should be noted that I1~4]I117 depends rather weakly on T~ because the excitation energies for Cl 3 and C24 are close together. The intensity ratio is most
Volume 123, number 8
PHYSICS LETTERSA
sensitive to the electron density in the range r/e,~ 10J3-1014 c m - 3 (regime (II)), so that this line pair provides a simple and good diagnostic tool for current tokamak plasmas. Moreover, the absolute value of ne may be easily derived without requiring appreciable correction for the detector sensitivity since the wavelengths of these lines are very close.
31 August 1987
~- 1.0 .=o.5 I
A
Measurement
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(b)
'?E t.~ U
,c= 0
3.
J
lO
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l
l
l
l
l
l
l
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l
1.0
%0.5
The Fe XXII lines were observed along a central chord of the poloidal cross section of a tokamak plasma in the JIPP T-IIU device. The experiment was carried out in a study of additional heating in the ion-cyclotron range of frequency (hereafter referred to as ICRF). We measured the line intensities using a grazing incidence monochromator with a Rowland circle of 2 m in diameter, mounting a platinum coated 600 g/ram grating and a photomultiplier with a CsI coated photocathode. The spectral resolution was about 0.2 A almost independently of wavelength; closely spaced lines of Fe XXII 117.17 A and Fe XXI 117.51 ,~ were successfully resolved. The relative spectral sensitivity of the monochromator was calibrated by the branching ratio method. The plasma Was primarily sustained by the ohmic current heating! The density was rapidly raised by puffing a H2/D2 mixtured gas at 115 ms shortly before ICRF was turned on at 120 ms. During the ICRF heating phase of about 40 ms, the electron density was kept at a level of 2-3 times the density in the preceding ohmic phase. In fig. 2a we show the time variation o f the intensity ratio which was obtained every lime bin of about 0.5 ms. For comparison, the line~aveFaged electron density measured by a microwave interferometer is shown in fig. 2b. The intensity ratio is well correlated with the lineaveraged density. In addition, we show two examples with plasmas under different conditions in order to experimentally demonstrate the density dependence. One was obtained in a plasma almost the same as in figs. 2a an~l 2b, except that there is no ICRF heating: the other was a plasma with neither ICRF heating nor gas puffing. The time variations of the intensity ratio irl these two cases are shown in figs. 2c and 2d, respectively. The increase of the intensity
i e.. = 1.0
i
i
'
~
i
i
I
i
i
J
~
I
(d)
"0.5 '
~ 1~avv '
200
Time (ms)
Fig. 2. Time variationsof (a) the line intensityratio between I 14 and I 17 .~, (b) the line-averagedelectrondensity for a tokamak plasma additionallyheated by ICRF with gas puffing.The same ratio as in (a) for an ohmicallyheated plasma is shown in (c) with gas puffing,and in (d) withoutgas puffing. ratio associated with the gas puffing at 105 ms in fig. 2c is slightly smaller and rises slower than that with additional ICRF heating in fig. 2a. This suggests that the increase in the intensity ratio may be at least partially attributed to the presence of the ICRF heating rather than only to gas puffing. In the absence of gas puffing and ICRF heating (fig. 2d), there is no measurable change of the intensity ratio. The correlation between the density measured with the intensity ratio and the microwave interferometer was also good in the two cases shown in figs. 2c and 2d; such good correlation has been observed for many discharges.
4. Calculation
We have simultaneously solved the population of 10 levels taking into account the excitation by proton and deuteron impacts (C~2, C~2), and calculated the line intensities. Competitive radiative and collisional processes in the transitions to and from all n = 2 levels are considered to obtain the absolute value of ne. The radiative transition probabilities and 407
Volume 123, number 8 0.5
i
j
PHYSICS LETTERS A
i , , , , ,
-
.
~ i
j
i,
i,
i,
.....(c) - (b)
i
i , ,
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,
/
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-
.
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.
.
.
.
(a)
.
.
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.- ;,:.:.'-.".'~'i;1:"":C0rona'"~
-I.0
12
. . . . . . . . .
I
13
. . . . . . . . .
2keV
I
14
.........
15
log ne (cm-3) Fig. 3. Theoretical density dependence of the line intensity ratio (in photons) of I 14 to l 17 ,~.. Dotted, broken and solid lines represent the cases, (a) np/nc=O and nd/n~=O, (b) np/n¢=0,1 and nd/ne=0.9 and (c) np/ne= 1 and na/nc=O, respectively. The arrows indicate the asymptotic values. Boxes represent the observed intensity ratio (size is one standard deviation), the line-averaged and the central electron densities.
the collision strengths for electron excitation were taken from ref. [ 8], and the rate coefficient for proton excitation was from ref. [ 12 ]. The excitation rate coefficient by deuteron impact was calculated from that by proton by accounting the mass difference. The line intensity ratio thus obtained is shown in fig. 3 as a function of the electron density for three values of the temperature. Note the effect of proton and deuteron impacts on the excitation from level 1 to 2 in the ground configuration. The rate coefficient for this process by proton/deuteron impact (C~2, C~2 ) dominates over that by electron impact ( G 2 ) at temperatures > 600 eV (fig. 1 ). In addition, C~2 and Co~2 are rapidly increasing functions of the temperature, while C~2 is a slowly decreasing one. Protons and deuterons, therefore, play an important role in the population of level 2 at temperatures of the order of 1 keV where the line emission of Fe XXII is of interest. Assuming the temperature of protons/deuterons is the same as that of electrons, we consider the following three cases; (a) n~,/ne=O and ndne=O (proton/deuteron excitation is ignored), (b) np/n~ =0.1 and no/n,=0.9 and (c) np/n~= 1 and ndn¢=O,
where np and rtd are the densities of protons and deuterons, respectively #t Two representative values of It~4/11~7 measured in the ICRF heating experiment are indicated in fig. 3 with one standard deviation confidence levels. The data were taken during 5 ms at t = 100 ms and 140 ms corresponding to the ohmic heating phase before gas puffing and to the ICRF heating phase thereafter, respectively. For comparison the line-averaged electron density and the density in the central region measured by Thomson scattering are also indicated at the same time. The results from cases (b) and (c) allow us to estimate that the density is about (2.5-3) × 1013 c m - 3 at t = 100 ms in the ohmic phase, while case (a) fails to give a consistent value. I~ ~4/I 117 at around 140 ms is somewhat larger than that expected from ne and te in the experiment. From the analysis of the fast-neutral-particles, we infer that a higher energy component of protons/deuterons produced by ICRF enhances the excitation from level 1 to 2 resulting in the line emission of 114/~. As the temperature of protons/deuterons become larger relatively to that of electrons, the intensity ratio increases more strongly with the proton/deuteron temperature. We briefly mention two other line pairs combined with a forbidden line (845 ~,). The line intensity ratios of 114 and 117 ~ relative to that at 845 ~,, versus the electron density, are calculated for the three temperature values and shown in fig. 4 by broken and solid lines, respectively. I~ 1 4 / / 8 4 5 is more sensitive to the density than I~ ~4/I~,7, and is nearly proportional to ne for n, > 10 1 4 c m - 3 whereas 1114//,, 7 tends to be less sensitive; therefore, I~,4/Is45 may be a density diagnostic tool, complementary to 1,14/Ii17, despite a stronger dependence on the temperature. On the other hand, the intensity ratio of 117 A/845 A may be a diagnostic tool of the proton/deuteron temperature higher than 600 eV although the ratio is affected by the electron density at n,> 1013 c m - 3 ; the intensity ratio 114 A/117 A is helpful to estimate the local ~t A recent calculation at ne=2.5 × 10 t3 cm -3 and Te= 1.3× 107 K by Feldman et al. [ 10] gives It t4/I~~7= 0.49 without proton. This value coincides with that obtained for nffnc=0.8 from our calculation based on refs. [8] and [ 12]; in ref. [8] referred by Feldman et al., no/n,=0.8 was implicitly taken into calculation although no data for proton excitation were presented
[12]. 408
31 August 1987
Volume 123, number 8
PHYSICS LETTERS A
3 ! August 1987
significant when the proton/deuteron temperature is higher than 600 eV and higher than that of electrons because of the negative and positive dependences on
zl I
the temperature of C~2 and C~2.
O. 5
'/ .
0.0
/
-
/
I"
//1
The authors would like to thank Professor S. Hayakawa for useful discussions, and also thank their colleagues of the JIPP T-IIU group.
I
II I
I ~ .....
..........
2
Acknowledgement
I /
,
ss S
-0.5
I
,,,
i,,,,,,,,
13 14 Log n e (cm "3)
15
Fig. 4. Theoretical idensity dependence of the intensity ratios (in photons) of 117 to 845 A lines (solid lines) and of 114 to845 A lines (broken lines), n f f n ~ = 1.0 is assumed in all the cases.
electron density for such a measurement. The electron temperature dependence and calibration of the detector may become severe problems in the case of the diagnostics ~vith the line pairs and forbidden line.
5. Concluding remarks
We would like to emphasize that the closely spaced pair of lines, 114 A/117 A is suitable for the electron density measurement in the range 10 ~2_ 10 ~s c m - 3 because of less sensitivity to the electron temperature and of the ease of observation with a spectrometer. The dependence on the proton/deuteron temperature is also weak if the temperature of protons/deuterons is lower than that of electrons as generally observedl for tokamaks, but it may become
References [ 1] T. Kato, K. Masai and J. Mizuno, J. Phys. Soc. Japan 52 0983) 3019. [2] H.E. Mason, G.A. Doschek, U. Feldman and A.K. Bhatia, Astron. Astrophys. 73 (1979) 74. [ 3 ] S. Suckewer and E. Hinnov, Phys. Rev. A 20 (1979) 578. [4] B.C. Stratton, H.W. Moos and M. Finkenthal, Astrophys. J. 279 0984) L31. [5] B.C. Stratton, H.W. Moos, S. Suckewer, U. Feldman, J.F. Seely and A.K. Bhatia, Phys. Rev. A 31 (1985 ) 2534. [6] G.A. Doschek and U. Feldman, J. Appl. Phys. 47 (1976) 3083. [7] U. Feldman, G.A. Doschek and W.E. Behring, Space Sci. Rev. 22 (1978) 191. [8] H.E. Mason and P.J. Storey, Mon. Not. R. Astron. Soc. 191 (1980) 631. [ 9 ] M. Loulergue, H.E. Mason, H. Nussbaumer and P.J. Storey, Astron. Astrophys. 150 (1985 ) 246. [ 10 ] U. Feldman, J.F. Scely and A.IC Bhatia, At. Data Nucl. Data Tables 32 (1985) 305. [ 11 ] R. Mewe and E.H.B.M. Gronenschiid, Astron. Astrophys. Suppl. 45 (1981) 11; R. Mewe, E.H.B.M. Gronenschild and G.H.J. van den Oord, Astron. Astrophys. Suppl. 62 (1985) 197, and references therein. [ 12 ] H.E. Mason, private communication (1986).
409
PHYSICSLETTERSA
31 August 1987
ELECTRON DENSITY DIAGNOSTICS BY Fe XXII LINE INTENSITY RATIO Kuniaki MASAI and Takako KATO Institute of Plasma Physics, Nagoya University,Nagoya 464, Japan Received 51January1987; revisedmanuscriptreceived 15 May 1987;acceptedfor publication9 June 1987 CommuniCatedby F. Troyon The electrondensityof a tokamakplasmais obtainedfrom the 114.41 and 117.17J~line intensitiesof Fe XXII. This measurement is fouhd to be usefulfor electrondensitiesin the range 10t2-1015 cm-3, on accountof its weakdependenceon temperature and of the proximityof these spectrallines.
1. Introduction On many tokamaks, the electron density is often measured by the Thomson scattering technique. This measurement is often used in the analysis of spectroscopic data, !for example, to obtain the impurity concentrations. Such an analysis is not free from the spatial distribution of the ion of interest, and is often complicated by a rapidly changing plasma. Conversely, the electron density derived from the line intensity ratio provides a continuous measurement. Therefore, diagnostics using line intensity ratios are of great interest i for impurity studies in tokamaks as well as in astrophysical plasmas. The intensityi ratio of energetically close lines of the same ion may be used to obtain density information, if one Of the lines is excited from a rectastable state. In a previous paper we investigated the electron densityidependence of the line intensities of oxygen III-V ions for use in the peripheral region of a tokamak plasma [ 1 ]. In the higher temperature regime, highly ionized iron with mulfiplet ground configurations may be similarly used. Measurements for solar flares [2] and tokamaks [3-5] have been reported as well! as theoretical calculations [6-10] and empirical formulae [ 11 ]. In the present! paper, we demonstrate that a pair o f F e XXII lineslprovides a useful means of the density diagnostics, ihTe lines under consideration are associated witll the transitions 2s22p(2p3/2-
2s2p2(2p3/2) 114.41 Jt and 2s22p(2p l/2)-2s2p2(2Sl/2 ) 117.17 J~. Our goal is to observe the time variation of the line intensities particularly when the density changes'rapidly. In the next section, we outline the line intensity ratio dependence on the electron density. The experimental results and the theoretical calculation including proton/deuteron excitation are described in sections 3 and 4, respectively.
2. Electron density dependence In this section, we consider a four-level atom excited only by electron impact and give a theoretical account of the proposed density diagnostics. The rate coefficients for collisional excitation as well as the level configurations of the transitions concerned and the wavelengths are shown in fig. 1. The energy levels are designated by indices, for instance 2s22p(2Pl/2 ) as level 1, and the collisional rate coefficients are distinguished thereby with subscripts as Cjk for the transition from levelj to k; Cik (Ckfl means excitation (de-excitation) for j < k . The rate coefficients by proton and deuteron impacts are distinguished from those by electron impact by the additional subscripts p and d, respectively. We denote by n,, nj and Aj~ the electron density, the population of level j and the radiative transition probability from level j to k, respectively. The relation between the intensity ratio and the
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
405
Volume 123, number 8 I
10-9!
PHYSICSLETTERSA
I I Ill]
I
I
I
I i'll
i
is the branching ratio for the transition from level 4 to k. (I) For ne< 1012 cm -3, n2 is negligible compared to nl because neCjkS~.A21 in eq. (2). Then eq. (1) reduces to
i
C26
10-~o -
i
II 14 b42 C14
_
i
1117 ~b31 C13~0.17 .
& zp~
C23 I I Illl
i
i
,
, ,,,I]
o.1 1.o Temperature ( keV )
Fig. 1. Temperature dependences of the rate coefficients for collisional excitation processesand the schematicenergy diagram. electron density depends on the domain in which lies the density n~. Three regimes, labeled (I), (II) and (III), respectively, can be identified. The essential parameter which differentiates the regimes is the population of the ground level 2. The intensity ratio of 114 to 117 A can be written approximately, 1114 ~ b42
['CI4 C24 n2 )
1117 ~
~,~--13+ ~
~-~-t ,
(1)
where
represents the branching ratio of the radiative transition from levelj to k. The relative population of the ground states can be expressed as n2 n¢( C12 "~C14842) nl ~ ne( C21 + C24B41) +A2t where A21 = 1.39X 104 s - t [8], and
B4k=(A4k+neC4k)(~,i A4i+ne x?i C4i) -1 406
(3)
Hence, as the electron density decreases, the population distributions approaches that of the so-called corona regime, which is fully realized at ne< 1011 cm -3. (II) With an increase in the electron density, level 2 becomes populated. In the region of n~ ~ 1013-1014 c m - s, eq. (1) can be approximated by keeping only terms proportional to n~ and the value of s varies little when n~ is near the value neo for which s is at its maximum, Smax: S m a x = ( 1 - - q ) / ( l + q ) at ne=n~o ~-"qa 21/(C21 -~-C24B41), where q is defined as
10 -u
I
31 August 1987
(2)
C24 C12-.~t-C14B42~-1/2 q-= 14 C1~ C21 +C24B41]
(4)
Then eq. (1) can be approximated by,
1114
I11-'--7~'q-
1 b42 b31
C14(ne~ (l-q)/(l+q) Ct3\neo/
(5)
The value ofn~o lies in the range (6-10) × 1013 c m -3 when Te ranges from 0.5 to 2 keV, while q remains nearly constant around 0.33. Thus the ratio (5) is nearly proportional to n~/2. (III) For n¢> 10 Is cm -3, neCjks dominates over A21 in eq. (2), and the ground levels 1 and 2 are marginally boltzmannian. As the electron density increases, B4k approaches C4k/Y~iC4,. Then eq. (2) reduces to n2/nt ~ C~2/C2~ -~ 2, according to their statistical weights, because the excitation energy is much smaller than T~ assumed to be of the order of 1 keV. Hence, eq. (1) can be approximated by
1114 b42 C24 C12 +C14B42 I117m[9--'-31C13 C21+C24841
b42 C24
~2b-~-3~~3 "~2"3' (6)
where the last two expressions are valid for n~> A41/C41, A42/C42 ~ 1020 cm -3. It should be noted that I1~4]I117 depends rather weakly on T~ because the excitation energies for Cl 3 and C24 are close together. The intensity ratio is most
Volume 123, number 8
PHYSICS LETTERSA
sensitive to the electron density in the range r/e,~ 10J3-1014 c m - 3 (regime (II)), so that this line pair provides a simple and good diagnostic tool for current tokamak plasmas. Moreover, the absolute value of ne may be easily derived without requiring appreciable correction for the detector sensitivity since the wavelengths of these lines are very close.
31 August 1987
~- 1.0 .=o.5 I
A
Measurement
I
(b)
'?E t.~ U
,c= 0
3.
J
lO
" ,_=
l
l
l
l
l
l
l
l
l
1.0
%0.5
The Fe XXII lines were observed along a central chord of the poloidal cross section of a tokamak plasma in the JIPP T-IIU device. The experiment was carried out in a study of additional heating in the ion-cyclotron range of frequency (hereafter referred to as ICRF). We measured the line intensities using a grazing incidence monochromator with a Rowland circle of 2 m in diameter, mounting a platinum coated 600 g/ram grating and a photomultiplier with a CsI coated photocathode. The spectral resolution was about 0.2 A almost independently of wavelength; closely spaced lines of Fe XXII 117.17 A and Fe XXI 117.51 ,~ were successfully resolved. The relative spectral sensitivity of the monochromator was calibrated by the branching ratio method. The plasma Was primarily sustained by the ohmic current heating! The density was rapidly raised by puffing a H2/D2 mixtured gas at 115 ms shortly before ICRF was turned on at 120 ms. During the ICRF heating phase of about 40 ms, the electron density was kept at a level of 2-3 times the density in the preceding ohmic phase. In fig. 2a we show the time variation o f the intensity ratio which was obtained every lime bin of about 0.5 ms. For comparison, the line~aveFaged electron density measured by a microwave interferometer is shown in fig. 2b. The intensity ratio is well correlated with the lineaveraged density. In addition, we show two examples with plasmas under different conditions in order to experimentally demonstrate the density dependence. One was obtained in a plasma almost the same as in figs. 2a an~l 2b, except that there is no ICRF heating: the other was a plasma with neither ICRF heating nor gas puffing. The time variations of the intensity ratio irl these two cases are shown in figs. 2c and 2d, respectively. The increase of the intensity
i e.. = 1.0
i
i
'
~
i
i
I
i
i
J
~
I
(d)
"0.5 '
~ 1~avv '
200
Time (ms)
Fig. 2. Time variationsof (a) the line intensityratio between I 14 and I 17 .~, (b) the line-averagedelectrondensity for a tokamak plasma additionallyheated by ICRF with gas puffing.The same ratio as in (a) for an ohmicallyheated plasma is shown in (c) with gas puffing,and in (d) withoutgas puffing. ratio associated with the gas puffing at 105 ms in fig. 2c is slightly smaller and rises slower than that with additional ICRF heating in fig. 2a. This suggests that the increase in the intensity ratio may be at least partially attributed to the presence of the ICRF heating rather than only to gas puffing. In the absence of gas puffing and ICRF heating (fig. 2d), there is no measurable change of the intensity ratio. The correlation between the density measured with the intensity ratio and the microwave interferometer was also good in the two cases shown in figs. 2c and 2d; such good correlation has been observed for many discharges.
4. Calculation
We have simultaneously solved the population of 10 levels taking into account the excitation by proton and deuteron impacts (C~2, C~2), and calculated the line intensities. Competitive radiative and collisional processes in the transitions to and from all n = 2 levels are considered to obtain the absolute value of ne. The radiative transition probabilities and 407
Volume 123, number 8 0.5
i
j
PHYSICS LETTERS A
i , , , , ,
-
.
~ i
j
i,
i,
i,
.....(c) - (b)
i
i , ,
J , ,
,
/
i
i
•
Boltzman Eq.
-
.
i,
.
.
.
.
(a)
.
.
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===
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o
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.- ;,:.:.'-.".'~'i;1:"":C0rona'"~
-I.0
12
. . . . . . . . .
I
13
. . . . . . . . .
2keV
I
14
.........
15
log ne (cm-3) Fig. 3. Theoretical density dependence of the line intensity ratio (in photons) of I 14 to l 17 ,~.. Dotted, broken and solid lines represent the cases, (a) np/nc=O and nd/n~=O, (b) np/n¢=0,1 and nd/ne=0.9 and (c) np/ne= 1 and na/nc=O, respectively. The arrows indicate the asymptotic values. Boxes represent the observed intensity ratio (size is one standard deviation), the line-averaged and the central electron densities.
the collision strengths for electron excitation were taken from ref. [ 8], and the rate coefficient for proton excitation was from ref. [ 12 ]. The excitation rate coefficient by deuteron impact was calculated from that by proton by accounting the mass difference. The line intensity ratio thus obtained is shown in fig. 3 as a function of the electron density for three values of the temperature. Note the effect of proton and deuteron impacts on the excitation from level 1 to 2 in the ground configuration. The rate coefficient for this process by proton/deuteron impact (C~2, C~2 ) dominates over that by electron impact ( G 2 ) at temperatures > 600 eV (fig. 1 ). In addition, C~2 and Co~2 are rapidly increasing functions of the temperature, while C~2 is a slowly decreasing one. Protons and deuterons, therefore, play an important role in the population of level 2 at temperatures of the order of 1 keV where the line emission of Fe XXII is of interest. Assuming the temperature of protons/deuterons is the same as that of electrons, we consider the following three cases; (a) n~,/ne=O and ndne=O (proton/deuteron excitation is ignored), (b) np/n~ =0.1 and no/n,=0.9 and (c) np/n~= 1 and ndn¢=O,
where np and rtd are the densities of protons and deuterons, respectively #t Two representative values of It~4/11~7 measured in the ICRF heating experiment are indicated in fig. 3 with one standard deviation confidence levels. The data were taken during 5 ms at t = 100 ms and 140 ms corresponding to the ohmic heating phase before gas puffing and to the ICRF heating phase thereafter, respectively. For comparison the line-averaged electron density and the density in the central region measured by Thomson scattering are also indicated at the same time. The results from cases (b) and (c) allow us to estimate that the density is about (2.5-3) × 1013 c m - 3 at t = 100 ms in the ohmic phase, while case (a) fails to give a consistent value. I~ ~4/I 117 at around 140 ms is somewhat larger than that expected from ne and te in the experiment. From the analysis of the fast-neutral-particles, we infer that a higher energy component of protons/deuterons produced by ICRF enhances the excitation from level 1 to 2 resulting in the line emission of 114/~. As the temperature of protons/deuterons become larger relatively to that of electrons, the intensity ratio increases more strongly with the proton/deuteron temperature. We briefly mention two other line pairs combined with a forbidden line (845 ~,). The line intensity ratios of 114 and 117 ~ relative to that at 845 ~,, versus the electron density, are calculated for the three temperature values and shown in fig. 4 by broken and solid lines, respectively. I~ 1 4 / / 8 4 5 is more sensitive to the density than I~ ~4/I~,7, and is nearly proportional to ne for n, > 10 1 4 c m - 3 whereas 1114//,, 7 tends to be less sensitive; therefore, I~,4/Is45 may be a density diagnostic tool, complementary to 1,14/Ii17, despite a stronger dependence on the temperature. On the other hand, the intensity ratio of 117 A/845 A may be a diagnostic tool of the proton/deuteron temperature higher than 600 eV although the ratio is affected by the electron density at n,> 1013 c m - 3 ; the intensity ratio 114 A/117 A is helpful to estimate the local ~t A recent calculation at ne=2.5 × 10 t3 cm -3 and Te= 1.3× 107 K by Feldman et al. [ 10] gives It t4/I~~7= 0.49 without proton. This value coincides with that obtained for nffnc=0.8 from our calculation based on refs. [8] and [ 12]; in ref. [8] referred by Feldman et al., no/n,=0.8 was implicitly taken into calculation although no data for proton excitation were presented
[12]. 408
31 August 1987
Volume 123, number 8
PHYSICS LETTERS A
3 ! August 1987
significant when the proton/deuteron temperature is higher than 600 eV and higher than that of electrons because of the negative and positive dependences on
zl I
the temperature of C~2 and C~2.
O. 5
'/ .
0.0
/
-
/
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//1
The authors would like to thank Professor S. Hayakawa for useful discussions, and also thank their colleagues of the JIPP T-IIU group.
I
II I
I ~ .....
..........
2
Acknowledgement
I /
,
ss S
-0.5
I
,,,
i,,,,,,,,
13 14 Log n e (cm "3)
15
Fig. 4. Theoretical idensity dependence of the intensity ratios (in photons) of 117 to 845 A lines (solid lines) and of 114 to845 A lines (broken lines), n f f n ~ = 1.0 is assumed in all the cases.
electron density for such a measurement. The electron temperature dependence and calibration of the detector may become severe problems in the case of the diagnostics ~vith the line pairs and forbidden line.
5. Concluding remarks
We would like to emphasize that the closely spaced pair of lines, 114 A/117 A is suitable for the electron density measurement in the range 10 ~2_ 10 ~s c m - 3 because of less sensitivity to the electron temperature and of the ease of observation with a spectrometer. The dependence on the proton/deuteron temperature is also weak if the temperature of protons/deuterons is lower than that of electrons as generally observedl for tokamaks, but it may become
References [ 1] T. Kato, K. Masai and J. Mizuno, J. Phys. Soc. Japan 52 0983) 3019. [2] H.E. Mason, G.A. Doschek, U. Feldman and A.K. Bhatia, Astron. Astrophys. 73 (1979) 74. [ 3 ] S. Suckewer and E. Hinnov, Phys. Rev. A 20 (1979) 578. [4] B.C. Stratton, H.W. Moos and M. Finkenthal, Astrophys. J. 279 0984) L31. [5] B.C. Stratton, H.W. Moos, S. Suckewer, U. Feldman, J.F. Seely and A.K. Bhatia, Phys. Rev. A 31 (1985 ) 2534. [6] G.A. Doschek and U. Feldman, J. Appl. Phys. 47 (1976) 3083. [7] U. Feldman, G.A. Doschek and W.E. Behring, Space Sci. Rev. 22 (1978) 191. [8] H.E. Mason and P.J. Storey, Mon. Not. R. Astron. Soc. 191 (1980) 631. [ 9 ] M. Loulergue, H.E. Mason, H. Nussbaumer and P.J. Storey, Astron. Astrophys. 150 (1985 ) 246. [ 10 ] U. Feldman, J.F. Scely and A.IC Bhatia, At. Data Nucl. Data Tables 32 (1985) 305. [ 11 ] R. Mewe and E.H.B.M. Gronenschiid, Astron. Astrophys. Suppl. 45 (1981) 11; R. Mewe, E.H.B.M. Gronenschild and G.H.J. van den Oord, Astron. Astrophys. Suppl. 62 (1985) 197, and references therein. [ 12 ] H.E. Mason, private communication (1986).
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