- Email: [email protected]
Role of atomic inelastic collisions in a Cs-He steady state discharge
I. Quanr. Spmo~c.
Rodiar.
Tramftr, Vol.
19. pp. 239-243.
Pergunon Press 1978.
Printed in Great Britain
ROLE OF ATOMIC INELASTIC COLLISIONS IN A Cs-He STEADY STATE DISCHARGE G. GOUSSET, B. SAYER,M. FERRAY and J.
LOZINGOT
Centre d’Etudes Nucltaires de Saclay, Service de Physique Atomique. B.P. No. 2-91190 Gif-sur-Yvette, France
(Received 2 August 1971; received for publication
14 October 1977)
Abstract-The population of va$ous excited states and the electron temperature in a mixture of cesium vapor and helium have been measured spectroscopically in a stationary electrical discharge where helium atoms remain in their ground state. An equilibrium between the populations of highly excited cesium levels was observed to be characterized by a Boltzmann temperature equal to the gas temperature. It is concluded that the populations of these high levels are more influenced by Cs* + He inelastic collisions than by Cs* + e collisions when [He]/[e] 2 I06. The influence of the helium atoms has also been observed on the relation between electron temperature and electron density.
INTRODUCTION IT IS WELL
known that, in many cases, the excitation or ionization of an excited atom A* in a collision with a neutral atom B, according to the reaction A*+B+A**+B Or
A*+B+A++e+B,
is less efficient than for the corresponding process in which the perturber is an electron. Consequently, inelastic atomic processes are in most cases assumed to be of minor importance in plasmas. But, in very weakly ionized media, where the ratio of the concentrations [B]/[e] would be large enough, the contribution of the process (1) is no longer negligible. If in such a medium the temperature of the electrons, T,, and the gas temperature, Tg, are different, inelastic collisions with electrons and atoms would tend to establish equilibria between the populations of the excited states A* at Boltzmann temperatures equal to T, or Tg, respectively. It may also be suspected that inelastic atomic collisions may affect the electron creation-loss balance. The purpose of the present work is to study these effects in a cesium plasma in the presence of a high .concentration of helium atoms. The processes are more interesting if the excited atoms differ from the colliding neutral atoms. Moreover, since the first excitation potential of He is much larger than the ionization potential of Cs, the helium atoms remain in their ground state in a discharge even for large [He]/[Cs] ratios. It should be noted that such alkali-rare-gas plasmas have been the subject of numerous experimental investigations because of their practical interest in MHD conversion. The conclusions of these studies, both in steady-state and transient discharges, are that the effect of rare-gases is limited to that of a thermal bath or a diffusion barrier, as long as the rare-gas atoms remain in their ground state.“-3’ In the present work, the characteristics of Cs-He steady-state discharges are investigated for ratios [He]/[e] larger than in the previous studies (up to 2 x 10’). Both the population of the excited states and the electron temperature have been measured as functions of electron and helium concentrations. The results are compared with those obtained in pure cesium.‘4’ The conclusions derived from the pure cesium experiment may be summarized as follows. At high electron densities (n, = [el> lOI cme3), the stationary regime is maintained by a balance between ionization and recombination processes; thus, n, T, and the population of the excited cesiuin levels are close to the thermodynamic equilibrium’ values with the electron gas. At low electron densities (n, < 1O’2cmm3),the radiative losses and, especially under the experimental conditions of Ref. (4), the losses of charged species by diffusion to the walls become 239
240
G.
GOUSSET et al.
preponderant. The stationary regime is, therefore, maintained by a balance between ionization and diffusion. Under these conditions, deviations from both the T, = f(n,) relationship and the relation between the populations of the excited states have been observed. In particular, the distribution of the population in the high energy levels corresponds to a Boltzmann temperature much lower than T,. The departure from T, due to diffusion would be reduced by the presence of the rare-gas acting only as a diffusion barrier. We shall see that the rare-gas atoms play a more active role when [He]/n, is larger than IO’. EXPERIMENTAL
STUDIES
The experimental set-up and the diagnostic techniques_ are similar to those previously described in Ref. (4) and are briefly summarized here. The experimental cell consists of a cylindrical glass tube (8 cm diameter-25 cm long). The tube is heated by an oven (To,,, = 625°K) and connected to a reservoir, located outside the oven, at a lower temperature. The cesium pressure is controlled by regulating the temperature of the reservoir. The cesium concentration is deduced from the equivalent half-width of the 8521 A resonance line, measured by absorption of the continuum spectrum of a tungsten-ribbon lamp. To interpret these half-width measurements, collisional broadening with both Cs”’ and Het6’atoms have been taken into account. The cesium concentrations deduced by this method are in good agreement with the vapor concentrations corresponding to equilibrium with liquid cesium at the temperature of the coolest point of the cell.“’ The electrical discharge is created between two molybdenum electrodes by a current-regulated power supply. Both the cathode and anode are heated (= 1000°C); if this is not done, cataphoresis occurs and, after a few minutes, the electric voltage drop between the electrodes increases rapidly and ionization of helium atoms occurs in front of the anode. When both electrodes are heated, provided p He is not too high, this cataphoresis effect does not appear; the cesium density remains uniform along the tube, and no helium lines can be detected. No heating effect of the gas by the discharge has been detected. The electron density integrated along a diameter is measured with a free-space microwaves interferometer (A = 4 mm). The electron density on the axis of the tube, nro, is deduced from this integrated value and from the radial distribution of the electrons inferred from optical measurements.(4) The populations of the excited states and the electron temperature are deduced from spectroscopic measurements. The apparatus consists of a monochromator and a photomultiplier. Both a classical technique using an amplifier, a recorder, and a photon-counting technique have been used. Absolute intensity measurements have been performed by comparing plasma emission to that of a standard tungsten-ribbon lamp. The excited-state concentrations on the axis of the tube have been deduced by using the Abel inversion method.‘4’ The electron temperature is determined from the continuum spectrum of the radiative recombination to the 6P level [Cs++ e+Cs(6P) + hv]. This method is well known”’ and has been used in pure cesium discharges. (4)But because of its importance later in the discussion of the results, the validity of the method in the presence of helium atoms must be investigated in more detail. It has been shown’4’that, in cesium plasmas where the electrons have Maxwellian energy distributions, the intensity of the recombination continuum Z(A) varies with the wavelength as Z(h) =
f$j$ e
exp{[Ei - (hc/h)]/kT,},
where usual notations are used for the physical constants, and Ei is the ionization energy of the atomic level for which recombination occurs. Thus, by plotting the experimental values of ln[A2Z(A)]as a function of l/A, a straight line is obtained from the slope of which T, may be deduced. The ability to obtain a straight line is related to the hypothesis of a Maxwellian distribution for the electron velocity. Only a dramatic change of the distribution function, corresponding to the spectral range investigated (4950-4100 A+O-0.05 eV) would be observable. At the threshold, when A = hc/Ei(6P) = 4950 A, Z(4950)Te3’2is proportional to n&cs+. A trivial condition for validity of this method of measuring the electron temperature is that all of the light emitted by the plasma in the wavelength range investigated originates from the recombination process. Lines or narrow bands induced by the presence of helium atoms would
Role of atomic inelastic collisions in a G.-He steady state discharge
241
be easy to detect by observing emission in small increments of wavelength (Fig. 1). More serious would be the contribution of a broad band extending over the spectral range investigated. We have observed that ln[A*1(h)] varies linearly with l/A (Fig. 1) as predicted by equation (2), and that 1”2(h)Tc3’4remains proportional to n, as determined by microwave phase shift for a change in n, of nearly two orders of magnitude (Fig. 2). These observations may be understood if nc,+ = n, and if all of the emitted light of the continuum originates from’ radiative recombination. EXPERIMENTAL
RESULTS
AND
DISCUSSION
We shall first consider the role played by atomic collisions on the population of excited cesium levels separated by a small potential energy gap. The two SD sublevels (AE = 98 cm-‘) will be first considered, then the Rydberg states. By examining the relation between the experimental values of T, and it, at different helium pressures, we shall be able to discuss the influence of helium atoms on the creation-loss balance of charged particles in the steady-state discharge. (1) Population of excited states It may be seen from Fig. 3 that the two 5D sublevels are close together but far from the other levels. At low atomic concentrations, the relative population of these sublevels is the result of balance of inelastic collisions with electrons and radiative processes. Under the influence of electronic collisions, the ratio of the populations R, must approach the value given by Boltzmann’s law at the electron temperature, viz. R
ce
=
Gd5D5/2)
_
ks(5~3/2)
AE 3 g-%/z evkT,=jexPkT,.
AE
85Dy2
When the helium atoms are present, the excitation transfer &(5&z)
+
H, %GcS(5&)
+
He
may be important. Under the influence of this process, the ratio of the populations of the two sublevels will tend towards R. = (3/2) exp (AEIkT,). The experimental values of the ratio R,,, for the 6S-5D forbidden lines emitted by the steady-state discharge are plotted on Fig. 3 as functions of helium pressure for a given electron density (n, = 1013cmm3).R, is proportional to R,, because the ratio of the transparencies of the
Fig. 1. A*f(A) normalized at A =4950A for the following electron densities: X, 1.2x lO”cm-‘: 0, 2.3 x IO’*cm-‘; 0,4.3 x 10” cm-‘; ncr = lOI cm-‘, pHc = 60 torr; I(A) has been corrected for the variations of the detection-system response as a function of wavelength.
G. GOUSSET et al.
242
I;-
1O-
l-
c
1017n (co-is)
10’2
l0
Fig. 2. The relative electron density deduced from the intensity of the recombination spectrum at the threshold as a function of axis electron density nro measured by microwave phase shift. 1(4950) has been corrected for the influence of the radial distribution of the emitters (n,, = lOI cm-3, pHe= 60 torr).
n
“m
=‘I2
130 10-3
I
I 10-z
1
PH,bd lo-'
1
10
10 2
Fig. 3. The ratio R, of the intensities of the two 6%SD forbidden lines as a function of helium pressure the value of R., in the absence of helium. The insert shows some (n,, = lOI cm-‘. n,, = 10” cme3). +I$& of the Cs energy levels.
ionized medium for the two lines is constant over the investigated range of helium pressure. The Doppler broadening has been indeed estimated to be preponderant under our experimental conditons. (The transparency of the medium for these forbidden lines is of the order of 90%.) However, the absolute values of R, should not be compared with R, because of uncertainties related mainly to the oscillator strengths of the two forbidden transitions. We observe, that the influence of helium atoms is important even at very small concentrations (a few hundredth of a torr). This observation indicates that inelastic atomic collisions have cross sections large enough to compete efficiently with inelastic electronic collisions when the ratio [He]/n, is greater than about a few hundred.? It should be noted that the variation of R, induced by
iThe results suggest that the populations of the SD sublevels are close to equilibrium at T, in pure cesium discharges (n,, = lOI5cm-‘) and that a significant departure from this equilibrium value is already observed when a helium concentration as small as IO” crnT3is present. Thus. the excitation transfer between 5D3,, and SD,,, induced by collisions with helium atoms is more efficient than that induced by collisions with cesium atoms. This situation is noticeably different from the case of excitation transfer between P,,, and Pvl sublevels where the collisions with Cs atoms appear much more efficient.“’
Role of atomic inelastic collisions in a Cs-He
steady state discharge
243
adding two torr of helium to a cesium discharge (n, = 10” cm-‘) is close to that which would be observed by changing the temperature characterizing the Boltzmann equilibrium between the two 50 sublevels from T, to T, If Cs* + He inelastic collisions play such an important role in the equilibrium between the 5D sublevels, we may infer that they must also be efficient in determining the equilibrium between the Rydberg states. In Fig. 4, we have considered the nF levels which have the largest popUlatiOtIS NnF because of their large statistical weight g&; ht(N#/g,p) is plotted as a function of the ionization energy of the nF levels (Fig. 4(a)) where N”F is deduced from the absolute intensity of the 5D - nF lines. A linear variation is observed both at high (n, > 1013cme3) and at low electron densities (n, C 10” cme3). From the slope of these straight lines, we may determine a “temperature” TB which approaches T, at high ne and is close to T, at low n, (Fig. 4(b)). For steady-state discharges in pure cesium, a decrease of TB had also been observed for low n,.(4) It was shown that the decrease of TB is due to loss of charged particles by diffusion and
Fig. 4(a). Plot of the nF state populations as a function of their ionization energies. --x--, experimental Boltzmann equilibrium at the measured values of T. and nru; pHc = 60 torr. results: -,
I
Ta(“K)
I
I
i
2000 -
1500-
Fig. 4(b). The Boltzmann temperature T, as a function of electron density (pHe= 60 torr).
G. GOUSSET
244
et al.
recombination at the walls and is not related to inelastic atomic collisions. In particular, it has been observed that, in pure cesium discharges (ncs = 10’4-10’5cm-‘), TB decreases. for low cesium pressures and may even reach values which are significantly lower than the gas temperature. In the present experiments, where helium is added to the cesium plasma, a limit TB is evidently obtained for. the lowest electron densities, and this limit is equal to TB’ This result indicates that inelastic collisions with atoms play a major role in the population balance of the highly excited states. Our observation of equilibrium for the populations of highly excited states at the gas (lo) These authors have reported temperature is different from that of GRIDNEVA and KASABOV. observations of a Boltzmann equilibrium corresponding to the gas temperature for highly excited states of cesium in a Cs-Ar discharge. But, under their experimental conditions, TB is obtained with a large uncertainty in the population of high nF levels (14 s n G 20, E 14F-E20F = 220cm-‘). Although their results would indicate that Ts = Tg at a surprisingly low ratio [He]/n,( 2: 16), a new interpretation of their experimental results”” suggests that the observed effect is due to the use of unreliable oscillator strengths.l Boltzmann equilibrium at the gas temperature is achieved when n, is lower than lOI*cme3 at PHe = 60 torr([He] = 10” cmm3). For the same range of [He]/n,( = 106), equilibrium has been observed between the sublevels of the 3-g principal quantum numbers in a pure helium discharge.“*’ (2) Ionization-recombination balance As mentioned in the introduction, inelastic collisions with neutral atoms can also participate in the creation-loss balance of electrons. Let us consider this balance in a steady-state discharge at low np. In pure cesium, the main electron-loss process is ambipolar diffusion to the walls, whereas the electrons are created by a step-by-step ionization mechanism. On the one hand, the rate of diffusion losses decreases with the gas pressure and increases slightly with electron temperature Te; on the other hand, the efficiency of the step-by-step ionization increases with the cesium density and rises very fast with T,. One would conclude, then, that, since the addition of helium reduces diffusion losses at a given nL, the electron loss-and-creation balance would be reached at a lower T, when helium is present. The experimental result, however, shows the opposite (Fig. 5). We observe an increase of T, with decreasing n,. This effect becomes greater with increasing pHe. Consequently, the balance in the steady-state discharge can only lead to equilibration if helium atoms either induce an additive loss process or reduce the ionization efficiency. Different possibilities may also be envisaged. The first possibility is related to the inffuence of inelastic collisions with atoms. A recent study has shown that the Cs’ + e + He recombination mechanism is not very efficient in
J
2000 2x10"
Fig. 5. The
electron
temperature
10'3
10'2
n.0(cm-31
as a function of electron density (nc, = 10” cm-‘): pHe = 20torr; X, pHe = 60 torr.
tThe measurements of the SD-r@ line intensities are rather due to Stark broadening when n, is of the order of 10’3cm-3.
imprecise
0,
pure cesium;
when n 2 16 because of overlapping
0,
of these lines
Role of atomic inelastic collisions in a Cs;He steady state discharge
24s
an afterglow where T, = Tg (13) As we have seen before, however, inelastic collisions with neutral atoms play an important role in establishing the populations of highly excited states which participate in the ionization-recombination balance. The greater the difference between T, and Tg, the more sensitive to atomic collisions are these populations. Consequently, it is possible that these inelastic collisions with atoms only play an important role in the ionizationrecombination balance when T, is noticeably different from Tg The helium atoms can also play another role by broadening the resonance lines. This broadening is responsible for an increase in the escape of the resonance radiation, which is by itself an important factor for departure from TE in plasmas. (4)Moreover, this effect may also be responsible for depletion in the high-energy tail of the electron velocity-distribution function.“4”5’ In this case, the efficiency of the 6S-6P excitation by electrons would be reduced and, consequently, the step-by-step ionization process would be less efficient than expected at the measured T, (where T, is defined and measured by reference to the core of the distribution function). CONCLUSIONS
The conclusion reached in previous experimental studies of d.c. discharges in mixtures of alkali vapor and rare-gas was that the role played by rare-gas atoms would be limited to that of a diffusion barrier as long as the rare-gas atoms remain in their ground state. No influences of atomic collisions have been detected in these media. In the present work, by considering higher ratios of neutral atom concentrations to electronic densities, evidence of the role played by atomic collisions has been obtained directly by observing the equilibria between the highly excited states at the gas temperature. The influence of the rare-gas concentration on the T, = f(n,) relation is more difficult to interpret. A model of the ionized gas, including the different elementary processes, such as the one which has been used by some of us to describe the pure cesium plasma,‘4’ is difficult to build when inelastic atom-atom collisions have to be included. It would need to take into account very highly excited states and to include, with their appropriate coefficients, both inelastic electronic and atomic collisions which affect these levels. It is of interest to compare the present results with those obtained by studying a Cs-He afterglow. (13)In this last experiment, it has been shown that the three-body Cs’ + e + e recombination mechanism remains predominant with regard to processes involving He atoms, even when the ratio [He]/n, is as large as several times 10’. The apparent contradiction seems to indicate that the inelastic atomic collisions play a more important role in a plasma when T, is noticeably different from T, Acknowledgements-The authors are grateful to Dr. R. GUTCHECK and Dr. J. BERLANDE for a critical reading of the manuscript. REFERENCES 1. L. P. HARRIS, 1. Appl. Phys. 36, 1543(1965). 2. N. D. MORGULIS and I. N. POLUSHKIN, High Temperature, 4,699 (1%6). 3. H. VANTONGEREN, Philips Res. Repts. Suppl. Eindhoven, Netherlands, No. 3 (1975). 4. B. SAYER, J. C. JEANNET and J. BERLANDE, I: Physique 33,993 (1972). 5. C. L. CHENand A. V. PHELPS,Phys. Reu. 173.62 (1%8). 6. R. 0. GARRF~T and S. Y. CHEN, Phys. Rev. l44,66 (1%6). 7. J. B. TAYLOR and 1. LANGMUIR, Phys. Reu. 51,753 (1937). 8. L. AGNEW and C. SUMMERS, Proc. of the 7th Inr. Conf. on Phenomena in Ionized Gases, Gradevinska Knijga Publishing House Beograd, Yugoslavia, Vol. II, p. 574 (1966). 9. M. PIMBERT, J. Physique 33,331 (1972). IO. S. M. GIUDNEVA and G. A. KASABOV, Electricity from MHD SM 74/69, Salzburg, Austria, (1966). Il. V. S. VOROBEV and A. 1. GLEIZER, Opt. Spectrosc. 37,450 (1974). 12. E. N. PAVLOVSKAYA and I. V. PODMOSHENSKII, Opt. Spectrosc. 23,477 (1%7); 34,9 (1973). 13. G. GOUSSET, B. SAYER and J. BERLANDE, Phys. Rev. A 16, 1070(1977). 14. J. F. SHAW, M. MITCHNER and C. H. KRUGER, Phys. kluids 13, 339 (1970). 15. L. VRIENS, J. Appl. Phys. 44, 3980(1973).
Rodiar.
Tramftr, Vol.
19. pp. 239-243.
Pergunon Press 1978.
Printed in Great Britain
ROLE OF ATOMIC INELASTIC COLLISIONS IN A Cs-He STEADY STATE DISCHARGE G. GOUSSET, B. SAYER,M. FERRAY and J.
LOZINGOT
Centre d’Etudes Nucltaires de Saclay, Service de Physique Atomique. B.P. No. 2-91190 Gif-sur-Yvette, France
(Received 2 August 1971; received for publication
14 October 1977)
Abstract-The population of va$ous excited states and the electron temperature in a mixture of cesium vapor and helium have been measured spectroscopically in a stationary electrical discharge where helium atoms remain in their ground state. An equilibrium between the populations of highly excited cesium levels was observed to be characterized by a Boltzmann temperature equal to the gas temperature. It is concluded that the populations of these high levels are more influenced by Cs* + He inelastic collisions than by Cs* + e collisions when [He]/[e] 2 I06. The influence of the helium atoms has also been observed on the relation between electron temperature and electron density.
INTRODUCTION IT IS WELL
known that, in many cases, the excitation or ionization of an excited atom A* in a collision with a neutral atom B, according to the reaction A*+B+A**+B Or
A*+B+A++e+B,
is less efficient than for the corresponding process in which the perturber is an electron. Consequently, inelastic atomic processes are in most cases assumed to be of minor importance in plasmas. But, in very weakly ionized media, where the ratio of the concentrations [B]/[e] would be large enough, the contribution of the process (1) is no longer negligible. If in such a medium the temperature of the electrons, T,, and the gas temperature, Tg, are different, inelastic collisions with electrons and atoms would tend to establish equilibria between the populations of the excited states A* at Boltzmann temperatures equal to T, or Tg, respectively. It may also be suspected that inelastic atomic collisions may affect the electron creation-loss balance. The purpose of the present work is to study these effects in a cesium plasma in the presence of a high .concentration of helium atoms. The processes are more interesting if the excited atoms differ from the colliding neutral atoms. Moreover, since the first excitation potential of He is much larger than the ionization potential of Cs, the helium atoms remain in their ground state in a discharge even for large [He]/[Cs] ratios. It should be noted that such alkali-rare-gas plasmas have been the subject of numerous experimental investigations because of their practical interest in MHD conversion. The conclusions of these studies, both in steady-state and transient discharges, are that the effect of rare-gases is limited to that of a thermal bath or a diffusion barrier, as long as the rare-gas atoms remain in their ground state.“-3’ In the present work, the characteristics of Cs-He steady-state discharges are investigated for ratios [He]/[e] larger than in the previous studies (up to 2 x 10’). Both the population of the excited states and the electron temperature have been measured as functions of electron and helium concentrations. The results are compared with those obtained in pure cesium.‘4’ The conclusions derived from the pure cesium experiment may be summarized as follows. At high electron densities (n, = [el> lOI cme3), the stationary regime is maintained by a balance between ionization and recombination processes; thus, n, T, and the population of the excited cesiuin levels are close to the thermodynamic equilibrium’ values with the electron gas. At low electron densities (n, < 1O’2cmm3),the radiative losses and, especially under the experimental conditions of Ref. (4), the losses of charged species by diffusion to the walls become 239
240
G.
GOUSSET et al.
preponderant. The stationary regime is, therefore, maintained by a balance between ionization and diffusion. Under these conditions, deviations from both the T, = f(n,) relationship and the relation between the populations of the excited states have been observed. In particular, the distribution of the population in the high energy levels corresponds to a Boltzmann temperature much lower than T,. The departure from T, due to diffusion would be reduced by the presence of the rare-gas acting only as a diffusion barrier. We shall see that the rare-gas atoms play a more active role when [He]/n, is larger than IO’. EXPERIMENTAL
STUDIES
The experimental set-up and the diagnostic techniques_ are similar to those previously described in Ref. (4) and are briefly summarized here. The experimental cell consists of a cylindrical glass tube (8 cm diameter-25 cm long). The tube is heated by an oven (To,,, = 625°K) and connected to a reservoir, located outside the oven, at a lower temperature. The cesium pressure is controlled by regulating the temperature of the reservoir. The cesium concentration is deduced from the equivalent half-width of the 8521 A resonance line, measured by absorption of the continuum spectrum of a tungsten-ribbon lamp. To interpret these half-width measurements, collisional broadening with both Cs”’ and Het6’atoms have been taken into account. The cesium concentrations deduced by this method are in good agreement with the vapor concentrations corresponding to equilibrium with liquid cesium at the temperature of the coolest point of the cell.“’ The electrical discharge is created between two molybdenum electrodes by a current-regulated power supply. Both the cathode and anode are heated (= 1000°C); if this is not done, cataphoresis occurs and, after a few minutes, the electric voltage drop between the electrodes increases rapidly and ionization of helium atoms occurs in front of the anode. When both electrodes are heated, provided p He is not too high, this cataphoresis effect does not appear; the cesium density remains uniform along the tube, and no helium lines can be detected. No heating effect of the gas by the discharge has been detected. The electron density integrated along a diameter is measured with a free-space microwaves interferometer (A = 4 mm). The electron density on the axis of the tube, nro, is deduced from this integrated value and from the radial distribution of the electrons inferred from optical measurements.(4) The populations of the excited states and the electron temperature are deduced from spectroscopic measurements. The apparatus consists of a monochromator and a photomultiplier. Both a classical technique using an amplifier, a recorder, and a photon-counting technique have been used. Absolute intensity measurements have been performed by comparing plasma emission to that of a standard tungsten-ribbon lamp. The excited-state concentrations on the axis of the tube have been deduced by using the Abel inversion method.‘4’ The electron temperature is determined from the continuum spectrum of the radiative recombination to the 6P level [Cs++ e+Cs(6P) + hv]. This method is well known”’ and has been used in pure cesium discharges. (4)But because of its importance later in the discussion of the results, the validity of the method in the presence of helium atoms must be investigated in more detail. It has been shown’4’that, in cesium plasmas where the electrons have Maxwellian energy distributions, the intensity of the recombination continuum Z(A) varies with the wavelength as Z(h) =
f$j$ e
exp{[Ei - (hc/h)]/kT,},
where usual notations are used for the physical constants, and Ei is the ionization energy of the atomic level for which recombination occurs. Thus, by plotting the experimental values of ln[A2Z(A)]as a function of l/A, a straight line is obtained from the slope of which T, may be deduced. The ability to obtain a straight line is related to the hypothesis of a Maxwellian distribution for the electron velocity. Only a dramatic change of the distribution function, corresponding to the spectral range investigated (4950-4100 A+O-0.05 eV) would be observable. At the threshold, when A = hc/Ei(6P) = 4950 A, Z(4950)Te3’2is proportional to n&cs+. A trivial condition for validity of this method of measuring the electron temperature is that all of the light emitted by the plasma in the wavelength range investigated originates from the recombination process. Lines or narrow bands induced by the presence of helium atoms would
Role of atomic inelastic collisions in a G.-He steady state discharge
241
be easy to detect by observing emission in small increments of wavelength (Fig. 1). More serious would be the contribution of a broad band extending over the spectral range investigated. We have observed that ln[A*1(h)] varies linearly with l/A (Fig. 1) as predicted by equation (2), and that 1”2(h)Tc3’4remains proportional to n, as determined by microwave phase shift for a change in n, of nearly two orders of magnitude (Fig. 2). These observations may be understood if nc,+ = n, and if all of the emitted light of the continuum originates from’ radiative recombination. EXPERIMENTAL
RESULTS
AND
DISCUSSION
We shall first consider the role played by atomic collisions on the population of excited cesium levels separated by a small potential energy gap. The two SD sublevels (AE = 98 cm-‘) will be first considered, then the Rydberg states. By examining the relation between the experimental values of T, and it, at different helium pressures, we shall be able to discuss the influence of helium atoms on the creation-loss balance of charged particles in the steady-state discharge. (1) Population of excited states It may be seen from Fig. 3 that the two 5D sublevels are close together but far from the other levels. At low atomic concentrations, the relative population of these sublevels is the result of balance of inelastic collisions with electrons and radiative processes. Under the influence of electronic collisions, the ratio of the populations R, must approach the value given by Boltzmann’s law at the electron temperature, viz. R
ce
=
Gd5D5/2)
_
ks(5~3/2)
AE 3 g-%/z evkT,=jexPkT,.
AE
85Dy2
When the helium atoms are present, the excitation transfer &(5&z)
+
H, %GcS(5&)
+
He
may be important. Under the influence of this process, the ratio of the populations of the two sublevels will tend towards R. = (3/2) exp (AEIkT,). The experimental values of the ratio R,,, for the 6S-5D forbidden lines emitted by the steady-state discharge are plotted on Fig. 3 as functions of helium pressure for a given electron density (n, = 1013cmm3).R, is proportional to R,, because the ratio of the transparencies of the
Fig. 1. A*f(A) normalized at A =4950A for the following electron densities: X, 1.2x lO”cm-‘: 0, 2.3 x IO’*cm-‘; 0,4.3 x 10” cm-‘; ncr = lOI cm-‘, pHc = 60 torr; I(A) has been corrected for the variations of the detection-system response as a function of wavelength.
G. GOUSSET et al.
242
I;-
1O-
l-
c
1017n (co-is)
10’2
l0
Fig. 2. The relative electron density deduced from the intensity of the recombination spectrum at the threshold as a function of axis electron density nro measured by microwave phase shift. 1(4950) has been corrected for the influence of the radial distribution of the emitters (n,, = lOI cm-3, pHe= 60 torr).
n
“m
=‘I2
130 10-3
I
I 10-z
1
PH,bd lo-'
1
10
10 2
Fig. 3. The ratio R, of the intensities of the two 6%SD forbidden lines as a function of helium pressure the value of R., in the absence of helium. The insert shows some (n,, = lOI cm-‘. n,, = 10” cme3). +I$& of the Cs energy levels.
ionized medium for the two lines is constant over the investigated range of helium pressure. The Doppler broadening has been indeed estimated to be preponderant under our experimental conditons. (The transparency of the medium for these forbidden lines is of the order of 90%.) However, the absolute values of R, should not be compared with R, because of uncertainties related mainly to the oscillator strengths of the two forbidden transitions. We observe, that the influence of helium atoms is important even at very small concentrations (a few hundredth of a torr). This observation indicates that inelastic atomic collisions have cross sections large enough to compete efficiently with inelastic electronic collisions when the ratio [He]/n, is greater than about a few hundred.? It should be noted that the variation of R, induced by
iThe results suggest that the populations of the SD sublevels are close to equilibrium at T, in pure cesium discharges (n,, = lOI5cm-‘) and that a significant departure from this equilibrium value is already observed when a helium concentration as small as IO” crnT3is present. Thus. the excitation transfer between 5D3,, and SD,,, induced by collisions with helium atoms is more efficient than that induced by collisions with cesium atoms. This situation is noticeably different from the case of excitation transfer between P,,, and Pvl sublevels where the collisions with Cs atoms appear much more efficient.“’
Role of atomic inelastic collisions in a Cs-He
steady state discharge
243
adding two torr of helium to a cesium discharge (n, = 10” cm-‘) is close to that which would be observed by changing the temperature characterizing the Boltzmann equilibrium between the two 50 sublevels from T, to T, If Cs* + He inelastic collisions play such an important role in the equilibrium between the 5D sublevels, we may infer that they must also be efficient in determining the equilibrium between the Rydberg states. In Fig. 4, we have considered the nF levels which have the largest popUlatiOtIS NnF because of their large statistical weight g&; ht(N#/g,p) is plotted as a function of the ionization energy of the nF levels (Fig. 4(a)) where N”F is deduced from the absolute intensity of the 5D - nF lines. A linear variation is observed both at high (n, > 1013cme3) and at low electron densities (n, C 10” cme3). From the slope of these straight lines, we may determine a “temperature” TB which approaches T, at high ne and is close to T, at low n, (Fig. 4(b)). For steady-state discharges in pure cesium, a decrease of TB had also been observed for low n,.(4) It was shown that the decrease of TB is due to loss of charged particles by diffusion and
Fig. 4(a). Plot of the nF state populations as a function of their ionization energies. --x--, experimental Boltzmann equilibrium at the measured values of T. and nru; pHc = 60 torr. results: -,
I
Ta(“K)
I
I
i
2000 -
1500-
Fig. 4(b). The Boltzmann temperature T, as a function of electron density (pHe= 60 torr).
G. GOUSSET
244
et al.
recombination at the walls and is not related to inelastic atomic collisions. In particular, it has been observed that, in pure cesium discharges (ncs = 10’4-10’5cm-‘), TB decreases. for low cesium pressures and may even reach values which are significantly lower than the gas temperature. In the present experiments, where helium is added to the cesium plasma, a limit TB is evidently obtained for. the lowest electron densities, and this limit is equal to TB’ This result indicates that inelastic collisions with atoms play a major role in the population balance of the highly excited states. Our observation of equilibrium for the populations of highly excited states at the gas (lo) These authors have reported temperature is different from that of GRIDNEVA and KASABOV. observations of a Boltzmann equilibrium corresponding to the gas temperature for highly excited states of cesium in a Cs-Ar discharge. But, under their experimental conditions, TB is obtained with a large uncertainty in the population of high nF levels (14 s n G 20, E 14F-E20F = 220cm-‘). Although their results would indicate that Ts = Tg at a surprisingly low ratio [He]/n,( 2: 16), a new interpretation of their experimental results”” suggests that the observed effect is due to the use of unreliable oscillator strengths.l Boltzmann equilibrium at the gas temperature is achieved when n, is lower than lOI*cme3 at PHe = 60 torr([He] = 10” cmm3). For the same range of [He]/n,( = 106), equilibrium has been observed between the sublevels of the 3-g principal quantum numbers in a pure helium discharge.“*’ (2) Ionization-recombination balance As mentioned in the introduction, inelastic collisions with neutral atoms can also participate in the creation-loss balance of electrons. Let us consider this balance in a steady-state discharge at low np. In pure cesium, the main electron-loss process is ambipolar diffusion to the walls, whereas the electrons are created by a step-by-step ionization mechanism. On the one hand, the rate of diffusion losses decreases with the gas pressure and increases slightly with electron temperature Te; on the other hand, the efficiency of the step-by-step ionization increases with the cesium density and rises very fast with T,. One would conclude, then, that, since the addition of helium reduces diffusion losses at a given nL, the electron loss-and-creation balance would be reached at a lower T, when helium is present. The experimental result, however, shows the opposite (Fig. 5). We observe an increase of T, with decreasing n,. This effect becomes greater with increasing pHe. Consequently, the balance in the steady-state discharge can only lead to equilibration if helium atoms either induce an additive loss process or reduce the ionization efficiency. Different possibilities may also be envisaged. The first possibility is related to the inffuence of inelastic collisions with atoms. A recent study has shown that the Cs’ + e + He recombination mechanism is not very efficient in
J
2000 2x10"
Fig. 5. The
electron
temperature
10'3
10'2
n.0(cm-31
as a function of electron density (nc, = 10” cm-‘): pHe = 20torr; X, pHe = 60 torr.
tThe measurements of the SD-r@ line intensities are rather due to Stark broadening when n, is of the order of 10’3cm-3.
imprecise
0,
pure cesium;
when n 2 16 because of overlapping
0,
of these lines
Role of atomic inelastic collisions in a Cs;He steady state discharge
24s
an afterglow where T, = Tg (13) As we have seen before, however, inelastic collisions with neutral atoms play an important role in establishing the populations of highly excited states which participate in the ionization-recombination balance. The greater the difference between T, and Tg, the more sensitive to atomic collisions are these populations. Consequently, it is possible that these inelastic collisions with atoms only play an important role in the ionizationrecombination balance when T, is noticeably different from Tg The helium atoms can also play another role by broadening the resonance lines. This broadening is responsible for an increase in the escape of the resonance radiation, which is by itself an important factor for departure from TE in plasmas. (4)Moreover, this effect may also be responsible for depletion in the high-energy tail of the electron velocity-distribution function.“4”5’ In this case, the efficiency of the 6S-6P excitation by electrons would be reduced and, consequently, the step-by-step ionization process would be less efficient than expected at the measured T, (where T, is defined and measured by reference to the core of the distribution function). CONCLUSIONS
The conclusion reached in previous experimental studies of d.c. discharges in mixtures of alkali vapor and rare-gas was that the role played by rare-gas atoms would be limited to that of a diffusion barrier as long as the rare-gas atoms remain in their ground state. No influences of atomic collisions have been detected in these media. In the present work, by considering higher ratios of neutral atom concentrations to electronic densities, evidence of the role played by atomic collisions has been obtained directly by observing the equilibria between the highly excited states at the gas temperature. The influence of the rare-gas concentration on the T, = f(n,) relation is more difficult to interpret. A model of the ionized gas, including the different elementary processes, such as the one which has been used by some of us to describe the pure cesium plasma,‘4’ is difficult to build when inelastic atom-atom collisions have to be included. It would need to take into account very highly excited states and to include, with their appropriate coefficients, both inelastic electronic and atomic collisions which affect these levels. It is of interest to compare the present results with those obtained by studying a Cs-He afterglow. (13)In this last experiment, it has been shown that the three-body Cs’ + e + e recombination mechanism remains predominant with regard to processes involving He atoms, even when the ratio [He]/n, is as large as several times 10’. The apparent contradiction seems to indicate that the inelastic atomic collisions play a more important role in a plasma when T, is noticeably different from T, Acknowledgements-The authors are grateful to Dr. R. GUTCHECK and Dr. J. BERLANDE for a critical reading of the manuscript. REFERENCES 1. L. P. HARRIS, 1. Appl. Phys. 36, 1543(1965). 2. N. D. MORGULIS and I. N. POLUSHKIN, High Temperature, 4,699 (1%6). 3. H. VANTONGEREN, Philips Res. Repts. Suppl. Eindhoven, Netherlands, No. 3 (1975). 4. B. SAYER, J. C. JEANNET and J. BERLANDE, I: Physique 33,993 (1972). 5. C. L. CHENand A. V. PHELPS,Phys. Reu. 173.62 (1%8). 6. R. 0. GARRF~T and S. Y. CHEN, Phys. Rev. l44,66 (1%6). 7. J. B. TAYLOR and 1. LANGMUIR, Phys. Reu. 51,753 (1937). 8. L. AGNEW and C. SUMMERS, Proc. of the 7th Inr. Conf. on Phenomena in Ionized Gases, Gradevinska Knijga Publishing House Beograd, Yugoslavia, Vol. II, p. 574 (1966). 9. M. PIMBERT, J. Physique 33,331 (1972). IO. S. M. GIUDNEVA and G. A. KASABOV, Electricity from MHD SM 74/69, Salzburg, Austria, (1966). Il. V. S. VOROBEV and A. 1. GLEIZER, Opt. Spectrosc. 37,450 (1974). 12. E. N. PAVLOVSKAYA and I. V. PODMOSHENSKII, Opt. Spectrosc. 23,477 (1%7); 34,9 (1973). 13. G. GOUSSET, B. SAYER and J. BERLANDE, Phys. Rev. A 16, 1070(1977). 14. J. F. SHAW, M. MITCHNER and C. H. KRUGER, Phys. kluids 13, 339 (1970). 15. L. VRIENS, J. Appl. Phys. 44, 3980(1973).