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Forbidden optical transitions stimulated by plasma turbulence in helium
J. Quanr. Specwosc. Radiar. Transfer. Vol. 11, pp. l-6. Pergamon
Press
1971. Printed
in Great
Britain
FORBIDDEN OPTICAL TRANSITIONS STIMULATED BY PLASMA TURBULENCE IN HELIUM N.
BEN-Y• SEF
and A. G. RUBIN
Air Force Cambridge Research Laboratories, Bedford, Massachusetts 01730 (Received 14 July 1970) Abstract-Satellites to the forbidden ls2p-ls3p transition stimulated by strong plasma oscillations were observed. Internal structure of the satellites related to the spectrum of the plasma turbulence was found. The light emitted at these satellites is polarized showing that the plasma electrostatic field is anisotropic.
INTRODUCTION
of obtaining information about the spectrum of plasma oscillations from satellites to forbidden spectral lines was investigated by BARANGER and Mozw.(‘) It was shown that the longitudinal electric field of the plasma oscillations can stimulate two satellites of the forbidden line which are separated from it by f Q, where R is the electron plasma frequency. In second-order perturbation theory, the total intensity of the satellites relative to that of the allowed line is THE POSSIBILITY
S,
= h2(Ei)R,,rJ6m2e2(AfQ)2,
where m is the electron mass, e the electron charge, A is the splitting (in angular frequency units) between the allowed and forbidden lines, (Ei) is the time average of the square of the plasma electric field. The quantity R,,, is a dimensionless radial integral (in units of the Bohr radius a0 squared), RW = ia?
. ’
KlmlxaJPm’)J2,
where x’ is the a component of the atomic electron coordinate operator and 1, m and l’, m’ are the angular and magnetic quantum numbers of allowed and forbidden levels. Defining &=
U waves (E;> U particles = h($N,kT,)
the strength of the satellites can then be written as S*S&-f-
kTR2
-
R
@,“>e2 = 3Sl’mkT
1R,P
2me4 I A+_!2
2
2
N. BEN-Y•SEFand A. G. RUBIN
Satellites of this kind were observed by KUNZE and GRIEM,(‘~~) BAVARIAN et LX~.(~) and COOPER et a1.(‘-‘) In these experiments, the resolution was relatively low and not much information was obtained in addition to the positions of the satellites. In this communication, the satellites to the helium 6678 A line will be shown with enough resolution to determine their position, relative intensity, polarization and internal structure, which is related to the structure of the plasma turbulence, EXPERIMENTAL
The plasma source was a coaxial plasma gun firing into a large chamber. The gun and chamber have been previously described. (8,9) The gun was modified to operate with a static gas filling, and also the screen at the gun muzzle was removed. Because of these modifications, the high current from the gun extends into the gas chamber causing turbulence. In addition, a shock is produced by the plasma from the gun flowing into the static gas. The gas used was helium at a pressure of 70 microns. The gun voltage was 12 kV. Spectroscopic measurements were taken with a $ m Czerny-Turner grating spectrometer using photographic and photoelectric detection. The instrumental broadening parameters were measured for both detection methods and the final results were corrected accordingly. The density of the plasma in the region of measurement was measured by Stark broadening of the He I and He II lines. The temperature was measured by means of the ratio of the relativeintensity of the He I 5876 A line to that of the He II 4686 A line. The relative intensities were measured photoelectrically with 6 microns entrance slit width and 4 microns exit slit width. After correction for instrumental broadening, the integrated profiles led to an electron temperature of (4.OkO.5) x lo4 “K, using Equation (13-15) in Ref. 10. The Stark broadening was measured for three lines, and the results are summarized in Table 1. TABLE 1 Line
“Full half width”
Density
He II 4686 He I5875 He 16678
0.64 A 0.52 8, 0.48 A
1.4 x 1016 cmm3 1.4 x lOI crne3 0.7 x 1016 cme3
The profile of the He II 4686 A line was investigated in the wings down to 0.05 of its maximum intensity, and good agreement was found with the calculated values in Table (&3) of Ref. 10. The measured half-width (full half-width) is accurate to about 0.1 A in each case. EXPERIMENTAL
RESULTS
A microdensitometer trace of the photographic spectrum in the region 6560A is shown in Fig. 1. The He II 6560 A and the He I 6678 A lines are clearly seen, as well as a few iron-impurity lines. In addition, two lines are visible at 6648 8, and 6623 A which show internal structure. To verify the impurity lines, the same experiment was performed with hydrogen, using the H, line for calibration purposes. All of the lines observed in the same spectral region as in Fig. 1 were present, except for the two helium lines and the lines at
Forbidden optical transitions stimulated by plasma turbulence in helium
WAVELENGTH
3
-
FIG. 1. Microdensitometer
trace of the plasma spectrum in the region 656&668OA. The spectroscopic plate was exposed to 160 shots to obtain sufficient density.
6623 A and 6648 hi. These two lines are, therefore, interpreted to be the plasma-excited satellites to the forbidden transition ls2pls3p whose characteristics were calculated in (1). Using the same notation as in Ref. 1, one obtains for the separation of the center of the two satellitesfromthe6678 A(ls2p-ls3dallowedtransition)thevalue ofA = (96+ 12) err- ‘. The calculated value is A = 104cm-‘, well within the experimental accuracy. The main source of inaccuracy is in the determination of the exact position of the 6678 A line because of its breadth. The separation of the two satellites is 2CI = (55.4 + 1.4) cm- ’ (using the central dip of each line as its center). This value corresponds to Q = (27.7 kO.7) cm- ’ and, in frequency units, F = CR = 8.3 x 10” set-‘. In Fig. 2, the enlarged microdensitometer trace in the region of the satellites is shown. One observes that there is an internal structure in the satellites and that the two satellites are mirror images of each other, apart from the difference in intensity. A structure such as this can be expected if the plasma electric field is not monochromatic but has an extended spectrum. The spectral region in the vicinity of the 5016 A He line (ls2s-ls3p transition) was investigated. The forbidden transition ls2s-ls3d is 104 cm- ’ below the allowed one so that one can expect a plasma-excited satellite at wavelengths longer than 5016a. One of the expected satellites was measured at a wavelength of 5035 A, the second one was not observed but, since its intensity should be lower and its predicted position is close to the 5048 A He I line, it is probably masked by it. The position of the observed satellite (the observed satellite is interpreted to be the near satellite) relative to the allowed line is A -R = (79 + 7) cm- ‘. Using the calculated value for A = 104 cm-‘, one obtains R = (25f7) cm-‘, a result
N. BEN-Y• SEFand A. G.
WAVELENGTH
FIG.
2.
RUBIN
-
Enlarged microdensitometer trace showing the internal structure of the satellites. The “dispersion” in this case is five times that of Fig. 1.
which is in agreement with the previously calculated value. The shape of the observed line resembles the shape of the two satellites shown in Figs. 1 and 2, as it shows the doublehumped structure also. It may be concluded that the observed line is indeed the expected satellite and the value for the frequency of the stimulating field is in agreement with the value calculated from the previously mentioned satellites. The relative intensities of the two satellites to the 6678 A and the He I 6678 A line were measured photoelectrically. The relative intensity of the two satellites is 2.4, and the relative intensity of the strong satellite to the allowed line is 0.101. The intensity of the electric field stimulating this transition can be calculated from this intensity ratio. From Equation (1) of Ref. 1, one obtains for the field the value (Ei) = 6.00 x lo4 e.s.u. Using the measured value of the temperature, one obtains &=
wave energy 0%) thermal energy = 8n($IkT)
= 2.87 x lo-‘.
The value of Emay be obtained in another way from the relative intensities of the two satellites. Using Equations (10) and (11) of Ref. 3, one obtains E = 4.00 x 10e2. The two values of E are of the same order of magnitude ; the difference between the two values is within the accuracy of the measurements, especially the first method which consists of comparing intensities differing by an order of magnitude. For a non-turbulent plasma, the energy in the electrostatic wave is given by KUNZE(*) as E fh =
2/27an,,
where n, is the number of particles in a Debye sphere. For the plasma under consideration, this value is n, = 110, so that E = 2.15 x 10e4. From this value, it may be seen that the
Forbidden optical transitions stimulated by plasma turbulence in helium
5
energy in the oscillation is two orders of magnitude higher than can be expected for a nonturbulent plasma so that the plasma investigated is highly turbulent. The structure of the satellites in Fig. 2 shows that the plasma field is composed of two main frequencies around the central frequency of F = 8.3 x 10” set- ‘. The frequency separation of the two branches is about 1 cm-‘, that is, 3 x lOlo set-‘. From a knowledge of the plasma density and the central frequency of the instability, one may estimate the wavelength of the instability by using a density of 1016 cmW3 corresponding to a plasma frequency 0 = 5.658 x 10” ; the angular frequency of the oscillations is 27tF = 5.21 x 10i2. Using the dispersion relation for a warm plasma, co2 = c-o;+ 3k2V;,
where l( is the thermal velocity ofthe electrons and is known from the temperature measurement. One now obtains k = 2x/A = 0.93 x 104cm-‘, which leads to ;1 = 6.76x 10M4cm. For the plasma under investigation, the D length is 1.4 x 10m5cm, so that the central wavelength of the oscillations is about 50 D lengths. POLARIZATION
The plasma field in a non-turbulent plasma, being of thermal nature, will be isotropic. In a turbulent plasma, on the other hand, the instabilities can have a particular direction of propagation so that the fields have preferred direction ; that is, an anisotropy is present in the field. An anisotropic field will also excite the satellites, but in this case the light emitted will be polarized. (‘s5) In the present case, the results presented show that the turbulence is non-thermal in nature and that some degree of polarization can be expected. A series of measurements was performed to check this characteristic. It was found that the light emitted in the satellites is polarized in the stream direction ; that is, in the axial direction. The measurements performed on neutral helium lines show no polarization at all whereas the ionized helium lines show some polarization in the same direction. The polarization measurements were performed using photoelectric detection. The integrated intensity of the stronger satellite was measured ; the weaker satellite had insufficient intensity for accurate measurement. A sheet of polarizing material in front of the entrance slit of the spectrometer was used as the polarization detector. A total of 25 shots was taken at each polarization, along and at right angles to the streaming direction. The measurement method was checked in several ways. First, the signal amplitude was measured in a series of five shots at each polarization alternately, to assure that there was no difference in the discharge or measurement apparatus between series at alternate polarization. The polarizations of some lines from a helium lamp were measured with the same method, yielding the result of no polarization. The neutral helium lines from the gun discharge were found to be unpolarized. As was noted previously, ionized helium lines from the gun discharge were found to be polarized. The results of the polarization measurements on the strong satellite show that the signal (normalized to one) in the stream direction is l&O.41 and in the perpendicular direction 0.59f0.24; the error shown is the standard deviation for 25 shots in each case. The signals for the neutral helium 5875 A line are in the stream direction 1 f0.119 and in the perpendicular direction 1.01 kO.164. One can conclude that the light emitted from the satellites excited by strong oscillations in the plasma is polarized.
6
N. BEN-Y•SEFand A. G. RUBIN CONCLUSIONS
It has been shown that spectroscopic study of the satellites to forbidden lines yields information about instabilities in the plasma. The frequency, wavelength, average amplitude and direction of the electric fields associated with the instability were determined experimentally. At present, no information is available about the type of instability present, but a more detailed study of the shape of the satellites may lead to an exact measurement of the turbulence spectra.
REFERENCES 1. M. BARANGERand B. MOXER,Phys. Rev. 123,25 (1961). 2. H. J. KUNZEand H. R. GRIEM,Phys. Reo. Let!. 21, 1078 (1968). 3. H. J. KUNZE, H. R. GRIEM,A. W. DE SILVA, G. C. GOLDENBAUM and I. J. SPALDING, Phys. Fluids 12,2669 (1969). 4. G. BAVARIAN,R. BENATTAR,J. BRETAGNE, J. L. CODARTand G. SULTAN, Phys. Lett 3OA,198 (1969). 5. W. S. COOPERIII and H. RINGLER,Phys. Rev. 179,226 (1969). 6. W. S. COOPERIII and R. A. Hess, Bull. Am. Phys. Sot., Ser. II 14, 1071 (1969). 7. W. W. HICKSand W. S. CARPERIII, Bull. Am. Phys. Sot., Ser II 14, 1071 (1969). 8. A. G. RUBIN,Phys. Fluids 11, 1566 (1968). 9. N. BEN-Y•SEFand A. G. RUBIN,J. Appl. Phys. NJ,4074 (1969). 10. H. R. GRIEM,Plasma Spectroscopy, McGraw-Hill, New York (1964).
Press
1971. Printed
in Great
Britain
FORBIDDEN OPTICAL TRANSITIONS STIMULATED BY PLASMA TURBULENCE IN HELIUM N.
BEN-Y• SEF
and A. G. RUBIN
Air Force Cambridge Research Laboratories, Bedford, Massachusetts 01730 (Received 14 July 1970) Abstract-Satellites to the forbidden ls2p-ls3p transition stimulated by strong plasma oscillations were observed. Internal structure of the satellites related to the spectrum of the plasma turbulence was found. The light emitted at these satellites is polarized showing that the plasma electrostatic field is anisotropic.
INTRODUCTION
of obtaining information about the spectrum of plasma oscillations from satellites to forbidden spectral lines was investigated by BARANGER and Mozw.(‘) It was shown that the longitudinal electric field of the plasma oscillations can stimulate two satellites of the forbidden line which are separated from it by f Q, where R is the electron plasma frequency. In second-order perturbation theory, the total intensity of the satellites relative to that of the allowed line is THE POSSIBILITY
S,
= h2(Ei)R,,rJ6m2e2(AfQ)2,
where m is the electron mass, e the electron charge, A is the splitting (in angular frequency units) between the allowed and forbidden lines, (Ei) is the time average of the square of the plasma electric field. The quantity R,,, is a dimensionless radial integral (in units of the Bohr radius a0 squared), RW = ia?
. ’
KlmlxaJPm’)J2,
where x’ is the a component of the atomic electron coordinate operator and 1, m and l’, m’ are the angular and magnetic quantum numbers of allowed and forbidden levels. Defining &=
U waves (E;> U particles = h($N,kT,)
the strength of the satellites can then be written as S*S&-f-
kTR2
-
R
@,“>e2 = 3Sl’mkT
1R,P
2me4 I A+_!2
2
2
N. BEN-Y•SEFand A. G. RUBIN
Satellites of this kind were observed by KUNZE and GRIEM,(‘~~) BAVARIAN et LX~.(~) and COOPER et a1.(‘-‘) In these experiments, the resolution was relatively low and not much information was obtained in addition to the positions of the satellites. In this communication, the satellites to the helium 6678 A line will be shown with enough resolution to determine their position, relative intensity, polarization and internal structure, which is related to the structure of the plasma turbulence, EXPERIMENTAL
The plasma source was a coaxial plasma gun firing into a large chamber. The gun and chamber have been previously described. (8,9) The gun was modified to operate with a static gas filling, and also the screen at the gun muzzle was removed. Because of these modifications, the high current from the gun extends into the gas chamber causing turbulence. In addition, a shock is produced by the plasma from the gun flowing into the static gas. The gas used was helium at a pressure of 70 microns. The gun voltage was 12 kV. Spectroscopic measurements were taken with a $ m Czerny-Turner grating spectrometer using photographic and photoelectric detection. The instrumental broadening parameters were measured for both detection methods and the final results were corrected accordingly. The density of the plasma in the region of measurement was measured by Stark broadening of the He I and He II lines. The temperature was measured by means of the ratio of the relativeintensity of the He I 5876 A line to that of the He II 4686 A line. The relative intensities were measured photoelectrically with 6 microns entrance slit width and 4 microns exit slit width. After correction for instrumental broadening, the integrated profiles led to an electron temperature of (4.OkO.5) x lo4 “K, using Equation (13-15) in Ref. 10. The Stark broadening was measured for three lines, and the results are summarized in Table 1. TABLE 1 Line
“Full half width”
Density
He II 4686 He I5875 He 16678
0.64 A 0.52 8, 0.48 A
1.4 x 1016 cmm3 1.4 x lOI crne3 0.7 x 1016 cme3
The profile of the He II 4686 A line was investigated in the wings down to 0.05 of its maximum intensity, and good agreement was found with the calculated values in Table (&3) of Ref. 10. The measured half-width (full half-width) is accurate to about 0.1 A in each case. EXPERIMENTAL
RESULTS
A microdensitometer trace of the photographic spectrum in the region 6560A is shown in Fig. 1. The He II 6560 A and the He I 6678 A lines are clearly seen, as well as a few iron-impurity lines. In addition, two lines are visible at 6648 8, and 6623 A which show internal structure. To verify the impurity lines, the same experiment was performed with hydrogen, using the H, line for calibration purposes. All of the lines observed in the same spectral region as in Fig. 1 were present, except for the two helium lines and the lines at
Forbidden optical transitions stimulated by plasma turbulence in helium
WAVELENGTH
3
-
FIG. 1. Microdensitometer
trace of the plasma spectrum in the region 656&668OA. The spectroscopic plate was exposed to 160 shots to obtain sufficient density.
6623 A and 6648 hi. These two lines are, therefore, interpreted to be the plasma-excited satellites to the forbidden transition ls2pls3p whose characteristics were calculated in (1). Using the same notation as in Ref. 1, one obtains for the separation of the center of the two satellitesfromthe6678 A(ls2p-ls3dallowedtransition)thevalue ofA = (96+ 12) err- ‘. The calculated value is A = 104cm-‘, well within the experimental accuracy. The main source of inaccuracy is in the determination of the exact position of the 6678 A line because of its breadth. The separation of the two satellites is 2CI = (55.4 + 1.4) cm- ’ (using the central dip of each line as its center). This value corresponds to Q = (27.7 kO.7) cm- ’ and, in frequency units, F = CR = 8.3 x 10” set-‘. In Fig. 2, the enlarged microdensitometer trace in the region of the satellites is shown. One observes that there is an internal structure in the satellites and that the two satellites are mirror images of each other, apart from the difference in intensity. A structure such as this can be expected if the plasma electric field is not monochromatic but has an extended spectrum. The spectral region in the vicinity of the 5016 A He line (ls2s-ls3p transition) was investigated. The forbidden transition ls2s-ls3d is 104 cm- ’ below the allowed one so that one can expect a plasma-excited satellite at wavelengths longer than 5016a. One of the expected satellites was measured at a wavelength of 5035 A, the second one was not observed but, since its intensity should be lower and its predicted position is close to the 5048 A He I line, it is probably masked by it. The position of the observed satellite (the observed satellite is interpreted to be the near satellite) relative to the allowed line is A -R = (79 + 7) cm- ‘. Using the calculated value for A = 104 cm-‘, one obtains R = (25f7) cm-‘, a result
N. BEN-Y• SEFand A. G.
WAVELENGTH
FIG.
2.
RUBIN
-
Enlarged microdensitometer trace showing the internal structure of the satellites. The “dispersion” in this case is five times that of Fig. 1.
which is in agreement with the previously calculated value. The shape of the observed line resembles the shape of the two satellites shown in Figs. 1 and 2, as it shows the doublehumped structure also. It may be concluded that the observed line is indeed the expected satellite and the value for the frequency of the stimulating field is in agreement with the value calculated from the previously mentioned satellites. The relative intensities of the two satellites to the 6678 A and the He I 6678 A line were measured photoelectrically. The relative intensity of the two satellites is 2.4, and the relative intensity of the strong satellite to the allowed line is 0.101. The intensity of the electric field stimulating this transition can be calculated from this intensity ratio. From Equation (1) of Ref. 1, one obtains for the field the value (Ei) = 6.00 x lo4 e.s.u. Using the measured value of the temperature, one obtains &=
wave energy 0%) thermal energy = 8n($IkT)
= 2.87 x lo-‘.
The value of Emay be obtained in another way from the relative intensities of the two satellites. Using Equations (10) and (11) of Ref. 3, one obtains E = 4.00 x 10e2. The two values of E are of the same order of magnitude ; the difference between the two values is within the accuracy of the measurements, especially the first method which consists of comparing intensities differing by an order of magnitude. For a non-turbulent plasma, the energy in the electrostatic wave is given by KUNZE(*) as E fh =
2/27an,,
where n, is the number of particles in a Debye sphere. For the plasma under consideration, this value is n, = 110, so that E = 2.15 x 10e4. From this value, it may be seen that the
Forbidden optical transitions stimulated by plasma turbulence in helium
5
energy in the oscillation is two orders of magnitude higher than can be expected for a nonturbulent plasma so that the plasma investigated is highly turbulent. The structure of the satellites in Fig. 2 shows that the plasma field is composed of two main frequencies around the central frequency of F = 8.3 x 10” set- ‘. The frequency separation of the two branches is about 1 cm-‘, that is, 3 x lOlo set-‘. From a knowledge of the plasma density and the central frequency of the instability, one may estimate the wavelength of the instability by using a density of 1016 cmW3 corresponding to a plasma frequency 0 = 5.658 x 10” ; the angular frequency of the oscillations is 27tF = 5.21 x 10i2. Using the dispersion relation for a warm plasma, co2 = c-o;+ 3k2V;,
where l( is the thermal velocity ofthe electrons and is known from the temperature measurement. One now obtains k = 2x/A = 0.93 x 104cm-‘, which leads to ;1 = 6.76x 10M4cm. For the plasma under investigation, the D length is 1.4 x 10m5cm, so that the central wavelength of the oscillations is about 50 D lengths. POLARIZATION
The plasma field in a non-turbulent plasma, being of thermal nature, will be isotropic. In a turbulent plasma, on the other hand, the instabilities can have a particular direction of propagation so that the fields have preferred direction ; that is, an anisotropy is present in the field. An anisotropic field will also excite the satellites, but in this case the light emitted will be polarized. (‘s5) In the present case, the results presented show that the turbulence is non-thermal in nature and that some degree of polarization can be expected. A series of measurements was performed to check this characteristic. It was found that the light emitted in the satellites is polarized in the stream direction ; that is, in the axial direction. The measurements performed on neutral helium lines show no polarization at all whereas the ionized helium lines show some polarization in the same direction. The polarization measurements were performed using photoelectric detection. The integrated intensity of the stronger satellite was measured ; the weaker satellite had insufficient intensity for accurate measurement. A sheet of polarizing material in front of the entrance slit of the spectrometer was used as the polarization detector. A total of 25 shots was taken at each polarization, along and at right angles to the streaming direction. The measurement method was checked in several ways. First, the signal amplitude was measured in a series of five shots at each polarization alternately, to assure that there was no difference in the discharge or measurement apparatus between series at alternate polarization. The polarizations of some lines from a helium lamp were measured with the same method, yielding the result of no polarization. The neutral helium lines from the gun discharge were found to be unpolarized. As was noted previously, ionized helium lines from the gun discharge were found to be polarized. The results of the polarization measurements on the strong satellite show that the signal (normalized to one) in the stream direction is l&O.41 and in the perpendicular direction 0.59f0.24; the error shown is the standard deviation for 25 shots in each case. The signals for the neutral helium 5875 A line are in the stream direction 1 f0.119 and in the perpendicular direction 1.01 kO.164. One can conclude that the light emitted from the satellites excited by strong oscillations in the plasma is polarized.
6
N. BEN-Y•SEFand A. G. RUBIN CONCLUSIONS
It has been shown that spectroscopic study of the satellites to forbidden lines yields information about instabilities in the plasma. The frequency, wavelength, average amplitude and direction of the electric fields associated with the instability were determined experimentally. At present, no information is available about the type of instability present, but a more detailed study of the shape of the satellites may lead to an exact measurement of the turbulence spectra.
REFERENCES 1. M. BARANGERand B. MOXER,Phys. Rev. 123,25 (1961). 2. H. J. KUNZEand H. R. GRIEM,Phys. Reo. Let!. 21, 1078 (1968). 3. H. J. KUNZE, H. R. GRIEM,A. W. DE SILVA, G. C. GOLDENBAUM and I. J. SPALDING, Phys. Fluids 12,2669 (1969). 4. G. BAVARIAN,R. BENATTAR,J. BRETAGNE, J. L. CODARTand G. SULTAN, Phys. Lett 3OA,198 (1969). 5. W. S. COOPERIII and H. RINGLER,Phys. Rev. 179,226 (1969). 6. W. S. COOPERIII and R. A. Hess, Bull. Am. Phys. Sot., Ser. II 14, 1071 (1969). 7. W. W. HICKSand W. S. CARPERIII, Bull. Am. Phys. Sot., Ser II 14, 1071 (1969). 8. A. G. RUBIN,Phys. Fluids 11, 1566 (1968). 9. N. BEN-Y•SEFand A. G. RUBIN,J. Appl. Phys. NJ,4074 (1969). 10. H. R. GRIEM,Plasma Spectroscopy, McGraw-Hill, New York (1964).