- Email: [email protected]
Stark-broadening of hydrogen Balmer lines in the presence of strong magnetic fields in plasmas
J. Quanr. Specrrosc. Radiar. Transfer. Vol. 9. pp. 317-331. Pergamon Press 1969. Printed in Great Britain
STARK-BROADENING OF HYDROGEN PRESENCE OF STRONG MAGNETIC
BALMER LINES IN THE FIELDS IN PLASMAS
H. W. DRAWIN,*H. HENNING,?L. HERMANSand NGUYEN-H•E$ Association EURATOM-CEA, Dtpartement de la Physique du Plasma et de la Fusion ContrBl&e, Fontenay-aux-Roses, and Laboratoire des Recherches Physiques, Facultt des Sciences, Paris. (Received
1 July 1968)
Abstract-The profiles of the Balmer H,, H,, H, and Hd lines have been measured for different electron densities N (N = 3 x IV5 . 1 x 1016cm-“) and for a magnetic field strength of H = 69 kgauss in the plasma region observed. The magnetic field has been created by a magnet coil surrounding a straight discharge tube. The energy necessary for the creation and maintenance of this field was stored in two condenser banks. The measurements showed a strong modification of the profiles of both the H, and the H, lines by the magnetic field when compared with profiles emitted from magnetically free plasmas. On the other hand, there is only a small influence of the magnetic field on H, and H,. Concerning the H, line, good agreement was found between the measured profiles and those calculated by Nguyen-Hoe, Drawin and Herman. The conditions under which the wing intensities of ordinary Stark profiles may be used for a determination of electron densities, in spite of the presence of a strong magretic field, have been checked. A new method for measuring electron densities from line profiles in strongly magnetized plasmas is proposed. INTRODUCTION
A MEASUREMENT of: Stark-broadened lines emitted from plasmas offers the possibility of determining the mean density of the charged particles. Especially in the case of hydrogen, the profiles of the lower laying Balmer lines are rather well known from theoretical calculations of GRIEM, KOLB and SHEN.(I) Thus, by comparing the experimental profiles with theoretical ones the electron density can be determined. A special application of this method consists in measuring the halfwidths of the lines; since the theoretical halfwidths as a function of the electron density are known (2*3)the latter can easily be obtained. The method has most recently been tested by GERARDOand HILL(~)for the H, line. However, this method breaks down when the lines are emitted from strongly magnetized plasmas. There are different magnetic effects acting on the line profiles. They can be summarized as follows :(5-7) (1) The main effect is due to the Zeeman splitting of the energy levels. Like the quasistatic (or low-frequency) field component of the plasma ions, the magnetic field creates a shift of energy levels of the H-atoms. For a discussion it is convenient to define the parameter 7, where average Stark-shift for electric field strength F. (1) ’ = Zeeman-shift for magnetic field strength H * Association EURATOM-CEA, Fort de Chltillon, 92 Fontenay-aux-Roses,
France. t Association EURATOM-CEA, Fort de Chltillon, 92 Fontenay-aux-Roses, France. Present address: Leybold-Heraeus, Khln-Bayenthal, West Germany. $ Laboratoire de Recherches Physiques, Facultt des Sciences, 9, quai Saint Bernard, Tour 22-Paris SC, France. 317
H. W. DRAWIN, H. HENNING. L. HERMANand NGUYEN-HOE
31x
Here, F,, denotes
the “normal
field strength”
of the electric
F,, = 2603e,N For excited states with principal Paschen Back cffcct
quantum
number
microtield
in the plasma
“.‘.
(2)
n, equation
$@I - I)r,,tr,,E;,
(I) becomes
in case of the
+lA,)
(3)
where A,, = 3.43 x 10-‘N”J/H, with N expressed in cm ’ and H in Gauss. For r = I. Stark and Zeeman effects have comparable strength. The influence of the Zecman effect upon the line profile5 will be large if T < 1. There will only be a slight influence of the Zceman effect if z > 1, and the Zeeman effect is negligible for T 9 1. (2) The presence of a magnetic field influences the shift and intensity of the ordinary Stark components. This influence is a function of H/F, and the angle between H and F (corresponding splitting patterns have been published by HERMAN et ~1.‘~‘). (3) The ordinary microfield in a plasma has equal probability for all directions, thus, no preferential polarization does exist. However, the presence of the magnetic field causes a polarization, and the degree of polarization parallel and perpendicular to the magnetic lines of force is a function of H/F,. Considering the Stark-broadening in the presence of magnetic fields, the angle of observation versus the direction of the magnetic field must be taken into account. (4) The magnetic field constrains the electrons to move in tightly spiralling orbits. The average Larmor radius (rR) in a plane perpendicular to H is given by (4) where (cl) denotes the average velocity component perpendicular to H. This fact makes the assumption of straight line paths in theoretical line profile calculations questionable when a strong magnetic field is present. However, as long as the average electron Larmor radius (rJ remains much larger than the Debye radius r,-which is considered as the upper limit of the impact parameter for electronic collisions contributing to the profile--the straight path approximation may bc assumed as valid. The limit for the straight path approximation is approximatively given by (rr)
2
rd.
When (rg) G r,, the curved paths must be taken been given by MASCHKE and VOSLAMBER.(~’
(5)
into account.
A detailed
(5) The movement of the emitters (neutrals and ions) of velocity
generates
a Lorentz
electric field of strength
discussion
has
V, in a magnetic
field
E,, where
This field causes an additional Stark effect displacement of the levels. The distribution functionf(E) of the Lorentz-field strength is proportional to the velocity distribution of V perpendicular to H. Thus, the additional broadening is proportional to V,f(E) or V:f’(E),
Stark-broadeningof hydrogenBalmer lines in the presence of strong magnetic fields in plasmas
319
according to linear or quadratic Stark effect. Putting numerical values into equation (6) one sees that this effect is extremely small and can only be observed for very high velocities and extremely high magnetic fields. In order to obtain detailed information about the influence of a strong magnetic field on the profiles of the hydrogen Balmer lines, measurements have been made for the conditions z < 1,
7~1
and
~>l.
These measurements provide a check of the theoretical calculations for the H,-line(791‘) and further, these measurements will show the influence of the magnetic field upon the higher Balmer lines, especially on the HP-line whjch is the most important one for plasma diagnostic purposes. EXPERIMENTAL
The experimental device is similar to that described by DRAWIN, HERMANand NGUYENsome years ago for preliminary measurements of Stark-Zeeman-broadened lines. The actual experimental set-up, however, shows several important modifications compared with the first device. HoE(“’
(1) Discharge
tube
The discharge tube used in this experiment is shown in Fig. 1. It was made from fused quartz and contained two tungsten-coated electrodes 32 cm apart. In principle, it is quite
GAS TUNGSTEN
INLET
COATED
ELECTRODE
UMPING
PERFORATION
HOLES
1 OBSERVATION
FIG. 1. Discharge tube and coil. The observations were made perpendicular to the direction of the magnetic field.
similar to that developed by WULFF. (12) All spectroscopic observations were made perpendicular to the axis of the discharge tube and thus perpendicular to the direction of the
320
H. W. DRAWIN, H. HENNING, L. HERMANand NGUYEN-HOE
magnetic field. The latter was generated by a magnet coil (n = 220 turns, Cu-tape 10 mm x 2 mm, L = 1.0 mHy) over the discharge tube. The central part of the outer discharge tube contained a coaxial quartz tube of a smaller diameter (2r = 1.5mm). The insertion of this tube was necessary to reduce the large radial extension of the Balmer lines and to avoid self-absorption in the H,-line by the cold gas cylinder surrounding the plasma column. Without the central tube, the lines could still be observed at radial distances far away from the electrically conducting cylinder. Since the electron density was extremely small in this cold gas region, the lines showed the usual Lorentz pattern. These sharp lines are obviously created by absorption and re-emission of the strong radiation of the plasma column. As a general rule, this does not matter, however, the final evaluation of such “side-on” observed lines extending over large radial distances decreases the precision of that parts of the line originating from the central region. This is due to the Abel-inversion. Moreover, the absorption-reabsorption process in the outer region would introduce uncontrollable corrections for self-absorption. By reducing the diameter of the central tube more and more we were able to shorten the radial extension of the lines and to avoid reabsorption in the H,-line almost completely. With an inner diameter of 15 mm the absorption in the center of H, did not exceed 10 per cent. In the line wings the reabsorption was negligibly small, and for the higher Balmer lines no noticeable self-absorption could be detected. (2) Electrical
circuit und operution
Electrical operation is as follows: The magnet coil is connected to a high-voltage condenser bank (25 kV, 40 kJ) followed by a delay line (5 kV, 35 kJ) as shown in Fig. 3.
5KV
Dlschorge
t;be
FIG. 2. Electric circuits for generating the magnetic
field and the plasma.
First, at time t,, the high-voltage bank C, is discharged into the coil, thus establishing the desired magnetic field strength H. It is reached after t, = 700 ~1s.Then, the low-voltage delay line (C,, L,) is connected to the coil. The energy in this line has such a level that the magnetic field can be maintained on a constant level during 2 msec. Some time after the magnetic field has reached its constant value a short high-voltage pulse (time t2) is applied to the electrodes of the discharge tube causing a break-down of the gas (hydrogen filling pressure p = 2. . . 5 torr). A constant current I (I = 400,. . , 1600 A) is delivered by the second delay line fired at time t,
al
I Plasma
bl
t
cl time
lH-+-++-•
0
1
2
3
Cms
FIG. 3. (a) Magnetic field strength H and current Z,, through the coil vs. the time t, (b) Plasma current Z,,,,, vs. time t, (c) and (d) Emission of the Ha-line vs. time t.
LIGHT (He) EMISSION
PLASMA CURRENT
b)
c)
[A0
time 2.5ms
c------C_ 0
time 05ms
FIG. 4. Plasma current ZplssmSvs. time t, and the corresponding streak photos taken at the same moment in the light of H,, for three different experimental conditions. (a) and (b) : poor alignmems, (c) : satisfactory adjustment of the discharge tube.
Stark-broadening of hydrogen Balmer lines in the presence of strong magnetic fields .in plasmas
321
Just before the magnetic field begins to decrease the current through the discharge tube is short-circuited (t4 = 2.8 msec) by an ignitron in parallel connection. Thus, one obtains a constant light-emission during a time internal of At = t, - t, = 1.8 msec. The temporal behaviour of the magnetic field H, the plasma current Iplasma,and the intensity J(H,) of the H,-line are shown in Fig. 3(a-d). (3) Photographic observations and evaluations Streak-photos of the central section of the discharge are shown in Fig. 4(a-c). The photos (a) and (b) are obtained for two different poor alignments of the discharge tube vs. the magnetic field. The photo (c) is obtained for satisfactory adjustment. The spectra were taken under the conditions of Fig. 4(c). We used a Bausch & Lomb-2 gratings-2 m Ebert-type spectrograph (f:24, first order reciprocal dispersions 16.4 A/mm and 3.87 A/mm) together with KODAK spectral plates OF. The density-intensity calibration curves were obtained by using 7-step filters (calibrated for each wavelength) illuminated by a flash of 1.8 msec duration and constant intensity. The constant intensity was obtained by connecting a delay line to a commercial Xenon flash tube. This line maintained the current, and thus, the intensity on a constant level. A thyristor connected parallel to the flash tube and switched at the desired moment allowed the shorting of the current through the flash tube after 1.8 msec. By this method we were able to get the same exposure time for both the plasma to be investigated and the reference source. All measured line projiles have been converted into line profiles as a function of the radial distance r from the discharge axis. The corresponding Abel-integral inversion has been performed on the IBM-computer 360/50. When evaluating lines consisting of differently polarized intensity components one has to account for different transmission coefficients of the optical system for the different directions of polarization. Our measurements showed that the ratio R = J(o)/J(x) of the transmission coefficients of our optical system for the a-components relative to the unshifted n-component had the following values : R(H,) = 0.43 ; R(H,) = 0.79 ; R(H,) = 0.85 ; R(H,) = 0.93. By using a polarization filter we were able to account for the preferential transmission of the n-component relative to the a-components. All line profiles given in this paper correspond to the proper intensity distributions which may be obtained before the light beam crosses or touches any optical equipment. (4) Laser measurements of electron density The electron density has been measured by Laser interferometry. The plasma has been probed by a Laser beam in axial direction. The measured electron density represents a value averaged over the whole length of the tube. The experimental device used for these measurements has been developed by BELLAND. (13) A schematic drawing of the optical set-up is shown in Fig. 5. RESULTS
The ABEL-integral inversion gave complete line profiles for at least 13 different radial distances. Only some characteristic line shapes will be published here. In all cases, the magnetic field strength was H = 69 kgauss in the plasma region observed.
322
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
DISCHARGE
I
DETECTOR LASER
SWEEP CAMERA
.I
SPECTROGRAPH (REOSC)
\
FIG. 5. Optical
M-up;
AI I, MI, and M 3 are mirrors
(1) Radial electron density distribution (a) The radial density distribution can be determined by applying the envelope method of VIDAL.(‘~) The great advantage of VILIAL’S method is that one only needs intensities at a few distinct wavelengths values (namely at the maxima and the minima of the line intensities near the series limit) to construct the envelope curves. Thus, when applied to non-homogeneous plasma, the ABEL-inversion is necessary only at these few distinct points. By applying these inversions we obtained N-values as indicated in Fig. 6. These electron densities are generally higher than those obtained by the following other two methods.
FIG. 6. Radial
-
OO electron
density
distribution
N(r) for a magnetic
field strength
ol- H = 69 kgauss.
Stark-broadening
of hydrogen
Balmer lines in the presence
of strong
magnetic
fields in plasmas
323
(b) The theoretical calculations (‘,l”) showed that the influence of the magnetic field on the line profiles becomes weak for sufficiently large distances A1 from the centre of the line and with sufficiently high densities. Quantitatively this can be expressed as follows: Let &A& be the wavelength shift of the Lorentz-o-component relative to the unshifted n-component, and let 2A;1,,, be the (full) halfwidth of a purely Stark-broadened line when no magnetic field is present. Then, the influence of a magnetic field upon the intensity distribution in the (far) line wings for a combined Stark- and Zeeman-broadened line can be neglected for all wavelength distances satisfying the conditions (7a) Further, the average electron Larmor radius (rg) must fulfill the following condition
(Is) 2 ld.
V-4
Then, for all wavelength distances A1 as given by the inequality (7a), the intensity distribution of a combined Stark- and Zeeman-broadened line practically coincides with the intensity distribution of a purely Stark-broadened line. Stark profiles in the absence of magnetic fields have been calculated by GRIEMet al. (l) Comparing our measured shapes with their calculated profiles in the wings yields under the above indicated conditions a radial electron density distribution as shown in Fig. 6. For this evaluation we used the first four Balmer lines. (c) The Laser measurements gave the following density distribution : for r I 3 mm : N = 2 6mm:N 0.9 to 1.1 x 1Or6cm- 3;forr = 5mm:N = 3~10’~cm-~f30percent;forr = 1 x 1015 cmm3. The Laser measurements match well with the densities obtained from the intensity distribution in the wings of the Balmer lines. For the highest densities there is a discrepancy of 35 per cent between the values determined from Vidal’s method and the other two methods. Since line wings and Laser measurements give internally consistent values we regard the solid curve in Fig. 6 as the actual density distribution of the discharge. (2) Line projles All lines shapes presented here have been normalized so that +a
s
I(A,I)d(Ail) = 1.
(8)
--oo (a) The HJine
Several characteristic profiles are shown in Figs. 7-10. At low electron densities one can note the Zeeman-a-component of the Lorentz-triplet at a wavelength distance +A& given by A& g g4.7 x 1013/I;H [A]
(9)
324
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
iO.82
’
I
Hd
i i
1
1
I
L
H = 69 KG
i
Fit;. 7. The H&e profile for n, = 3 x 10” cm ‘, T = 16x IO3“K, compared with theoretical calculations of C&EM et al.(” and NGUYEN-HOE et ~1.“~‘~’ The theoretical “GKS profile” was obtained by extrapolating the values published in Ref. 1 towards lower densities.
5 EXPERIMENT . . . . THEORY NDH N : 3.0. 10’5cm-3
2 -.-THEORY ,
GKS N ; 3.01 1015crn-3
2
FE 8. The profile of H, for N = 3 x IO” cm-’ on a semilogarithmic scale. In the line wings the measured profile is close to the “GKS profile” in spite of the presence of a magnetic field. The “NDH profile” shows slightly higher wing intensities, compared with the GKS profile.
Stark-broadening of hydrogen 3almer lines in the presence of strong magnetic fields in plasmas
325
where 110is the wavelength of the centre of the unshifted line in (A), and H is the magnetic field strength in (gauss). The Lande’-g-factor equals 1 for hydrogen in the case of PaschenBack effect. With increasing values of N, the o-components become less distinguishable, but even for N = 1 x 1016 cmp3 the influence of the Zeeman effect has not disappeared and the position of the o-component can well be localized.
0.3
0.50
’
I
I
I
I
HGt1
I (0.1
I H = 69KG
4-fEXPERIMENT 0.2
0
. . . . . . THEORY
NDH
N z 5.0.10’5crn-3
_._,
GKS
N : 6.0.10’5cm-3
THEORY
4
0
1
2
3
L
5
6
7
Ah (A) FIG. 9. The H&-line for N = 5 x 10ls cm-j
compared with theoretical calculations. In the line wings, the “GKS profile” gives slightly higher densities than the “NDH profile”.
The measured profiles have been compared with theoretical ones. Those published in Ref. 1 have been denoted by “Theory GKS” (see Figs. 7-10). As expected, one observes a rather large discrepancy between the measurements and these theoretical calculations in the central part of the lines. This is not surprising, since the “Theory GKS” has been treated without considering magnetic fields. Towards the line wings the agreement of the GKS-profiles and the measured ones becomes better and better, thus, confirming the inequality.“) The more complete theory of NGUYEN-HOE, DRAwtN and HERMAN(~*‘) has been denoted by “Theory NDH”, see the figures. In their calculations the Zeeman effect has been taken into account. There is a good agreement between the measured and calculated curves. Especially the Zeeman components are well reproduced.
H. W. DRAWIN. H. HENNING, 1.. HERMANand NGUYEN-Ht)t
326
I
I
I
1
I
I
i H,
i i i i
0.3
I (ahI
1
,
Hz69KG
4-kEXPERIMENT
i
I
THEORY
NDH
THEORY
GKS
I: N
\
1.0 L 10 t6crK3
0.2
0.1
C
1
1
0
‘AY 2.
FIG. IO. The H,-line
compared
with theoretical “GKS profile”
I
3
I
L
calculation for N = is for H = 0 gauss.
5
1
I
I
6
7
nAtA)_...+.
I x 1O”‘cm ‘.
Note
that the
(b) The Hp-line The profiles for two different electron densities are shown in the Figs. 11 and 12. The magnetic field causes a considerable change in the shape of the central part of the line. The usual dip at AR = 0 disappears; moreover, a maximum occurs instead of a minimum if the electron densities are low enough. This maximumis due to the formation of the Zeeman-rrcomponent. The intensity necessary to form this central part must be taken from the near line wings. However, the near line wings contain the a-components at the positions rt_Aii, which have also to be built up. In our special case, the o-components practically coincide with the two maxima of the HB-line for zero magnetic fields. It follows from this, that the intensity necessary for the formation of the rr- and o-components of a combined Stark-Zeeman effect broadened HE-line can only be taken from parts laying beyond +A&. This effect may be seen in Fig. 11: When AL > A&., the intensity rapidly decreases compared with the ordinary Stark-broadened lines (“Theory GKS”). However, as soon as the inequality (7a) is fulfilled, only a small difference exists between a pure Stark-profile and a profile broadened by combined Stark-Zeeman-effect.
Stark-broadening
of hydrogen
Balmer lines in the presence
::.::
of strong
THEORY
GKS
magnetic
for
fields in plasmas
H =O
0.1
dh (Al,
A’hZ F‘lti. 11. Measured
profile for HP-line with a magnetic field strength of H = 69 kgauss. This profile is compared with two “GKS profiles” (N = 3 x lOI and 4 x lOI cm- 3). 2
I
I
I
I
II
-z-
GKS
, N=9.1015
8
16
18
I
I
I
H/3
t ‘;; 0,l
=
a
I
1
I
Line , I 69 KG Experiment
w--D-
5
Theory
~6~’
2
0 1 2 A% FIG. 12. Measured
4
6
profile of H, compared
10
12
14
zh
(;
21 -
with a “GKS
profile”
for N = 9 x lOI cmm3.
327
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
328
At present there does not exist any theoretical calculations of Stark-Zeeman-broadened HP-lines. (c) The H,- and H&zes
With increasing principal quantum number the influence of the magnetic field becomes less important ; this is due to the following two reasons : (i) The wavelengths & become smaller, thus, Aiz tends more and more towards the centre of the line, see equation (9), (ii) The electrical interaction of the atom with the electric microfield of the plasma becomes so strong that the Zeeman effect looses its importance compared with the Stark effect (see equation (3)). In general, we have 5 > 1. Both effects are confirmed by the experiment, see Figs. 13’ 15.
.H
Line , I 69 KG
=
Experiment Theory 5
-
2
-
w
:
5
-
2
-
o”mO I
28
4/
6,
8/
IO 1
12 t
14 i
GKS,
16,
N=4
18I
20I
t
] 22
LA, FIG. 13. Measured
1015 cs3
profile for H, compared
Ah with the “GKS
profile”
24
(A)-
for N = 4 x IO”
cm
J.
In our experimental conditions, the Lorentz-triplets of both the H,-and li,-line could no longer be resolved, due to the strong intermolecular Stark effect. For a magnetic field of H = 69 kgauss, the Lorentz-triplet of H, can only be seen for electron densities N < 1 x 1Ol5 cm- 3. No measurements have been made for such low densities.
Stark-broadening
of hydrogen
Balmer lines in the presence
of strong
magnetic
fields in plasmas
329
HE-Line H =69KG -w_ Experimglt --- Theory GKS,N=6.10%n-3
0
L
8
12
16
20
2L
28
32 36
M
Lb
18
ax[&]-
FIG. 14. Measured
profile for H6 compared
with the “GKS profile”
(N = 6 x lOI cmm3).
FIG. 15. Comparison of the measured profile for Hd with the “GKS profile” for N = 1 x 1OL6cmm3. In the line wing the Ha-line was already perturbed by the H,-line. The final profile (solid curve through triangles) was obtained by subtracting the wing intensities of H, from the measured intensities of H,.
The H,-line should still be less sensitive to magnetic fields than H, for the same electron density. The experiment, however, shows that the H,-line is more affected than H,. The
330
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
reason is the following: like H,, the H,-line has already an intensity maximum at Ai = 0 in a magnetically free plasma. Since AA1,2(HI) $ A/Z,,,(H,) for the same electron density. and further AI, .< AA,( the magnetic effect on H, is generally small. This can be seen from Fig. 13. But this is not valid for the Ha-line. Like H,, the H,-line has a dip at Ai = 0 when no magnetic field is present, and the two intensity maxima are formed at wavelengths f A&,,,, . In the presence of a strong magnetic held, however, the TI- and o-components must be created. All three components lie very close together, and since A& ==zAL,, the H,-line should now show a maximum at AE. = 0 instead of a minimum. The experiment shows that this maximum can be observed for N c 7.10’” cm- ’ and H = 69 kgauss, see Fig. 14.
CONCLUSION
(1) ‘The measurements have shown that the magnetic field has a strong influence on the shape of Stark-broadened lines, especially for H, and H,. For fixed values of N and H. the influence of the magnetic field decreases rapidly with the higher members of the Balmer series. For a magnetic field strength H = 69 kgauss and electron densities N I l.lO’h by the combined Stark and Zeeman effect, cme3, the profiles of H, and H,, broadened deviate considerably from pure Stark profiles. Further, the halfwidths as a function of the electron density are not the same for pure Stark profiles and Stark-Zeeman broadened lines. It follows from this, that the determination of N from measured halfwidths of H, or H, will cause considerable errors when the Zeeman effect is not taken into account. This method for determining N can practically not be applied when t 5 1. (2) The measurements have further shown that the shape of the central part of H, changes considerably from low to high electron densities with a fixed magnetic field strength. At low densities, the minimum between the n- and o-components is well established, at higher densities it disappears. This effect may be used as a new method for determining N : it only needs measuring the intensity in the minimum between the components vs. that of the maximum in the o-component. If one knows this intensity ratio for a given magnetic field strength from theoretical calculations one can easily determine the electron density from measured intensity ratios. (15) Details of this method will be published soon. (3) Finally, the measurements have shown that the magnetic field has practically only a very small influence upon the intensity distribution in the far line wings. If the intensity distribution in the (far) line wings is measurable the electron density can be obtained from usual Stark-broadened profiles in spite of the presence of a strong magnetic field. The only conditions necessary to be fulfilled are given by the inequalities (7a, b). Acknowledgements-The authors are indebted to Miss M. LOMBARD for her help during the numerical evaluation and for the preparation of the electronic computer programme. The assistance of Mr. A. PAES and Mr. E. SABL~N before and during the measurements is gratefully acknowledged. The authors thank Dr. SELLAND for the Laser measurements and Dr. TITTEL for the measurement of the transmission coefficients.
REFERENCES I. H. R. GRIEM, A. C. K~LB and K. Y. SHEN, U.S. Naval Research Laboratory Report 5455, Washington D.C. (1960). 2. W. L. WIESE, Plusma Diagnostic Techniques (Edited by R. H. HUL~DLESTONEand S. L. LEONARD). Academic Press, New York and London (1965).
Stark-broadening of hydrogen Balmer lines in the presence
of strong
magnetic
fields in plasmas
331
3. R. A. HILL, JQSRT7,401 (1967). 4. J. B. GERARDOand R. A. HILL, Phys. Rev. Letters 17, 623 (1966). 5. H. W. DRAWIN, Spectroscopical Measurements on Cold and Hot Plasmas, Report EUR-CEA-FC 101, Fontenay-aux-Roses, May (1961). 6. NGUYEN-HOE,H. W. DRAWIN and L. HERMAN,Z. Narurf. Zla, 1515 (1966). 7. NGUYEN-HOE,H. W. DRAWIN and L. HERMAN,JQSRT7,429 (1967). 8. L. HERMAN,NGUYEN-HOE,H. W. DRAWIN, B. PETROPOULOS and C. DEUTSCH, Report CEA-R 2913, Centre Etudes Nucleaires, Fontenay-aux-Roses (1965). 9. E. K. MASCHKE and D. V~SLAMBER, Stark-broadening of hydrogen lines in strong magnetic fields, Report EUR-CEA-FC-354, Fontenay-aux-Roses. Januarv (1966). IO. NGUYEN-HOE,H. W. DRAW; and L. HERMAN,Report &A-R-3161, Centre d’Etudes Nucleaires, Fontenayaux-Roses (1967). 11. H. W. DRAWIN,L. HERMANand NGUYEN-HOE,Measurement of Broadened Linesfrom Plasmas in the Presence of Sfrong Magnetic Fields, Report EUR-CEA-FC-321, Fontenay-aux-Roses, October (1965). 12. H. WULFF, Proc. 7th Int. Conf. on Phenomena in Ionized Gases, Vol. I, p. 829, Belgrade (1965). 13. P. BELLAND. Mesure de la densite tlectronique d’un plasma par interferombrie Laser HeeNe (,I = 3,39 {I), Thesis, Faculte des Sciences de I’Universiti de Paris, Dtcembre 15 (1967). 14. C. R. VIDAL. JQSRT6.461 (1966). 15. H. W. DRAWIN, H. HENNING,L. HERMAN and NGUYEN-HOE,Verhandl. D.P.G. (VI), 3,435 (1968).
STARK-BROADENING OF HYDROGEN PRESENCE OF STRONG MAGNETIC
BALMER LINES IN THE FIELDS IN PLASMAS
H. W. DRAWIN,*H. HENNING,?L. HERMANSand NGUYEN-H•E$ Association EURATOM-CEA, Dtpartement de la Physique du Plasma et de la Fusion ContrBl&e, Fontenay-aux-Roses, and Laboratoire des Recherches Physiques, Facultt des Sciences, Paris. (Received
1 July 1968)
Abstract-The profiles of the Balmer H,, H,, H, and Hd lines have been measured for different electron densities N (N = 3 x IV5 . 1 x 1016cm-“) and for a magnetic field strength of H = 69 kgauss in the plasma region observed. The magnetic field has been created by a magnet coil surrounding a straight discharge tube. The energy necessary for the creation and maintenance of this field was stored in two condenser banks. The measurements showed a strong modification of the profiles of both the H, and the H, lines by the magnetic field when compared with profiles emitted from magnetically free plasmas. On the other hand, there is only a small influence of the magnetic field on H, and H,. Concerning the H, line, good agreement was found between the measured profiles and those calculated by Nguyen-Hoe, Drawin and Herman. The conditions under which the wing intensities of ordinary Stark profiles may be used for a determination of electron densities, in spite of the presence of a strong magretic field, have been checked. A new method for measuring electron densities from line profiles in strongly magnetized plasmas is proposed. INTRODUCTION
A MEASUREMENT of: Stark-broadened lines emitted from plasmas offers the possibility of determining the mean density of the charged particles. Especially in the case of hydrogen, the profiles of the lower laying Balmer lines are rather well known from theoretical calculations of GRIEM, KOLB and SHEN.(I) Thus, by comparing the experimental profiles with theoretical ones the electron density can be determined. A special application of this method consists in measuring the halfwidths of the lines; since the theoretical halfwidths as a function of the electron density are known (2*3)the latter can easily be obtained. The method has most recently been tested by GERARDOand HILL(~)for the H, line. However, this method breaks down when the lines are emitted from strongly magnetized plasmas. There are different magnetic effects acting on the line profiles. They can be summarized as follows :(5-7) (1) The main effect is due to the Zeeman splitting of the energy levels. Like the quasistatic (or low-frequency) field component of the plasma ions, the magnetic field creates a shift of energy levels of the H-atoms. For a discussion it is convenient to define the parameter 7, where average Stark-shift for electric field strength F. (1) ’ = Zeeman-shift for magnetic field strength H * Association EURATOM-CEA, Fort de Chltillon, 92 Fontenay-aux-Roses,
France. t Association EURATOM-CEA, Fort de Chltillon, 92 Fontenay-aux-Roses, France. Present address: Leybold-Heraeus, Khln-Bayenthal, West Germany. $ Laboratoire de Recherches Physiques, Facultt des Sciences, 9, quai Saint Bernard, Tour 22-Paris SC, France. 317
H. W. DRAWIN, H. HENNING. L. HERMANand NGUYEN-HOE
31x
Here, F,, denotes
the “normal
field strength”
of the electric
F,, = 2603e,N For excited states with principal Paschen Back cffcct
quantum
number
microtield
in the plasma
“.‘.
(2)
n, equation
$@I - I)r,,tr,,E;,
(I) becomes
in case of the
+lA,)
(3)
where A,, = 3.43 x 10-‘N”J/H, with N expressed in cm ’ and H in Gauss. For r = I. Stark and Zeeman effects have comparable strength. The influence of the Zecman effect upon the line profile5 will be large if T < 1. There will only be a slight influence of the Zceman effect if z > 1, and the Zeeman effect is negligible for T 9 1. (2) The presence of a magnetic field influences the shift and intensity of the ordinary Stark components. This influence is a function of H/F, and the angle between H and F (corresponding splitting patterns have been published by HERMAN et ~1.‘~‘). (3) The ordinary microfield in a plasma has equal probability for all directions, thus, no preferential polarization does exist. However, the presence of the magnetic field causes a polarization, and the degree of polarization parallel and perpendicular to the magnetic lines of force is a function of H/F,. Considering the Stark-broadening in the presence of magnetic fields, the angle of observation versus the direction of the magnetic field must be taken into account. (4) The magnetic field constrains the electrons to move in tightly spiralling orbits. The average Larmor radius (rR) in a plane perpendicular to H is given by (4) where (cl) denotes the average velocity component perpendicular to H. This fact makes the assumption of straight line paths in theoretical line profile calculations questionable when a strong magnetic field is present. However, as long as the average electron Larmor radius (rJ remains much larger than the Debye radius r,-which is considered as the upper limit of the impact parameter for electronic collisions contributing to the profile--the straight path approximation may bc assumed as valid. The limit for the straight path approximation is approximatively given by (rr)
2
rd.
When (rg) G r,, the curved paths must be taken been given by MASCHKE and VOSLAMBER.(~’
(5)
into account.
A detailed
(5) The movement of the emitters (neutrals and ions) of velocity
generates
a Lorentz
electric field of strength
discussion
has
V, in a magnetic
field
E,, where
This field causes an additional Stark effect displacement of the levels. The distribution functionf(E) of the Lorentz-field strength is proportional to the velocity distribution of V perpendicular to H. Thus, the additional broadening is proportional to V,f(E) or V:f’(E),
Stark-broadeningof hydrogenBalmer lines in the presence of strong magnetic fields in plasmas
319
according to linear or quadratic Stark effect. Putting numerical values into equation (6) one sees that this effect is extremely small and can only be observed for very high velocities and extremely high magnetic fields. In order to obtain detailed information about the influence of a strong magnetic field on the profiles of the hydrogen Balmer lines, measurements have been made for the conditions z < 1,
7~1
and
~>l.
These measurements provide a check of the theoretical calculations for the H,-line(791‘) and further, these measurements will show the influence of the magnetic field upon the higher Balmer lines, especially on the HP-line whjch is the most important one for plasma diagnostic purposes. EXPERIMENTAL
The experimental device is similar to that described by DRAWIN, HERMANand NGUYENsome years ago for preliminary measurements of Stark-Zeeman-broadened lines. The actual experimental set-up, however, shows several important modifications compared with the first device. HoE(“’
(1) Discharge
tube
The discharge tube used in this experiment is shown in Fig. 1. It was made from fused quartz and contained two tungsten-coated electrodes 32 cm apart. In principle, it is quite
GAS TUNGSTEN
INLET
COATED
ELECTRODE
UMPING
PERFORATION
HOLES
1 OBSERVATION
FIG. 1. Discharge tube and coil. The observations were made perpendicular to the direction of the magnetic field.
similar to that developed by WULFF. (12) All spectroscopic observations were made perpendicular to the axis of the discharge tube and thus perpendicular to the direction of the
320
H. W. DRAWIN, H. HENNING, L. HERMANand NGUYEN-HOE
magnetic field. The latter was generated by a magnet coil (n = 220 turns, Cu-tape 10 mm x 2 mm, L = 1.0 mHy) over the discharge tube. The central part of the outer discharge tube contained a coaxial quartz tube of a smaller diameter (2r = 1.5mm). The insertion of this tube was necessary to reduce the large radial extension of the Balmer lines and to avoid self-absorption in the H,-line by the cold gas cylinder surrounding the plasma column. Without the central tube, the lines could still be observed at radial distances far away from the electrically conducting cylinder. Since the electron density was extremely small in this cold gas region, the lines showed the usual Lorentz pattern. These sharp lines are obviously created by absorption and re-emission of the strong radiation of the plasma column. As a general rule, this does not matter, however, the final evaluation of such “side-on” observed lines extending over large radial distances decreases the precision of that parts of the line originating from the central region. This is due to the Abel-inversion. Moreover, the absorption-reabsorption process in the outer region would introduce uncontrollable corrections for self-absorption. By reducing the diameter of the central tube more and more we were able to shorten the radial extension of the lines and to avoid reabsorption in the H,-line almost completely. With an inner diameter of 15 mm the absorption in the center of H, did not exceed 10 per cent. In the line wings the reabsorption was negligibly small, and for the higher Balmer lines no noticeable self-absorption could be detected. (2) Electrical
circuit und operution
Electrical operation is as follows: The magnet coil is connected to a high-voltage condenser bank (25 kV, 40 kJ) followed by a delay line (5 kV, 35 kJ) as shown in Fig. 3.
5KV
Dlschorge
t;be
FIG. 2. Electric circuits for generating the magnetic
field and the plasma.
First, at time t,, the high-voltage bank C, is discharged into the coil, thus establishing the desired magnetic field strength H. It is reached after t, = 700 ~1s.Then, the low-voltage delay line (C,, L,) is connected to the coil. The energy in this line has such a level that the magnetic field can be maintained on a constant level during 2 msec. Some time after the magnetic field has reached its constant value a short high-voltage pulse (time t2) is applied to the electrodes of the discharge tube causing a break-down of the gas (hydrogen filling pressure p = 2. . . 5 torr). A constant current I (I = 400,. . , 1600 A) is delivered by the second delay line fired at time t,
al
I Plasma
bl
t
cl time
lH-+-++-•
0
1
2
3
Cms
FIG. 3. (a) Magnetic field strength H and current Z,, through the coil vs. the time t, (b) Plasma current Z,,,,, vs. time t, (c) and (d) Emission of the Ha-line vs. time t.
LIGHT (He) EMISSION
PLASMA CURRENT
b)
c)
[A0
time 2.5ms
c------C_ 0
time 05ms
FIG. 4. Plasma current ZplssmSvs. time t, and the corresponding streak photos taken at the same moment in the light of H,, for three different experimental conditions. (a) and (b) : poor alignmems, (c) : satisfactory adjustment of the discharge tube.
Stark-broadening of hydrogen Balmer lines in the presence of strong magnetic fields .in plasmas
321
Just before the magnetic field begins to decrease the current through the discharge tube is short-circuited (t4 = 2.8 msec) by an ignitron in parallel connection. Thus, one obtains a constant light-emission during a time internal of At = t, - t, = 1.8 msec. The temporal behaviour of the magnetic field H, the plasma current Iplasma,and the intensity J(H,) of the H,-line are shown in Fig. 3(a-d). (3) Photographic observations and evaluations Streak-photos of the central section of the discharge are shown in Fig. 4(a-c). The photos (a) and (b) are obtained for two different poor alignments of the discharge tube vs. the magnetic field. The photo (c) is obtained for satisfactory adjustment. The spectra were taken under the conditions of Fig. 4(c). We used a Bausch & Lomb-2 gratings-2 m Ebert-type spectrograph (f:24, first order reciprocal dispersions 16.4 A/mm and 3.87 A/mm) together with KODAK spectral plates OF. The density-intensity calibration curves were obtained by using 7-step filters (calibrated for each wavelength) illuminated by a flash of 1.8 msec duration and constant intensity. The constant intensity was obtained by connecting a delay line to a commercial Xenon flash tube. This line maintained the current, and thus, the intensity on a constant level. A thyristor connected parallel to the flash tube and switched at the desired moment allowed the shorting of the current through the flash tube after 1.8 msec. By this method we were able to get the same exposure time for both the plasma to be investigated and the reference source. All measured line projiles have been converted into line profiles as a function of the radial distance r from the discharge axis. The corresponding Abel-integral inversion has been performed on the IBM-computer 360/50. When evaluating lines consisting of differently polarized intensity components one has to account for different transmission coefficients of the optical system for the different directions of polarization. Our measurements showed that the ratio R = J(o)/J(x) of the transmission coefficients of our optical system for the a-components relative to the unshifted n-component had the following values : R(H,) = 0.43 ; R(H,) = 0.79 ; R(H,) = 0.85 ; R(H,) = 0.93. By using a polarization filter we were able to account for the preferential transmission of the n-component relative to the a-components. All line profiles given in this paper correspond to the proper intensity distributions which may be obtained before the light beam crosses or touches any optical equipment. (4) Laser measurements of electron density The electron density has been measured by Laser interferometry. The plasma has been probed by a Laser beam in axial direction. The measured electron density represents a value averaged over the whole length of the tube. The experimental device used for these measurements has been developed by BELLAND. (13) A schematic drawing of the optical set-up is shown in Fig. 5. RESULTS
The ABEL-integral inversion gave complete line profiles for at least 13 different radial distances. Only some characteristic line shapes will be published here. In all cases, the magnetic field strength was H = 69 kgauss in the plasma region observed.
322
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
DISCHARGE
I
DETECTOR LASER
SWEEP CAMERA
.I
SPECTROGRAPH (REOSC)
\
FIG. 5. Optical
M-up;
AI I, MI, and M 3 are mirrors
(1) Radial electron density distribution (a) The radial density distribution can be determined by applying the envelope method of VIDAL.(‘~) The great advantage of VILIAL’S method is that one only needs intensities at a few distinct wavelengths values (namely at the maxima and the minima of the line intensities near the series limit) to construct the envelope curves. Thus, when applied to non-homogeneous plasma, the ABEL-inversion is necessary only at these few distinct points. By applying these inversions we obtained N-values as indicated in Fig. 6. These electron densities are generally higher than those obtained by the following other two methods.
FIG. 6. Radial
-
OO electron
density
distribution
N(r) for a magnetic
field strength
ol- H = 69 kgauss.
Stark-broadening
of hydrogen
Balmer lines in the presence
of strong
magnetic
fields in plasmas
323
(b) The theoretical calculations (‘,l”) showed that the influence of the magnetic field on the line profiles becomes weak for sufficiently large distances A1 from the centre of the line and with sufficiently high densities. Quantitatively this can be expressed as follows: Let &A& be the wavelength shift of the Lorentz-o-component relative to the unshifted n-component, and let 2A;1,,, be the (full) halfwidth of a purely Stark-broadened line when no magnetic field is present. Then, the influence of a magnetic field upon the intensity distribution in the (far) line wings for a combined Stark- and Zeeman-broadened line can be neglected for all wavelength distances satisfying the conditions (7a) Further, the average electron Larmor radius (rg) must fulfill the following condition
(Is) 2 ld.
V-4
Then, for all wavelength distances A1 as given by the inequality (7a), the intensity distribution of a combined Stark- and Zeeman-broadened line practically coincides with the intensity distribution of a purely Stark-broadened line. Stark profiles in the absence of magnetic fields have been calculated by GRIEMet al. (l) Comparing our measured shapes with their calculated profiles in the wings yields under the above indicated conditions a radial electron density distribution as shown in Fig. 6. For this evaluation we used the first four Balmer lines. (c) The Laser measurements gave the following density distribution : for r I 3 mm : N = 2 6mm:N 0.9 to 1.1 x 1Or6cm- 3;forr = 5mm:N = 3~10’~cm-~f30percent;forr = 1 x 1015 cmm3. The Laser measurements match well with the densities obtained from the intensity distribution in the wings of the Balmer lines. For the highest densities there is a discrepancy of 35 per cent between the values determined from Vidal’s method and the other two methods. Since line wings and Laser measurements give internally consistent values we regard the solid curve in Fig. 6 as the actual density distribution of the discharge. (2) Line projles All lines shapes presented here have been normalized so that +a
s
I(A,I)d(Ail) = 1.
(8)
--oo (a) The HJine
Several characteristic profiles are shown in Figs. 7-10. At low electron densities one can note the Zeeman-a-component of the Lorentz-triplet at a wavelength distance +A& given by A& g g4.7 x 1013/I;H [A]
(9)
324
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
iO.82
’
I
Hd
i i
1
1
I
L
H = 69 KG
i
Fit;. 7. The H&e profile for n, = 3 x 10” cm ‘, T = 16x IO3“K, compared with theoretical calculations of C&EM et al.(” and NGUYEN-HOE et ~1.“~‘~’ The theoretical “GKS profile” was obtained by extrapolating the values published in Ref. 1 towards lower densities.
5 EXPERIMENT . . . . THEORY NDH N : 3.0. 10’5cm-3
2 -.-THEORY ,
GKS N ; 3.01 1015crn-3
2
FE 8. The profile of H, for N = 3 x IO” cm-’ on a semilogarithmic scale. In the line wings the measured profile is close to the “GKS profile” in spite of the presence of a magnetic field. The “NDH profile” shows slightly higher wing intensities, compared with the GKS profile.
Stark-broadening of hydrogen 3almer lines in the presence of strong magnetic fields in plasmas
325
where 110is the wavelength of the centre of the unshifted line in (A), and H is the magnetic field strength in (gauss). The Lande’-g-factor equals 1 for hydrogen in the case of PaschenBack effect. With increasing values of N, the o-components become less distinguishable, but even for N = 1 x 1016 cmp3 the influence of the Zeeman effect has not disappeared and the position of the o-component can well be localized.
0.3
0.50
’
I
I
I
I
HGt1
I (0.1
I H = 69KG
4-fEXPERIMENT 0.2
0
. . . . . . THEORY
NDH
N z 5.0.10’5crn-3
_._,
GKS
N : 6.0.10’5cm-3
THEORY
4
0
1
2
3
L
5
6
7
Ah (A) FIG. 9. The H&-line for N = 5 x 10ls cm-j
compared with theoretical calculations. In the line wings, the “GKS profile” gives slightly higher densities than the “NDH profile”.
The measured profiles have been compared with theoretical ones. Those published in Ref. 1 have been denoted by “Theory GKS” (see Figs. 7-10). As expected, one observes a rather large discrepancy between the measurements and these theoretical calculations in the central part of the lines. This is not surprising, since the “Theory GKS” has been treated without considering magnetic fields. Towards the line wings the agreement of the GKS-profiles and the measured ones becomes better and better, thus, confirming the inequality.“) The more complete theory of NGUYEN-HOE, DRAwtN and HERMAN(~*‘) has been denoted by “Theory NDH”, see the figures. In their calculations the Zeeman effect has been taken into account. There is a good agreement between the measured and calculated curves. Especially the Zeeman components are well reproduced.
H. W. DRAWIN. H. HENNING, 1.. HERMANand NGUYEN-Ht)t
326
I
I
I
1
I
I
i H,
i i i i
0.3
I (ahI
1
,
Hz69KG
4-kEXPERIMENT
i
I
THEORY
NDH
THEORY
GKS
I: N
\
1.0 L 10 t6crK3
0.2
0.1
C
1
1
0
‘AY 2.
FIG. IO. The H,-line
compared
with theoretical “GKS profile”
I
3
I
L
calculation for N = is for H = 0 gauss.
5
1
I
I
6
7
nAtA)_...+.
I x 1O”‘cm ‘.
Note
that the
(b) The Hp-line The profiles for two different electron densities are shown in the Figs. 11 and 12. The magnetic field causes a considerable change in the shape of the central part of the line. The usual dip at AR = 0 disappears; moreover, a maximum occurs instead of a minimum if the electron densities are low enough. This maximumis due to the formation of the Zeeman-rrcomponent. The intensity necessary to form this central part must be taken from the near line wings. However, the near line wings contain the a-components at the positions rt_Aii, which have also to be built up. In our special case, the o-components practically coincide with the two maxima of the HB-line for zero magnetic fields. It follows from this, that the intensity necessary for the formation of the rr- and o-components of a combined Stark-Zeeman effect broadened HE-line can only be taken from parts laying beyond +A&. This effect may be seen in Fig. 11: When AL > A&., the intensity rapidly decreases compared with the ordinary Stark-broadened lines (“Theory GKS”). However, as soon as the inequality (7a) is fulfilled, only a small difference exists between a pure Stark-profile and a profile broadened by combined Stark-Zeeman-effect.
Stark-broadening
of hydrogen
Balmer lines in the presence
::.::
of strong
THEORY
GKS
magnetic
for
fields in plasmas
H =O
0.1
dh (Al,
A’hZ F‘lti. 11. Measured
profile for HP-line with a magnetic field strength of H = 69 kgauss. This profile is compared with two “GKS profiles” (N = 3 x lOI and 4 x lOI cm- 3). 2
I
I
I
I
II
-z-
GKS
, N=9.1015
8
16
18
I
I
I
H/3
t ‘;; 0,l
=
a
I
1
I
Line , I 69 KG Experiment
w--D-
5
Theory
~6~’
2
0 1 2 A% FIG. 12. Measured
4
6
profile of H, compared
10
12
14
zh
(;
21 -
with a “GKS
profile”
for N = 9 x lOI cmm3.
327
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
328
At present there does not exist any theoretical calculations of Stark-Zeeman-broadened HP-lines. (c) The H,- and H&zes
With increasing principal quantum number the influence of the magnetic field becomes less important ; this is due to the following two reasons : (i) The wavelengths & become smaller, thus, Aiz tends more and more towards the centre of the line, see equation (9), (ii) The electrical interaction of the atom with the electric microfield of the plasma becomes so strong that the Zeeman effect looses its importance compared with the Stark effect (see equation (3)). In general, we have 5 > 1. Both effects are confirmed by the experiment, see Figs. 13’ 15.
.H
Line , I 69 KG
=
Experiment Theory 5
-
2
-
w
:
5
-
2
-
o”mO I
28
4/
6,
8/
IO 1
12 t
14 i
GKS,
16,
N=4
18I
20I
t
] 22
LA, FIG. 13. Measured
1015 cs3
profile for H, compared
Ah with the “GKS
profile”
24
(A)-
for N = 4 x IO”
cm
J.
In our experimental conditions, the Lorentz-triplets of both the H,-and li,-line could no longer be resolved, due to the strong intermolecular Stark effect. For a magnetic field of H = 69 kgauss, the Lorentz-triplet of H, can only be seen for electron densities N < 1 x 1Ol5 cm- 3. No measurements have been made for such low densities.
Stark-broadening
of hydrogen
Balmer lines in the presence
of strong
magnetic
fields in plasmas
329
HE-Line H =69KG -w_ Experimglt --- Theory GKS,N=6.10%n-3
0
L
8
12
16
20
2L
28
32 36
M
Lb
18
ax[&]-
FIG. 14. Measured
profile for H6 compared
with the “GKS profile”
(N = 6 x lOI cmm3).
FIG. 15. Comparison of the measured profile for Hd with the “GKS profile” for N = 1 x 1OL6cmm3. In the line wing the Ha-line was already perturbed by the H,-line. The final profile (solid curve through triangles) was obtained by subtracting the wing intensities of H, from the measured intensities of H,.
The H,-line should still be less sensitive to magnetic fields than H, for the same electron density. The experiment, however, shows that the H,-line is more affected than H,. The
330
H. W. DRAWIN, H. HENNING, L. HERMAN and NGUYEN-HOE
reason is the following: like H,, the H,-line has already an intensity maximum at Ai = 0 in a magnetically free plasma. Since AA1,2(HI) $ A/Z,,,(H,) for the same electron density. and further AI, .< AA,( the magnetic effect on H, is generally small. This can be seen from Fig. 13. But this is not valid for the Ha-line. Like H,, the H,-line has a dip at Ai = 0 when no magnetic field is present, and the two intensity maxima are formed at wavelengths f A&,,,, . In the presence of a strong magnetic held, however, the TI- and o-components must be created. All three components lie very close together, and since A& ==zAL,, the H,-line should now show a maximum at AE. = 0 instead of a minimum. The experiment shows that this maximum can be observed for N c 7.10’” cm- ’ and H = 69 kgauss, see Fig. 14.
CONCLUSION
(1) ‘The measurements have shown that the magnetic field has a strong influence on the shape of Stark-broadened lines, especially for H, and H,. For fixed values of N and H. the influence of the magnetic field decreases rapidly with the higher members of the Balmer series. For a magnetic field strength H = 69 kgauss and electron densities N I l.lO’h by the combined Stark and Zeeman effect, cme3, the profiles of H, and H,, broadened deviate considerably from pure Stark profiles. Further, the halfwidths as a function of the electron density are not the same for pure Stark profiles and Stark-Zeeman broadened lines. It follows from this, that the determination of N from measured halfwidths of H, or H, will cause considerable errors when the Zeeman effect is not taken into account. This method for determining N can practically not be applied when t 5 1. (2) The measurements have further shown that the shape of the central part of H, changes considerably from low to high electron densities with a fixed magnetic field strength. At low densities, the minimum between the n- and o-components is well established, at higher densities it disappears. This effect may be used as a new method for determining N : it only needs measuring the intensity in the minimum between the components vs. that of the maximum in the o-component. If one knows this intensity ratio for a given magnetic field strength from theoretical calculations one can easily determine the electron density from measured intensity ratios. (15) Details of this method will be published soon. (3) Finally, the measurements have shown that the magnetic field has practically only a very small influence upon the intensity distribution in the far line wings. If the intensity distribution in the (far) line wings is measurable the electron density can be obtained from usual Stark-broadened profiles in spite of the presence of a strong magnetic field. The only conditions necessary to be fulfilled are given by the inequalities (7a, b). Acknowledgements-The authors are indebted to Miss M. LOMBARD for her help during the numerical evaluation and for the preparation of the electronic computer programme. The assistance of Mr. A. PAES and Mr. E. SABL~N before and during the measurements is gratefully acknowledged. The authors thank Dr. SELLAND for the Laser measurements and Dr. TITTEL for the measurement of the transmission coefficients.
REFERENCES I. H. R. GRIEM, A. C. K~LB and K. Y. SHEN, U.S. Naval Research Laboratory Report 5455, Washington D.C. (1960). 2. W. L. WIESE, Plusma Diagnostic Techniques (Edited by R. H. HUL~DLESTONEand S. L. LEONARD). Academic Press, New York and London (1965).
Stark-broadening of hydrogen Balmer lines in the presence
of strong
magnetic
fields in plasmas
331
3. R. A. HILL, JQSRT7,401 (1967). 4. J. B. GERARDOand R. A. HILL, Phys. Rev. Letters 17, 623 (1966). 5. H. W. DRAWIN, Spectroscopical Measurements on Cold and Hot Plasmas, Report EUR-CEA-FC 101, Fontenay-aux-Roses, May (1961). 6. NGUYEN-HOE,H. W. DRAWIN and L. HERMAN,Z. Narurf. Zla, 1515 (1966). 7. NGUYEN-HOE,H. W. DRAWIN and L. HERMAN,JQSRT7,429 (1967). 8. L. HERMAN,NGUYEN-HOE,H. W. DRAWIN, B. PETROPOULOS and C. DEUTSCH, Report CEA-R 2913, Centre Etudes Nucleaires, Fontenay-aux-Roses (1965). 9. E. K. MASCHKE and D. V~SLAMBER, Stark-broadening of hydrogen lines in strong magnetic fields, Report EUR-CEA-FC-354, Fontenay-aux-Roses. Januarv (1966). IO. NGUYEN-HOE,H. W. DRAW; and L. HERMAN,Report &A-R-3161, Centre d’Etudes Nucleaires, Fontenayaux-Roses (1967). 11. H. W. DRAWIN,L. HERMANand NGUYEN-HOE,Measurement of Broadened Linesfrom Plasmas in the Presence of Sfrong Magnetic Fields, Report EUR-CEA-FC-321, Fontenay-aux-Roses, October (1965). 12. H. WULFF, Proc. 7th Int. Conf. on Phenomena in Ionized Gases, Vol. I, p. 829, Belgrade (1965). 13. P. BELLAND. Mesure de la densite tlectronique d’un plasma par interferombrie Laser HeeNe (,I = 3,39 {I), Thesis, Faculte des Sciences de I’Universiti de Paris, Dtcembre 15 (1967). 14. C. R. VIDAL. JQSRT6.461 (1966). 15. H. W. DRAWIN, H. HENNING,L. HERMAN and NGUYEN-HOE,Verhandl. D.P.G. (VI), 3,435 (1968).