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Electron density determination in argon cesium MHD-plasmas
Physica 123C (1984) 247-256 North-Holland, Amsterdam
E L E C T R O N DENSITY DETERMINATION IN ARGON CESIUM MHD-PLASMAS
J.M. W E T Z E R Division Direct Energy Conversion, University of Technology, P.O. Box 513, 5612 A Z Eindhoven, The Netherlands Received 28 June 1983 The method of electron density determination from continuum emission is often used in the nonstationai'y plasma of an MHD-generator because of its simplicity. An assumption in the analysis is that recombinative radiation forms the main contribution to the continuum. Next to this the method carries with it some other uncertainties. In this work the method is compared experimentally with the method of Stark broadening measurement of spectral lines, using a stationary argon cesium discharge. Both techniques involve corrections for plasma inhomogeneities. Agreement within 20% is found. The contribution of Cs2 molecules to the continuum emission, which is significant in saturated vapor at moderate temperatures (500-1000 K), is estimated to be of minor importance in the generator plasma.
1. Introduction
Measurement of plasma parameters in an M H D - g e n e r a t o r is usually complicated because the discharge structure is nonstationary, inhomogeneous and not accurately reproducible [1-3]. This is a serious restriction to the applicability of more or less advanced diagnostic techniques like line profile measurement or interferometric techniques, because these methods require either a homogeneous plasma or a welldefined inhomogeneity. When one is interested in the spatial distribution of plasma parameters, also scattering techniques become complicated because the discharge structure is both nonstationary and not reproducible. This restricts the possibility of scanning or repeated measurement. Thus relatively simple continuous diagnostic techniques are required, together with analysing techniques, in order to reconstruct the spatial distribution of plasma parameters. One such diagnostic technique, which is often used in M H D - g e n e r a t o r plasmas, is the determination of electron density from continuum emission [1-3]. This method however carries with it some uncertainties. In this work the ability of the method for application in M H D - g e n e r a t o r plasmas is discussed. An analysing technique to reconstruct spatial distributions from line integrated inten-
sities in generator plasmas will be presented elsewhere [4]. T o analyse continuum emission, information is required on the origin of the radiation. In the M H D plasma considered, consisting of cesium in an argon buffer gas, radiative recombination is the dominant process contributing to the continuum emission. In an argon cesium plasma without impurities the most likely source of additional radiation, atomic lines being avoided, is formed by cesium diatomic molecules. It has been shown by Lapp and Harris [5] that in saturated vapor a considerable fraction of cesium is present in molecular form. In this work the effect o f cesium molecular emission and absorption on the continuum is estimated. In general argon cesium plasmas will include impurities which will give rise to contributions to the continuum emission. Another possible source of error is the uncertainty of the cross section data of radiative recombination. In our analysis the data obtained by Norcross and Stone [6] are used. When comparing their values with the results of Agnew and Summers [7], Gridneva and Kosabov [8] and Burgess and Seaton [9], discrepancies of more than 30% occur. These uncertainties demand an experimental comparison with a method that is independent of both additional radiative contributions and
0378-4363/84/$03.00 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
248
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
recombination cross sections. For this purpose the line broadening of spectral lines of cesium is used. Lines have been selected whose width is primarily determined by Stark broadening. From the line profile the electron density has been determined using Griem's theory [10], and has been compared with the results of continuum emission analysis. To avoid experimental difficulties, a stationary discharge, with a diameter of 10 mm, has been used in an argon cesium plasma with a composition comparable to that of the actual MHD-generator plasma. Corrections for radial inhomogeneity have been performed using the measurements of radial profiles of Borghi [11] in the same discharge tube.
further evaluated assuming charge neutrality and a Maxwellian electron distribution function. The validity of the latter assumption has been verified for argon cesium MHD plasmas by Borghi [11]. Moreover, throughout the analysis the plasma is assumed to be optically thin at wavelength A, and argon is assumed not to contribute to the continuum, considering the temperatures involved. Combination of eqs. (2) and (3) and elaboration of the assumptions yields 2 hc 3 -1/2 -3/2 e j ( A ) d A = 2 n , ( - f f ) m e (27rkTe) AjdA
with 1
1
hc
1
1
Ai = (~--~//)Q{ve(A)}exp{-~-~ (~--~-~)}. 2. Theory
(4)
(5)
Summation of all contributions gives the total radiative power per unit volume and per unit solid angle in the wavelength interval dA
2.1. Radiative recombination Radiative recombination occurs when a free electron and an ion recombine to form a neutral atom in a state j, according to
e(X) dA = ~'~ ej(A)dh
(6)
J
(~j ---;~). e- + A ÷~ A t + hr.
(1)
The energy equation of this process yields c
c
1
2
h "-~= h "-~j+~mev,,
(2)
where hc/A is the energy of the released photon, hc/Aj is the binding energy of atomic state j and mev2/2 is the free electron's kinetic energy. The continuum arising from this process thus shows an edge at A = Aj. The radiative power per unit volume and per unit solid angle in a wavelength interval dA around wavelength A is given by hc
ej(A) dA = ~
+
n¢n veQj(ve)f(v,) doe,
(3)
where Qj(ve) is the cross section of radiative recombination into atomic state j, f(ve) is the electron velocity distribution and dv~ is the electron velocity interval corresponding to the wavelength interval dA through eq. (2). Eq. (3) is
According to Agnew and Summers [7] most of the radiative power in the visible originates from recombination into the 6P and 5D states of cesium. In our analysis also recombination into the 7P and 6D states is taken into account. The correspondin~g edges occur at 5010, 5825, 10 552 and 11 135A. Therefore measurements have been _performed at wavelengths smaller than 5010/~. The continuum intensity has been measured at 4100 and 4900/~. At these wavelengths the continuum is not affected by line radiation. For the evaluation of the measured intensities the radiative power is divided into an n~-dependent part and a Te-dependent part
~(x) = n~. f(,~, To).
(7)
The temperature-dependent part is shown in fig. 1, for A = 4100/~ and A = 4900 ~ . Expression (7) is used to obtain the electron density once the
J.M. Wetzer / Electron density determination in A r - C s plasmas
•7
10-30
nostics is not very sensitive to electron temperature in the regime where Te > 4000 K. The determination of the electron density, however, is rather accurate because the radiative power depends on the square of no, while the inaccuracy in electron temperature only weakly affects f(A, Te), or ne. The accuracy of the electron density is primarily determined by the accuracy of the measured intensities.
, I
~
'
'
249
'
..~,=
'<_" 10-31
-32 I0
2.2. Molecular contribution to the continuum
-33 10 I0000
5000
Te ( K )
Fig. 1. T e m p e r a t u r e d e p e n d e n c e of the radiative power from recombination of electrons with cesium ions at wavelengths 4100 and 4900 ~ .
electron temperature is known. The latter is derived from the ratio of intensities at different wavelengths
The cesium molecules present in the plasma can both emit or absorb radiation. To determine the effect on the measured continuum intensity, apart from plasma parameters information is needed about the molecular fraction and about the absorption and emission coefficients at the wavelengths of interest. The molecular concentration is calculated using chemical equilibrium, ncs2= n2~ • 8(T). exp(~---~),
(9)
e(A,)/e(X2) = f(X,, Te)/f(A2, Te) (A2~ 3 hc 1 1 = \A-~I] exP{k--~e (~22- A-~I)} "
(8,
Fig. 2 shows this ratio as a function of temperature for Zl = 4900 ~ and A2 = 4100 ~ . As can be seen from figs. 1 and 2 this diagtO0
k 1 = 4900 1
:" 1 ........
"~
19
5
1
i
I
I
I
I
I
I
I -""'r---
5000
10000
TO (K)
Fig. 2. Ratio of recombinative emission power values at wavelengths 4900 a n d 4100 ~ .
where ncs is the atomic concentration and D is the dissociation energy ( D = 0 . 4 5 e V ) . Since 8(T) depends relatively weakly on temperature, and only a small temperature range is considered, 8(T) can be approximated by a constant. The value used is 3.43 x 10-29 m 3, and is determined from the saturated vapor pressures at T = 7 0 0 K , pcs=27.6 Torr and Pcn= 0.625 Torr. D, pc~ and Pcs2 are taken from Lapp and Harris [5]. Fig. 3 shows the molecular fraction for conditions which are typical for MHDgenerator plasmas. The absorption cross section of cesium molecules has been measured by Lapl~ and Harris [5]. They report that around 4100 A no significant molecular band is present, while around 4900 a band exists with a maximum at 4800 ~ . The absorption cross section at 4900 ~- is 5 × 10-2t m 2. In the subsequent part of this section the effect of this band on the absorption and emission at 4900 ~ will be estimated separately. We consider a homogeneous plasma layer with thickness I. Only the absorption of light by molecules is regarded. Neglecting the emission of
J.M. Wetzer / Electron density determination in A r - C s plasmas
250
2hc 2
172
10-3
"~
10-4 ~
10-5
19 10
t 20 10
,,,"
t f 21 22 10 ncs(m-3) 10
Fig. 3, Molecular cesium fraction as a function of atomic cesium density for different gas temperatures.
the layer itself, the transmission is given by
I(x = l) I(x 0) = e x p ( - n c ~ " Q " l),
(10)
where x = 0 and x = l are the boundaries of the layer and Q is the absorption cross section of Cs2 molecules at A = 4900 ~ . Calculations have been performed in the range of cesium atomic densities between 102° m -3 and I(F2 m -3 and gas temperatures between 500 and 1000 K for I = 5 cm. For these conditions, which are characteristic for M H D - g e n e r a t o r plasmas, the transmission is larger than 97%. Hence the effect of cesium molecules can be neglected. The emission of cesium molecules has been calculated using thermodynamic equilibrium, and has been compared with recombinative emission. In equilibrium the molecular emissive power per unit volume per unit solid angle per wavelength interval is related to the absorption coefficient k(v) = ncs2" Q through
With eqs. (9) and (12) it is now possible to calculate the molecular emission once the temperatures involved are known. T o estimate the maximal molecular contribution that might occur it is assumed that the dissociation process is ruled by the h e a w particle translational temperature while the emission is assumed to be ruled by a vibrational temperature equal to the electron temperature. The recombinative emission is calculated using eqs. (4), (5) and (6). The ratio of molecular and recombinative emission is given in fig. 4 as a function of electron temperature for equilibrium conditions at a heavy particle temperature of 1000 K and cesium atomic densities in the range between 10~ m -3 and 10Z~m-3. It can be concluded that in the M H D generator discharge, where the electron temperature exceeds 4000 K, the molecular contribution is negligible. In practical experiments the measured intensity will be line-integrated, and will thus contain contributions of the colder plasma around the discharge, where molecular emission might play a role. The total intensity of these colder parts, however, will be smaller than the intensity from the discharge by orders of 10-I
++:+ 10--3
1.50 zooo
e(v) = k(v)B(v, Tc~),
(11)
where B(v, Tcn) is Planck's function. Evaluation in terms of wavelengths yields
hv
2500
3000
3500
Te(S)
,000
Fig. 4. Ratio of molecular and recombinative emission power of an equilibrium plasma as a function of electron temperature for different atomic cesium densities at a gas temperature of 1000 K.
J.M. Wetzer / Electron density determination in Ar-Cs plasmas magnitude, and usually will be below the detection limit considering the dynamic range of the photomultiplier. In reality the situation as it emerges from fig. 4 will be even more pronounced because the molecular emission will be governed by a temperature lower than the electron temperature.
2.3. Stark broadening of spectral lines The spectral lines of cesium in an argon cesium M H D plasma are broadened primarily by pressure broadening. The perturbing particles may be neutral (Van der Waals broadening, resonance broadening) or charged particles (Stark broadening). For many spectral lines of cesium, especially for the fundamental series, the main contribution to the linewidth is produced by the Stark effect because the free electrons interact rather efficiently with the weakly bound optical electron. These Stark dominated spectral lines are very attractive for diagnostical purposes because over a wide range the width is proportional to the electron density, and almost independent of the electron temperature. In our work the theory of Griem [10] has been used to relate linewidths to electron densities. In this theory the ion contribution is described in the quasi-static approximation while the electron contribution is described in the impact approximation. T h e profile is finally obtained by averaging over the different ion field contributions, taking into account the effect of ion-ion correlations and the D e b y e shielding by electrons. Over a wide range of conditions the resulting profile is Lorentzian with the full halfwidth given by
ion contribution and we(nJlO z2) is half the halfwidth due to the electron contribution. Eq. (13) is valid when the following requirements are fulfilled: A ~< 0.5,
R ~ 0.8,
~, = w~o/v > 1,
(14)
where v is the relative velocity between the perturbing ion and the perturbed atom. In all the experiments these requirements have been checked a posteriori. In fig. 5 the linewidth of some fundamental lines of cesium is plotted as a function of electron density for a Saha-plasma with a total cesium density of 5 × 1021m -3. Also the corresponding electron temperature is shown. Although the latter varies from 2000 K at ne = 1.3 x 1019 m -3 to 6000 K at ne = 5 x 1021m -3 the width remains proportional to the electron density in the whole range. Since the fundamental lines are more sensitive to electron density than the members of any other series, these lines have been selected for the experiments. The remaining pressure broadening mechanisms, Van der Waals broadening and 10
I
,
I
I
Nc
60O0 A
I 503/2 -
~w
l
oF5/2
,o'
5000
/ 4000 n=
1~
100 3000
wS = ( 1 + 1.75a~l-~)/ne'1/4(1-0.75R)}
1 t
lo"
19 10
with ne in m -a. ot and we are weak functions of temperature and are tabulated by Griem [10], while R is the ratio of the mean ion-ion separation Pi = (4¢rne/3)-ira and the D e b y e radius PD = (nee2/eokT) -1c2. A = a(nJlOZ2) TM represents the
251
I 10
20
I
I 10
21
I 01o (m-3)
2000 22 10
Fig. 5. Stark contribution w s to the linewidth of the fundamental lines of cesium 5D3rz-nFsrz for an equilibrium plasma with cesium density 5 x 10zl m-3, as a function of
electron density. Also the corresponding electron temperature is shown. The lines 5Dsrz-nFsr~Trzexhibit almost the same Stark contribution at equal principal quantum number n.
252
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
resonance broadening, usually have a small effect on the linewidth of above-mentioned lines, though not always negligible. Also for these mechanisms Griems description is used [10]. Resonance broadening results in unshifted Lorentzian profiles (except in the far wing) whose full halfwidth is given by
]~R ~ =
3e2
"l{gt'~i/2A3fn
t87r2~-oomoc2i~g.)
j~ c,,
(15)
where g~ and g, are the degeneracies of lower and upper level of the corresponding transition, A and f are the wavelength and absorption oscillator strengths of this transition and ncs is the neutral cesium density. The oscillator strength data are taken from Fabry [12]. Van der Waals broadening results in Lorentzian profiles with a full halfwidth given by era 2 ~9whSR~/0., wW= c [16m3E2J
13 0, "nAr
(16)
H e r e Ep is the energy of the first excited level of argon, and the matrix element R 2 is well estimated by
1
R~-2E®_E~ x[ ~
Z2EH q-
L i n e w i d t h c o n t r i b u t i o n s of V a n d e r W a a l s a n d r e s o n a n c e b r o a d e n i n g t o s o m e f u n d a m e n t a l lines of c e s i u m at nAr = 5 X 10u m -3, ncs = 5 × 1021 m -3 a n d T = 2000 K Transition
Wavelength
(x)
(x)
ww
wR
5D3/2--nFs;2 n = 6 7 8 9 i0
7229 6825 6586 6432 6326
3.2 x 3.8 x 4.5× 5.2 x 6.0 x
6
7280
3.3 × 10 -1
1.4 × 10 -3
7 8 9 10
6870 6629 6473 6366
3.8 4.5 5.3 6.1
6.8 3.8 2.4 1.6
(~) 10 -1 10 - t 10- t 10-t 10 -t
1.2 × 5.6 × 3.2× 2.0 x 1.4 x
10 -3 10 -4 10 -4 10 -4 10 -4
5Ds/2--nFsa,7/2 n =
x × × x
10-1 10 -1 10 -1 10 -1
× x × ×
10-4 10-4 10 -4 10 -4
cesium. The conditions are typical for M H D plasmas, nAr -----5 X 10u m -3, ncs = 5 × 1021 m -3 and T = 2000 K. From comparison of fig. 5 and table I it can be concluded that the Van der Waals contribution has to be corrected for, while the resonance contribution can be neglected. The accuracy of the Van der Waals broadening calculation is not crucial in the present experiments.
3. Experimental arrangement
EH
~5
Table I
1- 31~(lo+ l)}
(17)
EH and E~ are the ionization energies of hydrogen and the radiating cesium atom, Ea is the excitation energy of the upper state of the line, and la is its orbital quantum number, z is the effective charge acting on the radiating electron. All pressure broadening mechanisms discussed cause Lorentzian profiles. Therefore the resulting profile is Lorentzian and the linewidth is given by the sum of the different contributions. In table I values are given for the Van der Waals contribution and the resonance contribution to the linewidth of some fundamental lines of
T h e measurements have been performed with the set-up given in fig. 6. The discharge tube is mounted in an oven which is held at a constant temperature of 5 3 0 K (_10K). The detection system consists of a scanning monochromator (Jarrell-Ash 0.5 m) and a photomultiplier tube (EMI 9684). Intensity vs. wavelength curves are plotted on an X - Y recorder. The continuum emission is calibrated using a tungsten ribbon lamp, taking into account the transmission of the tube which decreases in time. The discharge tube .is shown in fig. 7. It consists of pyrex and contains molybdene electrodes and voltage probes. The argon pressure at room temperature is 200 Torr. The diameter of the discharge is 10 mm. T h e electron density has been varied from 1.5× 1 0 ~ m -3 to 4 . 0 x 102°m -3 by varying the
J.M. Wetzer I Electron density determination in Ar-Cs plasmas
253
.5..t.r ~
ITongsten
i ribbon lamp
/
~ ~
"
dd~arge tuba ~
_ ~
photomultplier J i t~
voltage meter X-Y recorder
Fig. 6. Set-up used in the present experiments
Fig. 7. Discharge tube used in the present experiments.
discharge current. In order to improve the signalto-noise ratio for measurement of the weak fundamental lines that show the largest width, the monochromator slit has been imaged in a plane perpendicular to the axis of the tube. Since no spatial resolution can be obtained in this way, corrections for inhomogeneity have been performed using the radial profiles measured by Borghi [11] in the same discharge tube. The correction concerns both the profile measurement and the continuum emission measurement. Also the monochromator profile has been corrected for. Since the fundamental lines (5D3/z-nFs/2, 5Ds/2-/~F5/27/2) exhibit the strongest dependence on electron density, these lines have been chosen in the experiments. The linewidth increases with principal quantum number of the upper level. However, because of both the lower population of this level and the larger width of the line, the signal-to-noise ratio decreases. The best results
under the present conditions have been found using the 6326 ~ line of cesium (5D3/z--10F5/2). The absorption of this line can be neglected, and near the centre the profile is not disturbed by adjacent lines.
4. Results and discussion
In fig. 8 the profiles of the fundamental lines 5D3/2--9F5/2 (6432~) and 5D3/2--10Fs/2 (6326~), measured at a discharge current of 2 A , are plotted. Fig. 9 shows the measured profiles of the line 5D3/2-10Fs/2 at two different discharge currents. In all cases the profiles are fitted with Lorentzian curves. Since we are mainly interested in the line centre, this part has been given a larger weight in the fitting procedure. It can be concluded that Lorentzian profiles coincide with the measured profiles in the centre and the near red wing of the lines, but underestimate the
254
J.M. Wetzer / Electron density determination in Ar-Cs plasmas 1.0 ~o
° 6432
~-'~
~
/~'~
o
4
2
3
.
stork b r o s d e n i n g / ~
.....
cont. intensit7
~
/®/
v
J
o
I
-8
0
8
X-X0 (~) Fig. 8. Normalized line profiles of the lines 5D3r~-nFs/2 for n = 9 (6432/~) and n = 10 (6326 ~ ) at a discharge current of 2 A. Drawn lines indicate Lorentzian fittings, dashed lines indicate the measured profiles. For clarity not all experimental points have been plotted. 1.0
.<.
0
i 0
l !
,
m 2 I (A)
Fig. 10. The electron density at the centre of the discharge tube as a function of discharge current, obtained from continuum emission and Stark broadening. (1) Homogeneity assumed. (2) Corrected for inhomogeneity.
[11] in the same discharge tube, the plasma parameters show a strong radial dependence. Fig. 11 shows the population density distribution of the 7D3/2 level of cesium, at a discharge current of 2 A. From this density the ne and Te distributions are calculated using the Saha-Boltzmann equilibrium. Two cesium density profiles have been used yielding the same 0
i 0
x-x, (~,)
i.0
Fig. 9. Normalized line profiles of the line 5Dan-10Fs/2 (6326 ~ ) at discharge currents of 1 and 2 A. See also the caption of fig. 8.
measured profiles in the blue wing. From the line 5D3rz--10Fs/2 electron densities have been derived using Griem's theory. These values are plotted in fig. 10, curves 1, as a function of a discharge current, together with the values obtained from continuum emission. Agreement is found to be within 30%. In the analysis so far inhomogeneities have not been taken into account. However, as is proven by excited state density measurements of Borghi
.5
_ ~ .(,__)
o
I
0
2.5
r (mm)
5.0
Fig. 11. Radial distribution of the 7D excited state density, measured by Borghi [11], at a discharge current of 2 A.
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
results. One is a homogeneous profile, the other is a parabolic profile which results from a simple energy balance between ohmic heating and conductive loss. The obtained radial distributions, given in fig. 12, enable us to obtain the electron density at the centre of the discharge (r = 0) from both continuum emission and line profile measurement. 1.0
-
•
~
O
n
e(r)
I
2.5
r |ram) 5.0
Fig. 12. Radialdistribution of electrondensityand electron t e m p e r a t u r e obtained from fig. 11.
In the case of continuum emission the electron density, found when assuming homogeneity, has to be multiplied by a correction factor ~. Since the continuum emission depends on the square of the electron density, but only weakly on the electron temperature, and because the latter shows only a weak radial dependence, the factor can be well estimated by 1
o
[ n.(0)l t-
(18)
with p = r/R where R is the discharge diameter. In the case of the line profile measurement the electron density in the centre of the discharge is determined from a computational model. With this model the linewidth of the emitted profile is calculated as a function of n~ (r = 0), using the obtained radial profiles of ne and Te. The corrected electron densities are plotted in fig. 10, curves 2. The two methods now agree within
255
20%, which is satisfactory for the application under consideration. The difference is not due to experimental errors. The error in the continuum intensity measurement is estimated to be less than 5%, yielding an error in the corresponding electron density of less than 2.5%. The error in the linewidth determination is estimated to be 6% at low discharge current and less at higher discharge current. The error in the electron density obtained from this linewidth is the same. An error in the Van der Waals broadening by a factor of two would result in an error of only 5% in the electron density obtained from line profile measurement. The remaining possible sources of error are the Stark coefficients used, the recombination cross sections, in particular their temperature dependence, and the effect of other contributions to the continuum than recombinative emission• Of these the latter two are the most likely sources. It should be noted, however, that if the discrepancies are due to Cs2 molecular radiation, the effect will be much smaller for plasma conditions as they occur in an actual M H D - g e n e r a t o r because of the higher temperatures of both heavy particles and electrons, enhancing both the dissociation process and the recombinative emission (see fig. 4).
5. Conclusion It is shown that the method of electron density determination from continuum emission measurement is applicable to argon cesium plasmas. Possible sources of error like additional radiative contributions, especially from cesium molecules, or the inaccuracy in the recombination cross sections do not heavily affect the resulting electron density• The accuracy obtained in a simulated M H D plasma, after corrections for inhomogeneity, is 20%. The accuracy expected in an actual generator plasma is better because of the higher temperatures involved.
Acknowledgement This work has been performed as a part of the
256
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
research program of the Shock Tube M H D project of the Direct Energy Conversion Group of the Eindhoven University of Technology. The author wishes to express his gratitude to C.A. Borghi, P.H.M. Feron, J.F. Uhlenbusch and A. Veefkind for their contribution and fruitful discussions.
References [1] W.M. Hellebrekers, Instability analysis in a nonequilibrium MHD generator, Ph.D. Thesis, Eindhoven University of Technology (1980). [2] A.F.C. Sens, V.A. Bityurin, J.M. Wetzer, A. Veefkind and J.F.G. Bravers, 20th Syrup. on Eng. Asp. of MHD, Irvine, CN (1982) p. 10.6. [3] A. Veefkind, J.W.M.A. Houben, J.H. Biota and L.H.T. Rietjens, A I A A J. 14 (1976) 1118.
[4] J.M. Wetzer, IEEE, PS-11, 2 (June 1983). [5] M. Lapp and L.P. Harris, J. Quant. Spectr. Radiat. Transfer 6 (1966) 169. [6] D.W. Norcross and P.M. Stone, J. Quant. Spectr. Radiat. Transfer 6 (1966) 277. [7] L. Agnew and C. Summers, Proc. 7th Int. Conf. on Phenomena in Ionized Gases, Beograd, Vol. 2 (1966) p. 574 Gradevinska Kujiga Publ. House, Beograd. [8] S.M. Gridneva and G.A. Kosabov, Proc. 3rd Int. Conf. on MHD, Vol. 1 (1966) p. 73. S.M. Gridneva and G.A. Kosabov, High. Temp. 5 (1967) 334. [9] A. Burgess and H.J. Seaton, Mon. Not. Roy. Astr. Soc. 120 (1959) 121. [10] H.R. Griem, Spectral Line Broadening by Plasmas (Academic Press, New York, 1974). [11] C.A. Borghi, Discharges in the inlet region of a noble gas MHD generator, Ph.D. Thesis, Eindhoven University of Technology (1982). [12] M. Fabry, J. Quant. Spectr. Radiat. Transfer 16 (1976) 127.
E L E C T R O N DENSITY DETERMINATION IN ARGON CESIUM MHD-PLASMAS
J.M. W E T Z E R Division Direct Energy Conversion, University of Technology, P.O. Box 513, 5612 A Z Eindhoven, The Netherlands Received 28 June 1983 The method of electron density determination from continuum emission is often used in the nonstationai'y plasma of an MHD-generator because of its simplicity. An assumption in the analysis is that recombinative radiation forms the main contribution to the continuum. Next to this the method carries with it some other uncertainties. In this work the method is compared experimentally with the method of Stark broadening measurement of spectral lines, using a stationary argon cesium discharge. Both techniques involve corrections for plasma inhomogeneities. Agreement within 20% is found. The contribution of Cs2 molecules to the continuum emission, which is significant in saturated vapor at moderate temperatures (500-1000 K), is estimated to be of minor importance in the generator plasma.
1. Introduction
Measurement of plasma parameters in an M H D - g e n e r a t o r is usually complicated because the discharge structure is nonstationary, inhomogeneous and not accurately reproducible [1-3]. This is a serious restriction to the applicability of more or less advanced diagnostic techniques like line profile measurement or interferometric techniques, because these methods require either a homogeneous plasma or a welldefined inhomogeneity. When one is interested in the spatial distribution of plasma parameters, also scattering techniques become complicated because the discharge structure is both nonstationary and not reproducible. This restricts the possibility of scanning or repeated measurement. Thus relatively simple continuous diagnostic techniques are required, together with analysing techniques, in order to reconstruct the spatial distribution of plasma parameters. One such diagnostic technique, which is often used in M H D - g e n e r a t o r plasmas, is the determination of electron density from continuum emission [1-3]. This method however carries with it some uncertainties. In this work the ability of the method for application in M H D - g e n e r a t o r plasmas is discussed. An analysing technique to reconstruct spatial distributions from line integrated inten-
sities in generator plasmas will be presented elsewhere [4]. T o analyse continuum emission, information is required on the origin of the radiation. In the M H D plasma considered, consisting of cesium in an argon buffer gas, radiative recombination is the dominant process contributing to the continuum emission. In an argon cesium plasma without impurities the most likely source of additional radiation, atomic lines being avoided, is formed by cesium diatomic molecules. It has been shown by Lapp and Harris [5] that in saturated vapor a considerable fraction of cesium is present in molecular form. In this work the effect o f cesium molecular emission and absorption on the continuum is estimated. In general argon cesium plasmas will include impurities which will give rise to contributions to the continuum emission. Another possible source of error is the uncertainty of the cross section data of radiative recombination. In our analysis the data obtained by Norcross and Stone [6] are used. When comparing their values with the results of Agnew and Summers [7], Gridneva and Kosabov [8] and Burgess and Seaton [9], discrepancies of more than 30% occur. These uncertainties demand an experimental comparison with a method that is independent of both additional radiative contributions and
0378-4363/84/$03.00 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
248
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
recombination cross sections. For this purpose the line broadening of spectral lines of cesium is used. Lines have been selected whose width is primarily determined by Stark broadening. From the line profile the electron density has been determined using Griem's theory [10], and has been compared with the results of continuum emission analysis. To avoid experimental difficulties, a stationary discharge, with a diameter of 10 mm, has been used in an argon cesium plasma with a composition comparable to that of the actual MHD-generator plasma. Corrections for radial inhomogeneity have been performed using the measurements of radial profiles of Borghi [11] in the same discharge tube.
further evaluated assuming charge neutrality and a Maxwellian electron distribution function. The validity of the latter assumption has been verified for argon cesium MHD plasmas by Borghi [11]. Moreover, throughout the analysis the plasma is assumed to be optically thin at wavelength A, and argon is assumed not to contribute to the continuum, considering the temperatures involved. Combination of eqs. (2) and (3) and elaboration of the assumptions yields 2 hc 3 -1/2 -3/2 e j ( A ) d A = 2 n , ( - f f ) m e (27rkTe) AjdA
with 1
1
hc
1
1
Ai = (~--~//)Q{ve(A)}exp{-~-~ (~--~-~)}. 2. Theory
(4)
(5)
Summation of all contributions gives the total radiative power per unit volume and per unit solid angle in the wavelength interval dA
2.1. Radiative recombination Radiative recombination occurs when a free electron and an ion recombine to form a neutral atom in a state j, according to
e(X) dA = ~'~ ej(A)dh
(6)
J
(~j ---;~). e- + A ÷~ A t + hr.
(1)
The energy equation of this process yields c
c
1
2
h "-~= h "-~j+~mev,,
(2)
where hc/A is the energy of the released photon, hc/Aj is the binding energy of atomic state j and mev2/2 is the free electron's kinetic energy. The continuum arising from this process thus shows an edge at A = Aj. The radiative power per unit volume and per unit solid angle in a wavelength interval dA around wavelength A is given by hc
ej(A) dA = ~
+
n¢n veQj(ve)f(v,) doe,
(3)
where Qj(ve) is the cross section of radiative recombination into atomic state j, f(ve) is the electron velocity distribution and dv~ is the electron velocity interval corresponding to the wavelength interval dA through eq. (2). Eq. (3) is
According to Agnew and Summers [7] most of the radiative power in the visible originates from recombination into the 6P and 5D states of cesium. In our analysis also recombination into the 7P and 6D states is taken into account. The correspondin~g edges occur at 5010, 5825, 10 552 and 11 135A. Therefore measurements have been _performed at wavelengths smaller than 5010/~. The continuum intensity has been measured at 4100 and 4900/~. At these wavelengths the continuum is not affected by line radiation. For the evaluation of the measured intensities the radiative power is divided into an n~-dependent part and a Te-dependent part
~(x) = n~. f(,~, To).
(7)
The temperature-dependent part is shown in fig. 1, for A = 4100/~ and A = 4900 ~ . Expression (7) is used to obtain the electron density once the
J.M. Wetzer / Electron density determination in A r - C s plasmas
•7
10-30
nostics is not very sensitive to electron temperature in the regime where Te > 4000 K. The determination of the electron density, however, is rather accurate because the radiative power depends on the square of no, while the inaccuracy in electron temperature only weakly affects f(A, Te), or ne. The accuracy of the electron density is primarily determined by the accuracy of the measured intensities.
, I
~
'
'
249
'
..~,=
'<_" 10-31
-32 I0
2.2. Molecular contribution to the continuum
-33 10 I0000
5000
Te ( K )
Fig. 1. T e m p e r a t u r e d e p e n d e n c e of the radiative power from recombination of electrons with cesium ions at wavelengths 4100 and 4900 ~ .
electron temperature is known. The latter is derived from the ratio of intensities at different wavelengths
The cesium molecules present in the plasma can both emit or absorb radiation. To determine the effect on the measured continuum intensity, apart from plasma parameters information is needed about the molecular fraction and about the absorption and emission coefficients at the wavelengths of interest. The molecular concentration is calculated using chemical equilibrium, ncs2= n2~ • 8(T). exp(~---~),
(9)
e(A,)/e(X2) = f(X,, Te)/f(A2, Te) (A2~ 3 hc 1 1 = \A-~I] exP{k--~e (~22- A-~I)} "
(8,
Fig. 2 shows this ratio as a function of temperature for Zl = 4900 ~ and A2 = 4100 ~ . As can be seen from figs. 1 and 2 this diagtO0
k 1 = 4900 1
:" 1 ........
"~
19
5
1
i
I
I
I
I
I
I
I -""'r---
5000
10000
TO (K)
Fig. 2. Ratio of recombinative emission power values at wavelengths 4900 a n d 4100 ~ .
where ncs is the atomic concentration and D is the dissociation energy ( D = 0 . 4 5 e V ) . Since 8(T) depends relatively weakly on temperature, and only a small temperature range is considered, 8(T) can be approximated by a constant. The value used is 3.43 x 10-29 m 3, and is determined from the saturated vapor pressures at T = 7 0 0 K , pcs=27.6 Torr and Pcn= 0.625 Torr. D, pc~ and Pcs2 are taken from Lapp and Harris [5]. Fig. 3 shows the molecular fraction for conditions which are typical for MHDgenerator plasmas. The absorption cross section of cesium molecules has been measured by Lapl~ and Harris [5]. They report that around 4100 A no significant molecular band is present, while around 4900 a band exists with a maximum at 4800 ~ . The absorption cross section at 4900 ~- is 5 × 10-2t m 2. In the subsequent part of this section the effect of this band on the absorption and emission at 4900 ~ will be estimated separately. We consider a homogeneous plasma layer with thickness I. Only the absorption of light by molecules is regarded. Neglecting the emission of
J.M. Wetzer / Electron density determination in A r - C s plasmas
250
2hc 2
172
10-3
"~
10-4 ~
10-5
19 10
t 20 10
,,,"
t f 21 22 10 ncs(m-3) 10
Fig. 3, Molecular cesium fraction as a function of atomic cesium density for different gas temperatures.
the layer itself, the transmission is given by
I(x = l) I(x 0) = e x p ( - n c ~ " Q " l),
(10)
where x = 0 and x = l are the boundaries of the layer and Q is the absorption cross section of Cs2 molecules at A = 4900 ~ . Calculations have been performed in the range of cesium atomic densities between 102° m -3 and I(F2 m -3 and gas temperatures between 500 and 1000 K for I = 5 cm. For these conditions, which are characteristic for M H D - g e n e r a t o r plasmas, the transmission is larger than 97%. Hence the effect of cesium molecules can be neglected. The emission of cesium molecules has been calculated using thermodynamic equilibrium, and has been compared with recombinative emission. In equilibrium the molecular emissive power per unit volume per unit solid angle per wavelength interval is related to the absorption coefficient k(v) = ncs2" Q through
With eqs. (9) and (12) it is now possible to calculate the molecular emission once the temperatures involved are known. T o estimate the maximal molecular contribution that might occur it is assumed that the dissociation process is ruled by the h e a w particle translational temperature while the emission is assumed to be ruled by a vibrational temperature equal to the electron temperature. The recombinative emission is calculated using eqs. (4), (5) and (6). The ratio of molecular and recombinative emission is given in fig. 4 as a function of electron temperature for equilibrium conditions at a heavy particle temperature of 1000 K and cesium atomic densities in the range between 10~ m -3 and 10Z~m-3. It can be concluded that in the M H D generator discharge, where the electron temperature exceeds 4000 K, the molecular contribution is negligible. In practical experiments the measured intensity will be line-integrated, and will thus contain contributions of the colder plasma around the discharge, where molecular emission might play a role. The total intensity of these colder parts, however, will be smaller than the intensity from the discharge by orders of 10-I
++:+ 10--3
1.50 zooo
e(v) = k(v)B(v, Tc~),
(11)
where B(v, Tcn) is Planck's function. Evaluation in terms of wavelengths yields
hv
2500
3000
3500
Te(S)
,000
Fig. 4. Ratio of molecular and recombinative emission power of an equilibrium plasma as a function of electron temperature for different atomic cesium densities at a gas temperature of 1000 K.
J.M. Wetzer / Electron density determination in Ar-Cs plasmas magnitude, and usually will be below the detection limit considering the dynamic range of the photomultiplier. In reality the situation as it emerges from fig. 4 will be even more pronounced because the molecular emission will be governed by a temperature lower than the electron temperature.
2.3. Stark broadening of spectral lines The spectral lines of cesium in an argon cesium M H D plasma are broadened primarily by pressure broadening. The perturbing particles may be neutral (Van der Waals broadening, resonance broadening) or charged particles (Stark broadening). For many spectral lines of cesium, especially for the fundamental series, the main contribution to the linewidth is produced by the Stark effect because the free electrons interact rather efficiently with the weakly bound optical electron. These Stark dominated spectral lines are very attractive for diagnostical purposes because over a wide range the width is proportional to the electron density, and almost independent of the electron temperature. In our work the theory of Griem [10] has been used to relate linewidths to electron densities. In this theory the ion contribution is described in the quasi-static approximation while the electron contribution is described in the impact approximation. T h e profile is finally obtained by averaging over the different ion field contributions, taking into account the effect of ion-ion correlations and the D e b y e shielding by electrons. Over a wide range of conditions the resulting profile is Lorentzian with the full halfwidth given by
ion contribution and we(nJlO z2) is half the halfwidth due to the electron contribution. Eq. (13) is valid when the following requirements are fulfilled: A ~< 0.5,
R ~ 0.8,
~, = w~o/v > 1,
(14)
where v is the relative velocity between the perturbing ion and the perturbed atom. In all the experiments these requirements have been checked a posteriori. In fig. 5 the linewidth of some fundamental lines of cesium is plotted as a function of electron density for a Saha-plasma with a total cesium density of 5 × 1021m -3. Also the corresponding electron temperature is shown. Although the latter varies from 2000 K at ne = 1.3 x 1019 m -3 to 6000 K at ne = 5 x 1021m -3 the width remains proportional to the electron density in the whole range. Since the fundamental lines are more sensitive to electron density than the members of any other series, these lines have been selected for the experiments. The remaining pressure broadening mechanisms, Van der Waals broadening and 10
I
,
I
I
Nc
60O0 A
I 503/2 -
~w
l
oF5/2
,o'
5000
/ 4000 n=
1~
100 3000
wS = ( 1 + 1.75a~l-~)/ne'1/4(1-0.75R)}
1 t
lo"
19 10
with ne in m -a. ot and we are weak functions of temperature and are tabulated by Griem [10], while R is the ratio of the mean ion-ion separation Pi = (4¢rne/3)-ira and the D e b y e radius PD = (nee2/eokT) -1c2. A = a(nJlOZ2) TM represents the
251
I 10
20
I
I 10
21
I 01o (m-3)
2000 22 10
Fig. 5. Stark contribution w s to the linewidth of the fundamental lines of cesium 5D3rz-nFsrz for an equilibrium plasma with cesium density 5 x 10zl m-3, as a function of
electron density. Also the corresponding electron temperature is shown. The lines 5Dsrz-nFsr~Trzexhibit almost the same Stark contribution at equal principal quantum number n.
252
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
resonance broadening, usually have a small effect on the linewidth of above-mentioned lines, though not always negligible. Also for these mechanisms Griems description is used [10]. Resonance broadening results in unshifted Lorentzian profiles (except in the far wing) whose full halfwidth is given by
]~R ~ =
3e2
"l{gt'~i/2A3fn
t87r2~-oomoc2i~g.)
j~ c,,
(15)
where g~ and g, are the degeneracies of lower and upper level of the corresponding transition, A and f are the wavelength and absorption oscillator strengths of this transition and ncs is the neutral cesium density. The oscillator strength data are taken from Fabry [12]. Van der Waals broadening results in Lorentzian profiles with a full halfwidth given by era 2 ~9whSR~/0., wW= c [16m3E2J
13 0, "nAr
(16)
H e r e Ep is the energy of the first excited level of argon, and the matrix element R 2 is well estimated by
1
R~-2E®_E~ x[ ~
Z2EH q-
L i n e w i d t h c o n t r i b u t i o n s of V a n d e r W a a l s a n d r e s o n a n c e b r o a d e n i n g t o s o m e f u n d a m e n t a l lines of c e s i u m at nAr = 5 X 10u m -3, ncs = 5 × 1021 m -3 a n d T = 2000 K Transition
Wavelength
(x)
(x)
ww
wR
5D3/2--nFs;2 n = 6 7 8 9 i0
7229 6825 6586 6432 6326
3.2 x 3.8 x 4.5× 5.2 x 6.0 x
6
7280
3.3 × 10 -1
1.4 × 10 -3
7 8 9 10
6870 6629 6473 6366
3.8 4.5 5.3 6.1
6.8 3.8 2.4 1.6
(~) 10 -1 10 - t 10- t 10-t 10 -t
1.2 × 5.6 × 3.2× 2.0 x 1.4 x
10 -3 10 -4 10 -4 10 -4 10 -4
5Ds/2--nFsa,7/2 n =
x × × x
10-1 10 -1 10 -1 10 -1
× x × ×
10-4 10-4 10 -4 10 -4
cesium. The conditions are typical for M H D plasmas, nAr -----5 X 10u m -3, ncs = 5 × 1021 m -3 and T = 2000 K. From comparison of fig. 5 and table I it can be concluded that the Van der Waals contribution has to be corrected for, while the resonance contribution can be neglected. The accuracy of the Van der Waals broadening calculation is not crucial in the present experiments.
3. Experimental arrangement
EH
~5
Table I
1- 31~(lo+ l)}
(17)
EH and E~ are the ionization energies of hydrogen and the radiating cesium atom, Ea is the excitation energy of the upper state of the line, and la is its orbital quantum number, z is the effective charge acting on the radiating electron. All pressure broadening mechanisms discussed cause Lorentzian profiles. Therefore the resulting profile is Lorentzian and the linewidth is given by the sum of the different contributions. In table I values are given for the Van der Waals contribution and the resonance contribution to the linewidth of some fundamental lines of
T h e measurements have been performed with the set-up given in fig. 6. The discharge tube is mounted in an oven which is held at a constant temperature of 5 3 0 K (_10K). The detection system consists of a scanning monochromator (Jarrell-Ash 0.5 m) and a photomultiplier tube (EMI 9684). Intensity vs. wavelength curves are plotted on an X - Y recorder. The continuum emission is calibrated using a tungsten ribbon lamp, taking into account the transmission of the tube which decreases in time. The discharge tube .is shown in fig. 7. It consists of pyrex and contains molybdene electrodes and voltage probes. The argon pressure at room temperature is 200 Torr. The diameter of the discharge is 10 mm. T h e electron density has been varied from 1.5× 1 0 ~ m -3 to 4 . 0 x 102°m -3 by varying the
J.M. Wetzer I Electron density determination in Ar-Cs plasmas
253
.5..t.r ~
ITongsten
i ribbon lamp
/
~ ~
"
dd~arge tuba ~
_ ~
photomultplier J i t~
voltage meter X-Y recorder
Fig. 6. Set-up used in the present experiments
Fig. 7. Discharge tube used in the present experiments.
discharge current. In order to improve the signalto-noise ratio for measurement of the weak fundamental lines that show the largest width, the monochromator slit has been imaged in a plane perpendicular to the axis of the tube. Since no spatial resolution can be obtained in this way, corrections for inhomogeneity have been performed using the radial profiles measured by Borghi [11] in the same discharge tube. The correction concerns both the profile measurement and the continuum emission measurement. Also the monochromator profile has been corrected for. Since the fundamental lines (5D3/z-nFs/2, 5Ds/2-/~F5/27/2) exhibit the strongest dependence on electron density, these lines have been chosen in the experiments. The linewidth increases with principal quantum number of the upper level. However, because of both the lower population of this level and the larger width of the line, the signal-to-noise ratio decreases. The best results
under the present conditions have been found using the 6326 ~ line of cesium (5D3/z--10F5/2). The absorption of this line can be neglected, and near the centre the profile is not disturbed by adjacent lines.
4. Results and discussion
In fig. 8 the profiles of the fundamental lines 5D3/2--9F5/2 (6432~) and 5D3/2--10Fs/2 (6326~), measured at a discharge current of 2 A , are plotted. Fig. 9 shows the measured profiles of the line 5D3/2-10Fs/2 at two different discharge currents. In all cases the profiles are fitted with Lorentzian curves. Since we are mainly interested in the line centre, this part has been given a larger weight in the fitting procedure. It can be concluded that Lorentzian profiles coincide with the measured profiles in the centre and the near red wing of the lines, but underestimate the
254
J.M. Wetzer / Electron density determination in Ar-Cs plasmas 1.0 ~o
° 6432
~-'~
~
/~'~
o
4
2
3
.
stork b r o s d e n i n g / ~
.....
cont. intensit7
~
/®/
v
J
o
I
-8
0
8
X-X0 (~) Fig. 8. Normalized line profiles of the lines 5D3r~-nFs/2 for n = 9 (6432/~) and n = 10 (6326 ~ ) at a discharge current of 2 A. Drawn lines indicate Lorentzian fittings, dashed lines indicate the measured profiles. For clarity not all experimental points have been plotted. 1.0
.<.
0
i 0
l !
,
m 2 I (A)
Fig. 10. The electron density at the centre of the discharge tube as a function of discharge current, obtained from continuum emission and Stark broadening. (1) Homogeneity assumed. (2) Corrected for inhomogeneity.
[11] in the same discharge tube, the plasma parameters show a strong radial dependence. Fig. 11 shows the population density distribution of the 7D3/2 level of cesium, at a discharge current of 2 A. From this density the ne and Te distributions are calculated using the Saha-Boltzmann equilibrium. Two cesium density profiles have been used yielding the same 0
i 0
x-x, (~,)
i.0
Fig. 9. Normalized line profiles of the line 5Dan-10Fs/2 (6326 ~ ) at discharge currents of 1 and 2 A. See also the caption of fig. 8.
measured profiles in the blue wing. From the line 5D3rz--10Fs/2 electron densities have been derived using Griem's theory. These values are plotted in fig. 10, curves 1, as a function of a discharge current, together with the values obtained from continuum emission. Agreement is found to be within 30%. In the analysis so far inhomogeneities have not been taken into account. However, as is proven by excited state density measurements of Borghi
.5
_ ~ .(,__)
o
I
0
2.5
r (mm)
5.0
Fig. 11. Radial distribution of the 7D excited state density, measured by Borghi [11], at a discharge current of 2 A.
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
results. One is a homogeneous profile, the other is a parabolic profile which results from a simple energy balance between ohmic heating and conductive loss. The obtained radial distributions, given in fig. 12, enable us to obtain the electron density at the centre of the discharge (r = 0) from both continuum emission and line profile measurement. 1.0
-
•
~
O
n
e(r)
I
2.5
r |ram) 5.0
Fig. 12. Radialdistribution of electrondensityand electron t e m p e r a t u r e obtained from fig. 11.
In the case of continuum emission the electron density, found when assuming homogeneity, has to be multiplied by a correction factor ~. Since the continuum emission depends on the square of the electron density, but only weakly on the electron temperature, and because the latter shows only a weak radial dependence, the factor can be well estimated by 1
o
[ n.(0)l t-
(18)
with p = r/R where R is the discharge diameter. In the case of the line profile measurement the electron density in the centre of the discharge is determined from a computational model. With this model the linewidth of the emitted profile is calculated as a function of n~ (r = 0), using the obtained radial profiles of ne and Te. The corrected electron densities are plotted in fig. 10, curves 2. The two methods now agree within
255
20%, which is satisfactory for the application under consideration. The difference is not due to experimental errors. The error in the continuum intensity measurement is estimated to be less than 5%, yielding an error in the corresponding electron density of less than 2.5%. The error in the linewidth determination is estimated to be 6% at low discharge current and less at higher discharge current. The error in the electron density obtained from this linewidth is the same. An error in the Van der Waals broadening by a factor of two would result in an error of only 5% in the electron density obtained from line profile measurement. The remaining possible sources of error are the Stark coefficients used, the recombination cross sections, in particular their temperature dependence, and the effect of other contributions to the continuum than recombinative emission• Of these the latter two are the most likely sources. It should be noted, however, that if the discrepancies are due to Cs2 molecular radiation, the effect will be much smaller for plasma conditions as they occur in an actual M H D - g e n e r a t o r because of the higher temperatures of both heavy particles and electrons, enhancing both the dissociation process and the recombinative emission (see fig. 4).
5. Conclusion It is shown that the method of electron density determination from continuum emission measurement is applicable to argon cesium plasmas. Possible sources of error like additional radiative contributions, especially from cesium molecules, or the inaccuracy in the recombination cross sections do not heavily affect the resulting electron density• The accuracy obtained in a simulated M H D plasma, after corrections for inhomogeneity, is 20%. The accuracy expected in an actual generator plasma is better because of the higher temperatures involved.
Acknowledgement This work has been performed as a part of the
256
J.M. Wetzer / Electron density determination in Ar-Cs plasmas
research program of the Shock Tube M H D project of the Direct Energy Conversion Group of the Eindhoven University of Technology. The author wishes to express his gratitude to C.A. Borghi, P.H.M. Feron, J.F. Uhlenbusch and A. Veefkind for their contribution and fruitful discussions.
References [1] W.M. Hellebrekers, Instability analysis in a nonequilibrium MHD generator, Ph.D. Thesis, Eindhoven University of Technology (1980). [2] A.F.C. Sens, V.A. Bityurin, J.M. Wetzer, A. Veefkind and J.F.G. Bravers, 20th Syrup. on Eng. Asp. of MHD, Irvine, CN (1982) p. 10.6. [3] A. Veefkind, J.W.M.A. Houben, J.H. Biota and L.H.T. Rietjens, A I A A J. 14 (1976) 1118.
[4] J.M. Wetzer, IEEE, PS-11, 2 (June 1983). [5] M. Lapp and L.P. Harris, J. Quant. Spectr. Radiat. Transfer 6 (1966) 169. [6] D.W. Norcross and P.M. Stone, J. Quant. Spectr. Radiat. Transfer 6 (1966) 277. [7] L. Agnew and C. Summers, Proc. 7th Int. Conf. on Phenomena in Ionized Gases, Beograd, Vol. 2 (1966) p. 574 Gradevinska Kujiga Publ. House, Beograd. [8] S.M. Gridneva and G.A. Kosabov, Proc. 3rd Int. Conf. on MHD, Vol. 1 (1966) p. 73. S.M. Gridneva and G.A. Kosabov, High. Temp. 5 (1967) 334. [9] A. Burgess and H.J. Seaton, Mon. Not. Roy. Astr. Soc. 120 (1959) 121. [10] H.R. Griem, Spectral Line Broadening by Plasmas (Academic Press, New York, 1974). [11] C.A. Borghi, Discharges in the inlet region of a noble gas MHD generator, Ph.D. Thesis, Eindhoven University of Technology (1982). [12] M. Fabry, J. Quant. Spectr. Radiat. Transfer 16 (1976) 127.