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Plasma effects in the spectrum of high Balmer lines
I. Quanr.
Sprcfros. Rodiat.
Transfer. Vol. 16, pp. 529-536. Pergamon Press 1976. Printed in Great Britain.
PLASMA EFFECTS IN THE SPECTRUM OF HIGH BALMER LINES G. HIMMEL Institut fiir Experimentalphysik, Ruhr-Universitlt Bochum, Germany (Received 4 October 1975) Abstract-Measurements of high Balmer lines (nuVFer = 12 to 19) emitted from a hydrogen discharge of relatively low plasma density show that the spectrum may be well reproduced by a superposition of symmetric Stark profiles, which accounts for the broadening effect generated by ions and quasistatic electrons. The small deviations which were found most probably involve inelastic electron collisions connecting adjacent upper levels. Within experimental accuracy, a shift is not detectable either for odd or for even series members. This finding is inconsistent with the observations of other authors according to which odd Balmer lines are shifted to the red.
SINCEa considerably
1. INTRODUCTION understanding of Stark broadening
has been obtained during the last decade, increasing effort has been concentrated on the investigation of more subtle features such as effects producing shifts and line asymmetries which are not due to first-order interactions of the radiators with their plasma environment. For a review of studies of this type, see Ref. (1). Measurements of line shifts and asymmetries, if these are readily observable in a given range of parameters, may provide a useful diagnostic tool for laboratory as well as for stellar plasmas; they are supplementary to the usually applied halfwidth measurements. From the astrophysical point of view, knowledge of plasma effects leading to line asymmetries and shifts, which are strongly correlated, is of importance because measurements have to be corrected for these effects in order to reveal velocity or gravitational shifts. Many investigations are basically intended to provide critique and extension of preceding fundamental work on the broadening of hydrogenic plasma lines. In hydrogen, shifts or asymmetries are small in comparison with symmetric broadening which originates from the overwhelming influence of the first-order dipole interaction. Experimental studies performed with high accuracy have confirmed that these effects are indeed observable at high electron densities. For Lyman-a, comprehensive calculations are available which agree qualitatively with experimental data. On the other hand, at relatively low electron densities, only transitions from highly excited levels will permit detection of interesting plasma effects which are not attributed to ordinary symmetric broadening. In this connection, BENGTSON and CHESTER”’ published experimental results showing large displacements of the odd Balmer lines His and H,, to the red, whereas even lines (i.e. lines without a central Stark component) are not affected. This finding lacks any explanation. Therefore, and because of the fact that no other experimental data comparable to the work of Bengtson and Chester were available, the study described below was performed; this study aims at the fullest possible investigation of such data and at a critical check of the foregoing results. improved
2. EXPERIMENTAL
PROCEDURE
The special features of the RF discharge, which was used both for this study and for the study of Ref. (2), are described elsewhere in detail, including the homogeneous “blue spot” plasma which develops in a static magnetic field and the diagnostic methods applied.““’ In summary, a somewhat higher electron density than formerly, i.e. N, = 1.75x 10” cmm3,was achieved in this case, while the temperature of the electrons and neutrals (T. = T,, = 1750°K) did not change considerably. For a comparison with the study of Bengtson and Chester, the two following additional points are worth emphasis: (i) In order to determine the spectral line positions accurately, reliable wavelength standards are required by which the scale of the monochromator must be calibrated. Instead of an iron arc as a source of reference wavelengths, a set of microwave discharge lamps 529
G. HMMEL
530
or a hollow cathode loaded with Fe and operated with 1 torr Ne as carrier gas was used. This was done because it is generally recognized that lines of the open Fe arc, as used in Ref. (2), are liable to displacements by pole and pressure effects, so that even for moderately precise measurements better standards are desirable.‘” (ii) The experimental accuracy attainable depends heavily upon the extent to which instrumental drifts (i.e. those evoked by thermal effects of the order of magnitude 0.1 @C) may be overcome. Thus, the measuring time must be kept short enough to ensure constant experimental conditions. In principle, it would be helpful to have a photographic record both of the Balmer spectrum and of the reference spectrum using different sections of the monochromator slits at the same time. The measuring sensitivity of the photoelectric method, however, is essential, especially in view of the extremely low intensities which are met in the case of higher Balmer lines. It is also of little use to view the plasma and the reference source simultaneously since, in this case, the intensities are superimposed because the wings of the Balmer lines usually blend with the lines of the reference source; this blending can easily lead to a higher degree of inaccuracy in the experiment. Figure 1 shows schematically the arrangement used in this work, which offers an alternative to the method of Ref. (2). The light emitted from the standard source is channelled into the main path of the plasma light by means of a chopper which has highly reflective blades. In this way, the plasma light and the light from the standard source are fed periodically (f = 20 c.p.s.) into the entrance slit of the grating monochromator. This monochromator is operated in the first order, in contrast to the higher order work in Ref. (2). Behind the exit slit, a photomultiplier accepts the light of both sources. The photoelectric signal is given alternately to the inputs of two separate lock-in amplifiers by means of an electronic switching circuit. The analogue outputs of the amplifiers are connected to a 2-pen recorder which provides independent records of both spectra, one above the order. The digital outputs are used to drive a tape punch for the subsequent computer evaluation. For phase matching, including synchronization of each branch of the signal line, two phase-locked oscillators are installed and triggered by the reference output of the light chopper. These oscillators activate both the reference circuits of the lock-in amplifiers and the electronic switching circuit just mentioned. Thanks to this complete uncoupling, the amplification can be chosen independently for every signal channel. This technique promises an improvement upon the situation in which the light sources are used separately; because, with two light sources used in this way, signal-to-noise ratio is not sacrificed since the lock-in method manages with one half of a signal cycle in either branch. By setting the time-constant RC equal to 2 set in both channels, the signal noise is partially smoothed out without any considerable distortion of the recorded line shapes. Figure 2 shows typical recorder traces. The small peak which appears on the outermost blue wing of the Balmer line HI5 was produced by a crosscoupling of both signal
$I WST PLO1
Fig. 1. Schematic diagram of the experimental set-up. Explanation of the abbreviations: WST, standard light source; PL, HF-plasma; CH, light chopper; MO, grating monochromator; PM, photomultiplier; PSA 1, 2, lock-in amplifiers; SC 1,2, electronic switching circuit; PLO 1,2,phase locked oscillators; RC 1,2, reference circuits.
Plasma effects in the spectrum of high Balmer lines
531
Fig. 2. Recorder trace of the Balmer line H,,taken simultaneous1 with the reference spectrum: (a) Fe 3709.246A;(b) Ne(II) 3709.64A; (c) Fe 3711.225A; (d) Fe 3711.4111., (e) Ne(II) 3713.09A. Dashed arrows indicate changes in the amplificationfactors.
channels due to a momentary phase mismatch, the latter being normally avoidable by a careful adjustment of the phase-locked oscillators. This peak is attributable to the reference line which lies nearby; its position indicates a small horizontal displacement of the recorder traces as a result of a small horizontal spacing between the two writing pens. Fortunately, it is easy to correct for this displacement when relative line positions are evaluated from the records. 3. RESULTS (a) Predominance
of quasistatic
broadening
Invoking Unsold’s limit?’ one may assume that the quasistatic broadening of both protons and electrons delivers a sufficiently correct description of the wings of high Balmer lines up to the line core. This delineation is corroborated by the results of the modern theory which confirms the validity of the quasistatic approach throughout its classic domain.“) Indeed, the experimental line wings, e.g. of HI2 and HI,, show excellent agreement with calculations performed by means of a quasistatic code (see Fig. 3). This code, however, takes into account only the quasistatic part of the electron phase-space distribution.‘*’ Therefore, it is possible to dispense largely with additional dynamical corrections which are, in any case, small under the prevailing conditions, at least as far as adiabatic processes are concerned. To a certain degree, these premises facilitate the following analysis in comparison with the other case of low Balmer lines, particularly at high temperatures. The last situation is characterized by contributions from different broadening mechanisms and requires an involved computation. (b) Background considerations At very low intensities, the measured line wings of Fig. 3 correspond closely to the asymptotic wing formula, viz. I - AA-5’2.This finding supports the reliability of the procedure according to which the minimum signal at the half distance between Zfla and HI1 is regarded as background intensity (originating, e.g. from scattered light and/or continuous radiation). Therefore, the same amount of background intensity is assumed to be applicable to the higher Balmer lines where the real background is strongly masked by the overlapping wings of neighboring series members. (c) Line merging
The intensity ratios taken from the envelope curves connecting maxima and minima within the series are presented in Fig. 4. The points which were evaluated from the measurements are compared with a theoretical curve obtained by superimposing the intensities of quasistatic line profiles according to Ref. (8). The relative line intensities were determined by using the tabulated f-values and assuming the upper energy levels to be populated at LTE. It should be noted that the residual Stark structure in the line center maintained by the quasistatic theory could not be observed in any case. Actually, it is rendered indistinct by electron-impact broadening which is not included in the calculations although it is effective at the line center. In order to simulate real conditions, all central structures were smoothed, leaving the area under the intensity curve unchanged, as is shown in Fig. 5. For the other theoretical curve in Fig. 4, the approximations of
G. HIMMEL
532
H 13
H12
0005
- 1-1
20
10
05
02
01
02
05
10
20
1.\
IA)
Fig. 3. Typical measurements (crosses) of the profile of HIZ (“red” side) and of HI, (“blue” side) with quasistatic calculations’B’(solid curve). The profiles are presented as normalized functions of the intensity with respect to Ah.
R 10;
50
20
10'
5
2
lO( 117
120
125
130
log n
Fig. 4. Measured ratios of the envelope curves (filled circles) with respect to calculated ratios [solid curve-calculations in this study; dashed line-calculations corresponding to Ref. (9)]. The arrow labelled “IT” indicates the point on the log n-axis distinguished for the Inglis Teller relation.
VIDAL(~)were used. There is no substantial difference between both calculations, apart from the fact that this study starts from a more rigorous treatment of the Stark effect and that it includes Doppler and apparatus broadening. The deviations of the single experimental points from the calculations are not very serious, especially when the uncertainty of the background is estimated
Plasma effects in the spectrum of high Balmer lines
533
Fig. 5. Diagramillustrating the method of evaluation for strongly overlapping line wings.
in a realistic way.t Nevertheless, it becomes apparent that the ratio of the envelope curves decreases somewhat more steeply towards the melting point than is shown by the theoretical treatment. (d) Line widths The definition used for the line widths in Fig. 6 is given graphically in Fig. 5. The experimental widths were derived from the records after the residual noise had been smoothed. The overall comparison with theoretical widths shows satisfactory agreement; but, for the higher Balmer lines (IfI5 - HI,), a small tendency appears towards enhanced broadening of the measured lines as compared to the calculations. This enhancement seems to be consistent with the overall behaviour of the ratio of the envelope curves mentioned above. At first glance, one might argue that in Fig. 6 the enhancement disappears again towards the melting point. In reality; the line widths as defined here become stabilized with growing nuppcrbecause there is compensation between the effects produced by decreasing extension of the usable line profile and by the increase in line broadening. (e) Line positions There are two suitable procedures for indicating the position of a strongly broadened spectral line. One procedure involves use of the integral expression for the line mean, m
ti=
I 0
m
A
.I(h)dh
/I
10) dh, 0
where I(A) denotes the intensity at the wavelength A. It should be noted that this procedure automatically emphasizes the distant line wings, thus clearly marking the effects which are caused by the contribution of relatively high plasma fields. tThe determination of the background is explained in Section 3b. For relatively low principal quantum numbers, the uncertainty of the background intensity causes an inaccuracy in the experimental points which is estimated to be around +25%. Near the melting point, however, the influence of the background intensity weakens and the remaining inaccuracy does not exceed +3%.
534
G. HIMMEL
20
1.5
10
c/
/
1: \
/
05
7-
12
13
1L
15
16
17
16
19 nuppcr
Fig. 6. Widths of high Balmer lines as functions of the upper principal quantum number; comparison of the measurements (crosses) with quasistatic calculations’” (solid lines) and with a curve indicating values of 2. AA, for some Balmer lines under consideration (dashed line; Ah, indicates Undid’s limit@‘).The meaning of the line widths, which differs from the usual notation, is explained in Fig. 5. The quoted errors correspond to maximum deviations in the experimental results.
The other procedure makes use of the line widths at different heights of the line profile. In this study, the three line widths of Fig. 5 are employed. The line center is given by the average of the three points that bisect the line widths. For H,2-H15, the first procedure is chosen because each line is relatively well separated, while the second procedure proves to be best for the lines HIa - HI9 because of considerable overlapping of line wings. The line pos;tions of Table 1 are given relative to the wavelengths of selected standard lines or to the positions of adjacent Balmer lines. Near the melting point, the overlapping lines give rise to a small net shift in the direction of decreasing wavelengths. Its magnitude (e.g. 0.03 A for HIP) is taken from the calculated spectrum and used for correcting the Table 1. Wavelengths of high Balmer lines”” relative to selected reference lines(‘I) in units of A. The wavelength differences of the Balmer lines were measured in a single light source. The quoted errors correspond to maximum deviations in the experimental results
92
Ne
I 3754.216
- 4.062
- 4.06
+ 0.03
*13
Fe
I 3734.867
- 0.437
- 0.51
?4
Fe
1 3722.564
- 0.624
- 0.63
+ 0.02 _ + 0.02
+ 0.749
+ 0.74
+
+
2.725
+
2.71
+ 0.03
+ _
"16
57
Ne
1
3701.225
+ 2.630
+
2.64
KI
I
3698.045
-
0.891
-
0.90
+
0.02
I
3695.054
+
2.100
+
2.10
+
0.03
Ne
I
"20
3701.225
- 4.071
-
4.06
+
0.03
3691.557
+ 5.597
+
5.62
+
0.04
3690.897
+ 0.660
+ 0.66
+ 0.02
3686.R33
+ 4.724
+ 4.73
+ 0.04 _
Ne I 3685.736
+
+ 1.10
_+ 0.03
H
- 4.023
- 4.05
+ 0.05
AT
?9
0.03
Fe
H
"18
0.02
H
I
3686.833
1.097
Plasma effects in the spectrum of high Balmer lines
535
measured line distances. Accordingly, the values of Table 1 are obtained from the measured values by elimination of the particular shift just mentioned. 4. DISCUSSION
The high degree of agreement of the theoretical wavelengths of high Balmer lines obtained with the measurements contradicts the findings of Ref. (2), which indicated a considerable shift in the upper levels in the case of odd principal quantum numbers. The shifts were found both in the laboratory plasma source and in the emission of Sirius. One argument against overestimating the importance of this inconsistency is that a direct comparison of observations is not possible because different plasma parameters were used. Indeed, the plasma density to which the authors refer is somewhat lower in comparison with this study, viz. 1.2 x lOI cmm3,while the temperature is slightly higher. On the other hand, these differences should not alter the conditions substantially and it is more plausible to assume that they aggravate the inconsistency rather than reduce it. In this context, it seems desirable to determine which theoretical model if any qualifies for explaining detectable line shifts under the prevailing conditions. The quadrupole interaction need not be considered because the effects of ions and quasistatic electrons nearly cancel each other.“.‘2’ Similarly, in the linear dipole approximation, the modification of the intensities of the Stark components cancels out. Furthermore, the quadratic Stark effect falls below the threshold of observability, although the effects of ions and electrons are nearly additive. Thus, for HI9 the predicted red shift does not exceed 8.5 x 10m3A at the Holtsmark (normal) field strength (F, = 1.33e.s.u.). In other words, the wing intensity of HI9 is raised near the red side minimum only by about I%, whereas near the blue side minimum it is lowered by approximately the same percentage. Moreover, one can neglect preionization from bound states under the influence of strong electric fields, which mainly weakens the red line wings since the effect has a rather steep threshold which is not easily reached in the given range of plasma parameters. The monopole interaction stemming from the isotropic distribution of the plasma charges is considered best in conjunction with Ref. (13). For H,, - H19,the rather tedious computer evaluation of the formulae given there yields a net shift of about 0.02 A in the direction of increasing wavelengths. This value, which stays just at the limit of experimental accuracy, is too small to explain the results of Bengtson and Chester. It is even too small to permit any conclusion to be drawn from the negative experimental result obtained in this study. All that remains, then, is a further investigation of inelastic electron collisions connecting levels which are split by the ion fields. In spite of the fact that for hydrogen a quantitative treatment of the effects involved is not yet feasible, the approach of BOIKO”~’ shows that, in principle, both line shifts and increased line broadening ought to be accounted for in the case of overlapping lines. These effects are expressed the more clearly the more the electron density is increased. It is doubtful, however, whether in the plasma under consideration a shift of the order of magnitude given in Ref. (2) is brought about in this way. At best, the slightly increased broadening of the line wings in comparison with the quasistatic calculations, which is described above, might be traceable to such inelastic process.? This assumption is supported by observations which are inconsistent with the behaviour of the dynamical effects for isolated hydrogen lines. Again, neither the quadrupole effect nor the quadratic Stark effect will generate any deviation that can be measured by the detection system. 5. CONCLUSION
Comparison of the measured spectrum of high Balmer lines with a superposition of quasistatic line profiles does not reveal any striking discrepancy, apart from the fact that residual quasistatic structures in the line center are rendered indistinct by electron-impact broadening. In particular, no line shift is found. A critical discussion of all sources of possible line shifts suggests that the effects measured by Bengtson and Chester are caused by some kind of systematic error, at least as far as the investigation of the laboratory plasma is concerned. The increased broadening of the wings of Balmer lines with n upwr> 14, which was found in this study, is most probably produced by inelastic processes. There is still no useful formalism covering the given range of parameters to elucidate the significance of such processes. tFor an estimate of the “strong collision” contribution eqn (478) of Ref. (1) was used.
QSRT Vol. 16No.6-E
G. HIMMEL
Acknowledgements-I wish to thank Prof. Dr. HANSSCHL~~TER for valuable discussion and encouragement during the course of this work. The investigations are part of the joint efforts within the Sonderforschungsbereich 162“Plasmaphysik Bochum/Jiilich”. REFERENCES 1. H. GRIEM,Special Line Broadening by Plasmas. Academic Press, New York (1974). 2. R. D. BEN&SONand G. R. CHESTER, kstrophys. J. 178, 565 (1972). 3. R. D. SCHL~~TER. Z. Naturforsch. 16a. 972 (l%l). 4. G. HIMMEL and fi. SCHL&R, Strahlungsvorgiingein Plasmen mit statischem Magnetfefd, Forschungsbericht des Landes Nordrhein-Westfalen No. 2363. Westdeutscher Verlag, Opladen (1973). 5. Trans. Int. Astr. Union llA, 100 (1%2). 6. A. UNSOLD, Physik der Stemafmosphiiren, p. 312. Springer, Berlin (1%8). 7. C. R. VIDAL,J. COOPER and E. W. SMITH,JQSRT 11, 263 (1971). 8. G. FUSSMANN and G. HIMMEL, JQSRT 13, 393 (1972). 9. C. R. VIDAL,.QSRT 6, 461 (1966). 10. A. R. STR~GANOV and N. S. SVENTITSKII, Tables of Spectral Lines of Neutral and Ionized Atoms. IFI/Plenum, New York (l%S). 11. G. R. HARRISON, MIT-Wavelength Tables. MIT Press, Cambridge, Mass. (1%9). 12. H. NGUYEN-HOE, W. DRAWIN and L. HERMAN, JQSRT 4, 847 (1964). 13. 0. THEIMER and P. KEPPLE,Phys. Rev. Al, 957 (1970). 14. V. I. BOIKO,Eksp. Tear. Fiz. 68, 854 (1975).
Sprcfros. Rodiat.
Transfer. Vol. 16, pp. 529-536. Pergamon Press 1976. Printed in Great Britain.
PLASMA EFFECTS IN THE SPECTRUM OF HIGH BALMER LINES G. HIMMEL Institut fiir Experimentalphysik, Ruhr-Universitlt Bochum, Germany (Received 4 October 1975) Abstract-Measurements of high Balmer lines (nuVFer = 12 to 19) emitted from a hydrogen discharge of relatively low plasma density show that the spectrum may be well reproduced by a superposition of symmetric Stark profiles, which accounts for the broadening effect generated by ions and quasistatic electrons. The small deviations which were found most probably involve inelastic electron collisions connecting adjacent upper levels. Within experimental accuracy, a shift is not detectable either for odd or for even series members. This finding is inconsistent with the observations of other authors according to which odd Balmer lines are shifted to the red.
SINCEa considerably
1. INTRODUCTION understanding of Stark broadening
has been obtained during the last decade, increasing effort has been concentrated on the investigation of more subtle features such as effects producing shifts and line asymmetries which are not due to first-order interactions of the radiators with their plasma environment. For a review of studies of this type, see Ref. (1). Measurements of line shifts and asymmetries, if these are readily observable in a given range of parameters, may provide a useful diagnostic tool for laboratory as well as for stellar plasmas; they are supplementary to the usually applied halfwidth measurements. From the astrophysical point of view, knowledge of plasma effects leading to line asymmetries and shifts, which are strongly correlated, is of importance because measurements have to be corrected for these effects in order to reveal velocity or gravitational shifts. Many investigations are basically intended to provide critique and extension of preceding fundamental work on the broadening of hydrogenic plasma lines. In hydrogen, shifts or asymmetries are small in comparison with symmetric broadening which originates from the overwhelming influence of the first-order dipole interaction. Experimental studies performed with high accuracy have confirmed that these effects are indeed observable at high electron densities. For Lyman-a, comprehensive calculations are available which agree qualitatively with experimental data. On the other hand, at relatively low electron densities, only transitions from highly excited levels will permit detection of interesting plasma effects which are not attributed to ordinary symmetric broadening. In this connection, BENGTSON and CHESTER”’ published experimental results showing large displacements of the odd Balmer lines His and H,, to the red, whereas even lines (i.e. lines without a central Stark component) are not affected. This finding lacks any explanation. Therefore, and because of the fact that no other experimental data comparable to the work of Bengtson and Chester were available, the study described below was performed; this study aims at the fullest possible investigation of such data and at a critical check of the foregoing results. improved
2. EXPERIMENTAL
PROCEDURE
The special features of the RF discharge, which was used both for this study and for the study of Ref. (2), are described elsewhere in detail, including the homogeneous “blue spot” plasma which develops in a static magnetic field and the diagnostic methods applied.““’ In summary, a somewhat higher electron density than formerly, i.e. N, = 1.75x 10” cmm3,was achieved in this case, while the temperature of the electrons and neutrals (T. = T,, = 1750°K) did not change considerably. For a comparison with the study of Bengtson and Chester, the two following additional points are worth emphasis: (i) In order to determine the spectral line positions accurately, reliable wavelength standards are required by which the scale of the monochromator must be calibrated. Instead of an iron arc as a source of reference wavelengths, a set of microwave discharge lamps 529
G. HMMEL
530
or a hollow cathode loaded with Fe and operated with 1 torr Ne as carrier gas was used. This was done because it is generally recognized that lines of the open Fe arc, as used in Ref. (2), are liable to displacements by pole and pressure effects, so that even for moderately precise measurements better standards are desirable.‘” (ii) The experimental accuracy attainable depends heavily upon the extent to which instrumental drifts (i.e. those evoked by thermal effects of the order of magnitude 0.1 @C) may be overcome. Thus, the measuring time must be kept short enough to ensure constant experimental conditions. In principle, it would be helpful to have a photographic record both of the Balmer spectrum and of the reference spectrum using different sections of the monochromator slits at the same time. The measuring sensitivity of the photoelectric method, however, is essential, especially in view of the extremely low intensities which are met in the case of higher Balmer lines. It is also of little use to view the plasma and the reference source simultaneously since, in this case, the intensities are superimposed because the wings of the Balmer lines usually blend with the lines of the reference source; this blending can easily lead to a higher degree of inaccuracy in the experiment. Figure 1 shows schematically the arrangement used in this work, which offers an alternative to the method of Ref. (2). The light emitted from the standard source is channelled into the main path of the plasma light by means of a chopper which has highly reflective blades. In this way, the plasma light and the light from the standard source are fed periodically (f = 20 c.p.s.) into the entrance slit of the grating monochromator. This monochromator is operated in the first order, in contrast to the higher order work in Ref. (2). Behind the exit slit, a photomultiplier accepts the light of both sources. The photoelectric signal is given alternately to the inputs of two separate lock-in amplifiers by means of an electronic switching circuit. The analogue outputs of the amplifiers are connected to a 2-pen recorder which provides independent records of both spectra, one above the order. The digital outputs are used to drive a tape punch for the subsequent computer evaluation. For phase matching, including synchronization of each branch of the signal line, two phase-locked oscillators are installed and triggered by the reference output of the light chopper. These oscillators activate both the reference circuits of the lock-in amplifiers and the electronic switching circuit just mentioned. Thanks to this complete uncoupling, the amplification can be chosen independently for every signal channel. This technique promises an improvement upon the situation in which the light sources are used separately; because, with two light sources used in this way, signal-to-noise ratio is not sacrificed since the lock-in method manages with one half of a signal cycle in either branch. By setting the time-constant RC equal to 2 set in both channels, the signal noise is partially smoothed out without any considerable distortion of the recorded line shapes. Figure 2 shows typical recorder traces. The small peak which appears on the outermost blue wing of the Balmer line HI5 was produced by a crosscoupling of both signal
$I WST PLO1
Fig. 1. Schematic diagram of the experimental set-up. Explanation of the abbreviations: WST, standard light source; PL, HF-plasma; CH, light chopper; MO, grating monochromator; PM, photomultiplier; PSA 1, 2, lock-in amplifiers; SC 1,2, electronic switching circuit; PLO 1,2,phase locked oscillators; RC 1,2, reference circuits.
Plasma effects in the spectrum of high Balmer lines
531
Fig. 2. Recorder trace of the Balmer line H,,taken simultaneous1 with the reference spectrum: (a) Fe 3709.246A;(b) Ne(II) 3709.64A; (c) Fe 3711.225A; (d) Fe 3711.4111., (e) Ne(II) 3713.09A. Dashed arrows indicate changes in the amplificationfactors.
channels due to a momentary phase mismatch, the latter being normally avoidable by a careful adjustment of the phase-locked oscillators. This peak is attributable to the reference line which lies nearby; its position indicates a small horizontal displacement of the recorder traces as a result of a small horizontal spacing between the two writing pens. Fortunately, it is easy to correct for this displacement when relative line positions are evaluated from the records. 3. RESULTS (a) Predominance
of quasistatic
broadening
Invoking Unsold’s limit?’ one may assume that the quasistatic broadening of both protons and electrons delivers a sufficiently correct description of the wings of high Balmer lines up to the line core. This delineation is corroborated by the results of the modern theory which confirms the validity of the quasistatic approach throughout its classic domain.“) Indeed, the experimental line wings, e.g. of HI2 and HI,, show excellent agreement with calculations performed by means of a quasistatic code (see Fig. 3). This code, however, takes into account only the quasistatic part of the electron phase-space distribution.‘*’ Therefore, it is possible to dispense largely with additional dynamical corrections which are, in any case, small under the prevailing conditions, at least as far as adiabatic processes are concerned. To a certain degree, these premises facilitate the following analysis in comparison with the other case of low Balmer lines, particularly at high temperatures. The last situation is characterized by contributions from different broadening mechanisms and requires an involved computation. (b) Background considerations At very low intensities, the measured line wings of Fig. 3 correspond closely to the asymptotic wing formula, viz. I - AA-5’2.This finding supports the reliability of the procedure according to which the minimum signal at the half distance between Zfla and HI1 is regarded as background intensity (originating, e.g. from scattered light and/or continuous radiation). Therefore, the same amount of background intensity is assumed to be applicable to the higher Balmer lines where the real background is strongly masked by the overlapping wings of neighboring series members. (c) Line merging
The intensity ratios taken from the envelope curves connecting maxima and minima within the series are presented in Fig. 4. The points which were evaluated from the measurements are compared with a theoretical curve obtained by superimposing the intensities of quasistatic line profiles according to Ref. (8). The relative line intensities were determined by using the tabulated f-values and assuming the upper energy levels to be populated at LTE. It should be noted that the residual Stark structure in the line center maintained by the quasistatic theory could not be observed in any case. Actually, it is rendered indistinct by electron-impact broadening which is not included in the calculations although it is effective at the line center. In order to simulate real conditions, all central structures were smoothed, leaving the area under the intensity curve unchanged, as is shown in Fig. 5. For the other theoretical curve in Fig. 4, the approximations of
G. HIMMEL
532
H 13
H12
0005
- 1-1
20
10
05
02
01
02
05
10
20
1.\
IA)
Fig. 3. Typical measurements (crosses) of the profile of HIZ (“red” side) and of HI, (“blue” side) with quasistatic calculations’B’(solid curve). The profiles are presented as normalized functions of the intensity with respect to Ah.
R 10;
50
20
10'
5
2
lO( 117
120
125
130
log n
Fig. 4. Measured ratios of the envelope curves (filled circles) with respect to calculated ratios [solid curve-calculations in this study; dashed line-calculations corresponding to Ref. (9)]. The arrow labelled “IT” indicates the point on the log n-axis distinguished for the Inglis Teller relation.
VIDAL(~)were used. There is no substantial difference between both calculations, apart from the fact that this study starts from a more rigorous treatment of the Stark effect and that it includes Doppler and apparatus broadening. The deviations of the single experimental points from the calculations are not very serious, especially when the uncertainty of the background is estimated
Plasma effects in the spectrum of high Balmer lines
533
Fig. 5. Diagramillustrating the method of evaluation for strongly overlapping line wings.
in a realistic way.t Nevertheless, it becomes apparent that the ratio of the envelope curves decreases somewhat more steeply towards the melting point than is shown by the theoretical treatment. (d) Line widths The definition used for the line widths in Fig. 6 is given graphically in Fig. 5. The experimental widths were derived from the records after the residual noise had been smoothed. The overall comparison with theoretical widths shows satisfactory agreement; but, for the higher Balmer lines (IfI5 - HI,), a small tendency appears towards enhanced broadening of the measured lines as compared to the calculations. This enhancement seems to be consistent with the overall behaviour of the ratio of the envelope curves mentioned above. At first glance, one might argue that in Fig. 6 the enhancement disappears again towards the melting point. In reality; the line widths as defined here become stabilized with growing nuppcrbecause there is compensation between the effects produced by decreasing extension of the usable line profile and by the increase in line broadening. (e) Line positions There are two suitable procedures for indicating the position of a strongly broadened spectral line. One procedure involves use of the integral expression for the line mean, m
ti=
I 0
m
A
.I(h)dh
/I
10) dh, 0
where I(A) denotes the intensity at the wavelength A. It should be noted that this procedure automatically emphasizes the distant line wings, thus clearly marking the effects which are caused by the contribution of relatively high plasma fields. tThe determination of the background is explained in Section 3b. For relatively low principal quantum numbers, the uncertainty of the background intensity causes an inaccuracy in the experimental points which is estimated to be around +25%. Near the melting point, however, the influence of the background intensity weakens and the remaining inaccuracy does not exceed +3%.
534
G. HIMMEL
20
1.5
10
c/
/
1: \
/
05
7-
12
13
1L
15
16
17
16
19 nuppcr
Fig. 6. Widths of high Balmer lines as functions of the upper principal quantum number; comparison of the measurements (crosses) with quasistatic calculations’” (solid lines) and with a curve indicating values of 2. AA, for some Balmer lines under consideration (dashed line; Ah, indicates Undid’s limit@‘).The meaning of the line widths, which differs from the usual notation, is explained in Fig. 5. The quoted errors correspond to maximum deviations in the experimental results.
The other procedure makes use of the line widths at different heights of the line profile. In this study, the three line widths of Fig. 5 are employed. The line center is given by the average of the three points that bisect the line widths. For H,2-H15, the first procedure is chosen because each line is relatively well separated, while the second procedure proves to be best for the lines HIa - HI9 because of considerable overlapping of line wings. The line pos;tions of Table 1 are given relative to the wavelengths of selected standard lines or to the positions of adjacent Balmer lines. Near the melting point, the overlapping lines give rise to a small net shift in the direction of decreasing wavelengths. Its magnitude (e.g. 0.03 A for HIP) is taken from the calculated spectrum and used for correcting the Table 1. Wavelengths of high Balmer lines”” relative to selected reference lines(‘I) in units of A. The wavelength differences of the Balmer lines were measured in a single light source. The quoted errors correspond to maximum deviations in the experimental results
92
Ne
I 3754.216
- 4.062
- 4.06
+ 0.03
*13
Fe
I 3734.867
- 0.437
- 0.51
?4
Fe
1 3722.564
- 0.624
- 0.63
+ 0.02 _ + 0.02
+ 0.749
+ 0.74
+
+
2.725
+
2.71
+ 0.03
+ _
"16
57
Ne
1
3701.225
+ 2.630
+
2.64
KI
I
3698.045
-
0.891
-
0.90
+
0.02
I
3695.054
+
2.100
+
2.10
+
0.03
Ne
I
"20
3701.225
- 4.071
-
4.06
+
0.03
3691.557
+ 5.597
+
5.62
+
0.04
3690.897
+ 0.660
+ 0.66
+ 0.02
3686.R33
+ 4.724
+ 4.73
+ 0.04 _
Ne I 3685.736
+
+ 1.10
_+ 0.03
H
- 4.023
- 4.05
+ 0.05
AT
?9
0.03
Fe
H
"18
0.02
H
I
3686.833
1.097
Plasma effects in the spectrum of high Balmer lines
535
measured line distances. Accordingly, the values of Table 1 are obtained from the measured values by elimination of the particular shift just mentioned. 4. DISCUSSION
The high degree of agreement of the theoretical wavelengths of high Balmer lines obtained with the measurements contradicts the findings of Ref. (2), which indicated a considerable shift in the upper levels in the case of odd principal quantum numbers. The shifts were found both in the laboratory plasma source and in the emission of Sirius. One argument against overestimating the importance of this inconsistency is that a direct comparison of observations is not possible because different plasma parameters were used. Indeed, the plasma density to which the authors refer is somewhat lower in comparison with this study, viz. 1.2 x lOI cmm3,while the temperature is slightly higher. On the other hand, these differences should not alter the conditions substantially and it is more plausible to assume that they aggravate the inconsistency rather than reduce it. In this context, it seems desirable to determine which theoretical model if any qualifies for explaining detectable line shifts under the prevailing conditions. The quadrupole interaction need not be considered because the effects of ions and quasistatic electrons nearly cancel each other.“.‘2’ Similarly, in the linear dipole approximation, the modification of the intensities of the Stark components cancels out. Furthermore, the quadratic Stark effect falls below the threshold of observability, although the effects of ions and electrons are nearly additive. Thus, for HI9 the predicted red shift does not exceed 8.5 x 10m3A at the Holtsmark (normal) field strength (F, = 1.33e.s.u.). In other words, the wing intensity of HI9 is raised near the red side minimum only by about I%, whereas near the blue side minimum it is lowered by approximately the same percentage. Moreover, one can neglect preionization from bound states under the influence of strong electric fields, which mainly weakens the red line wings since the effect has a rather steep threshold which is not easily reached in the given range of plasma parameters. The monopole interaction stemming from the isotropic distribution of the plasma charges is considered best in conjunction with Ref. (13). For H,, - H19,the rather tedious computer evaluation of the formulae given there yields a net shift of about 0.02 A in the direction of increasing wavelengths. This value, which stays just at the limit of experimental accuracy, is too small to explain the results of Bengtson and Chester. It is even too small to permit any conclusion to be drawn from the negative experimental result obtained in this study. All that remains, then, is a further investigation of inelastic electron collisions connecting levels which are split by the ion fields. In spite of the fact that for hydrogen a quantitative treatment of the effects involved is not yet feasible, the approach of BOIKO”~’ shows that, in principle, both line shifts and increased line broadening ought to be accounted for in the case of overlapping lines. These effects are expressed the more clearly the more the electron density is increased. It is doubtful, however, whether in the plasma under consideration a shift of the order of magnitude given in Ref. (2) is brought about in this way. At best, the slightly increased broadening of the line wings in comparison with the quasistatic calculations, which is described above, might be traceable to such inelastic process.? This assumption is supported by observations which are inconsistent with the behaviour of the dynamical effects for isolated hydrogen lines. Again, neither the quadrupole effect nor the quadratic Stark effect will generate any deviation that can be measured by the detection system. 5. CONCLUSION
Comparison of the measured spectrum of high Balmer lines with a superposition of quasistatic line profiles does not reveal any striking discrepancy, apart from the fact that residual quasistatic structures in the line center are rendered indistinct by electron-impact broadening. In particular, no line shift is found. A critical discussion of all sources of possible line shifts suggests that the effects measured by Bengtson and Chester are caused by some kind of systematic error, at least as far as the investigation of the laboratory plasma is concerned. The increased broadening of the wings of Balmer lines with n upwr> 14, which was found in this study, is most probably produced by inelastic processes. There is still no useful formalism covering the given range of parameters to elucidate the significance of such processes. tFor an estimate of the “strong collision” contribution eqn (478) of Ref. (1) was used.
QSRT Vol. 16No.6-E
G. HIMMEL
Acknowledgements-I wish to thank Prof. Dr. HANSSCHL~~TER for valuable discussion and encouragement during the course of this work. The investigations are part of the joint efforts within the Sonderforschungsbereich 162“Plasmaphysik Bochum/Jiilich”. REFERENCES 1. H. GRIEM,Special Line Broadening by Plasmas. Academic Press, New York (1974). 2. R. D. BEN&SONand G. R. CHESTER, kstrophys. J. 178, 565 (1972). 3. R. D. SCHL~~TER. Z. Naturforsch. 16a. 972 (l%l). 4. G. HIMMEL and fi. SCHL&R, Strahlungsvorgiingein Plasmen mit statischem Magnetfefd, Forschungsbericht des Landes Nordrhein-Westfalen No. 2363. Westdeutscher Verlag, Opladen (1973). 5. Trans. Int. Astr. Union llA, 100 (1%2). 6. A. UNSOLD, Physik der Stemafmosphiiren, p. 312. Springer, Berlin (1%8). 7. C. R. VIDAL,J. COOPER and E. W. SMITH,JQSRT 11, 263 (1971). 8. G. FUSSMANN and G. HIMMEL, JQSRT 13, 393 (1972). 9. C. R. VIDAL,.QSRT 6, 461 (1966). 10. A. R. STR~GANOV and N. S. SVENTITSKII, Tables of Spectral Lines of Neutral and Ionized Atoms. IFI/Plenum, New York (l%S). 11. G. R. HARRISON, MIT-Wavelength Tables. MIT Press, Cambridge, Mass. (1%9). 12. H. NGUYEN-HOE, W. DRAWIN and L. HERMAN, JQSRT 4, 847 (1964). 13. 0. THEIMER and P. KEPPLE,Phys. Rev. Al, 957 (1970). 14. V. I. BOIKO,Eksp. Tear. Fiz. 68, 854 (1975).