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The spectroscopic measurement of temperature in transparent argon plasmas
J. Qunnt.
Spectrosc.
Radiat.
Transfer.
Vol. 2, pp. 297-299.PergamonPressLtd. Printedin GreatBritain
THE SPECTROSCOPIC MEASUREMENT OF TEMPERATURE IN TRANSPARENT ARGON PLASMAS* CARL F. KNoPPt,
CHAD F. GOTTSCHLICH$
Gas Dynamics Laboratory,
Northwestern
(Received
and ALI BULENT CAMBEL~ University,
Evanston,
Ill.
7 June 1962)
experimental data may be obtained by either direct or IN PLASMA arc jet diagnostics indirect measuring devices. In general, the latter are preferable because the temperatures encountered are very high. Furthermore, immersed probes disturb the flow and may also cause the formation of a plasma sheath around the sensing element. It is the purpose of this note to describe the highlights of a spectroscopic technique which has been used to advantage in measuring the temperature of plasmas. There are several spectrometric methods which offer potentialities in plasma diagnostics. These methods are compared and discussed by PEARCE(~). In general, absorption spectroscopy is impractical in plasma diagnostics because the radiation intensities are quite high. Therefore, emission spectroscopy was used in this study. The technique described here is an adaptation of an astrophysical method developed originally by FOWLER and MILNE(~) and later treated analytically by LARENZ(~) for the case of transparent plasmas. In this present note the experimental utilization of the Fowler-Milne method is discussed and observations in connection with an argon arc jet are described. The Fowler-Milne method is a single line technique. It is particularly useful in engineering applications because it obviates knowledge of the transition probabilities of the gas under study. In order to obtain meaningful data there are four conditions which must be satisfied. These are: (a) thermal equilibrium must exist; (b) at least one of the species in the gas must exhibit a radiation intensity maximum; (c) the geometry of the jet must be radially symmetric; and (d) the extent of self-absorption by the gas should be negligible. The argon plasma studied in this note was generated in the hyperthermal facility described in Ref. 4. For the purposes of this experiment, the arc jet was exhausted to the atmosphere through a subsonic nozzle. The power input was 4 kW at 200 A and 20 V. The gas flow rate was 57g min- l. The intensity measurements were made with a Perkin-Elmer Model 12-C monochrometer modified for emission spectroscopy.
*This work was supported, in part, by the Air Force Office of Scientific Research No. AF OSR 49(638)-879. tSenior Research Assistant in Mechanical Engineering. IAssistant Professor in Mechanical Engineering. §Walter P. Murphy Professor and Chairman, Mechanical Engineering. 291
under Contract
298
F.GOTT.SCHLICH and ALI BULENT CAMBEL
CARL F.KNOPP,CHAD
To ascertain
the existence
of equilibrium
conditions,
COMPTON'S criterion,‘“)
namely.
E -- < 0.5 I’
was applied. In equation (I), Eis the electric field strength in the arc and 12 is the pressure. The conditions in these studies were: E = 20 V cm-l and y = 760 mm. Consequently. Compton’s ratio was much less than one half and equilibrium could be expected even in the arc itself. Because the flow was subsonic it would seem that equilibrium would prevail downstream where the spectroscopic measurements were made. The Fowler-Milne method relates a measured intensity-co-ordinate profile to a calculated intensity-temperature curve. A temperature.co-ordinate relation may be established by normalizing the measured and the calculated quantities, thus obtaining a one to one correspondence and allowing the elimination of intensity which appears as the common parameter. This explains the necessity of an intensity maximum for one of the gas constituents. More specifically, the occurrence of an intensity maximum indicates that the temperature of the gas is sufficient to produce a significant reduction in the number of particles of the species being observed. It follows that the use of the Fowler-Milne method is restricted to plasmas which are ionized appreciably. A typical normalized intensity-co-ordinate profile using the 4158.6 A line of atomic argon is shown as curve A in Fig. 1. The normalized calculated intensity-temperature I,O-
16m :
$ 2
a 0.5 -
l-4
0' 0
I 0.04
Curves
r(inches) I
5
Key
A: 8: C’
1 0.08 A&C
I 20
I
I
IO T (“KxlO-‘I
INTENSITY-COORDINATE INTENSITY-TEMPERATURE RADIAL TEMPERATURE FIG.
I 0.12
15 Curve
B PROFILE RELATION DISTRIBUTION
1.
relation for the 4158.6 A line of atomic argon is graphed in curve B. Curve C results from the elimination of the intensity parameter between curves A and B and it represents the radial temperature distribution.
The spectroscopic
measurement
of temperature in transparent argon plasmas
299
In determining the intensity-co-ordinate relation for the plasma, it should be noted that the observed intensity is an average intensity distribution, produced by the thermal gradient existing along the axis of observation. If the plasma is radially symmetric this average intensity distribution may be inverted analytically to a radial distribution of intensity (such as that shown in curve A) by a Volterra-type integral of the form R
Here, r is the radial distance from the azimuthal axis of symmetry of the plasma stream; y is the horizontal co-ordinate perpendicular to the flow, and R is the maximum value which r may assume. This integral equation has been solved numerically by NESTOR and OLSEN@). Observations made at the Gas Dynamics Laboratory indicate that arc heating of gases in a plasma jet generally produces a radially-symmetric high temperature plasma. The last criterion, namely that the plasma be non-self-absorbing, is necessary in order to ensure that the true radiant intensity of the plasma is being measured. To determine if the plasma stream produced by the arc jet is optically thin, a 9 in. parabolic mirror of the type used in schlieren systems was employed in conjuction with the monochrometer. The mirror was placed along the optical axis of the spectrometer at the opposite side of the plasma and at a distance equal to twice the focal length of the mirror. This resulted in the reflected image of the plasma being focused upon the plasma with a magnification of one. It was found from relative intensity measurements that the intensity of the plasma and its image were consistently 95 per cent greater than the intensity of the plasma alone. This measurement provided the evidence that the plasma under consideration was optically thin. On the basis of the aforementioned observations it can be suggested that the method of Fowler-Milne may be used to advantage in determining the temperature of laboratorytype plasma arcs commonly used in studies of hypersonics and magneto-gasdynamic power generation. REFERENCES
I. 2. 3. 4.
W. J. PEARCE,Plasma Jet Temperature Study, WADC Technical Report 59-346, (1960). R. H. FOWLER and E. A. MILNE, Mon. Not. Roy. Astr. Sot. 83,403 (1923); 84,499 (1924). R. W. LARENZ, Concerning a Method for the Measurement of Very High Temperatures in Nearly Transparent Arc Columns, NASA TT F-54, 1960. C. F. KNOPP, C. F. GOT~SCHLICH and A. B. CAMBEL, A Spectroscopic Technique for the Measurement of Temperature in Transparent Plasmas AF OSR-1100, April, (1961). K. T. COMPTON,Phys. Rev., 22, 432 (1923). 0. H. NESTORand H. N. OLSEN, S.Z.A.M. Rev 2 (1960).
Spectrosc.
Radiat.
Transfer.
Vol. 2, pp. 297-299.PergamonPressLtd. Printedin GreatBritain
THE SPECTROSCOPIC MEASUREMENT OF TEMPERATURE IN TRANSPARENT ARGON PLASMAS* CARL F. KNoPPt,
CHAD F. GOTTSCHLICH$
Gas Dynamics Laboratory,
Northwestern
(Received
and ALI BULENT CAMBEL~ University,
Evanston,
Ill.
7 June 1962)
experimental data may be obtained by either direct or IN PLASMA arc jet diagnostics indirect measuring devices. In general, the latter are preferable because the temperatures encountered are very high. Furthermore, immersed probes disturb the flow and may also cause the formation of a plasma sheath around the sensing element. It is the purpose of this note to describe the highlights of a spectroscopic technique which has been used to advantage in measuring the temperature of plasmas. There are several spectrometric methods which offer potentialities in plasma diagnostics. These methods are compared and discussed by PEARCE(~). In general, absorption spectroscopy is impractical in plasma diagnostics because the radiation intensities are quite high. Therefore, emission spectroscopy was used in this study. The technique described here is an adaptation of an astrophysical method developed originally by FOWLER and MILNE(~) and later treated analytically by LARENZ(~) for the case of transparent plasmas. In this present note the experimental utilization of the Fowler-Milne method is discussed and observations in connection with an argon arc jet are described. The Fowler-Milne method is a single line technique. It is particularly useful in engineering applications because it obviates knowledge of the transition probabilities of the gas under study. In order to obtain meaningful data there are four conditions which must be satisfied. These are: (a) thermal equilibrium must exist; (b) at least one of the species in the gas must exhibit a radiation intensity maximum; (c) the geometry of the jet must be radially symmetric; and (d) the extent of self-absorption by the gas should be negligible. The argon plasma studied in this note was generated in the hyperthermal facility described in Ref. 4. For the purposes of this experiment, the arc jet was exhausted to the atmosphere through a subsonic nozzle. The power input was 4 kW at 200 A and 20 V. The gas flow rate was 57g min- l. The intensity measurements were made with a Perkin-Elmer Model 12-C monochrometer modified for emission spectroscopy.
*This work was supported, in part, by the Air Force Office of Scientific Research No. AF OSR 49(638)-879. tSenior Research Assistant in Mechanical Engineering. IAssistant Professor in Mechanical Engineering. §Walter P. Murphy Professor and Chairman, Mechanical Engineering. 291
under Contract
298
F.GOTT.SCHLICH and ALI BULENT CAMBEL
CARL F.KNOPP,CHAD
To ascertain
the existence
of equilibrium
conditions,
COMPTON'S criterion,‘“)
namely.
E -- < 0.5 I’
was applied. In equation (I), Eis the electric field strength in the arc and 12 is the pressure. The conditions in these studies were: E = 20 V cm-l and y = 760 mm. Consequently. Compton’s ratio was much less than one half and equilibrium could be expected even in the arc itself. Because the flow was subsonic it would seem that equilibrium would prevail downstream where the spectroscopic measurements were made. The Fowler-Milne method relates a measured intensity-co-ordinate profile to a calculated intensity-temperature curve. A temperature.co-ordinate relation may be established by normalizing the measured and the calculated quantities, thus obtaining a one to one correspondence and allowing the elimination of intensity which appears as the common parameter. This explains the necessity of an intensity maximum for one of the gas constituents. More specifically, the occurrence of an intensity maximum indicates that the temperature of the gas is sufficient to produce a significant reduction in the number of particles of the species being observed. It follows that the use of the Fowler-Milne method is restricted to plasmas which are ionized appreciably. A typical normalized intensity-co-ordinate profile using the 4158.6 A line of atomic argon is shown as curve A in Fig. 1. The normalized calculated intensity-temperature I,O-
16m :
$ 2
a 0.5 -
l-4
0' 0
I 0.04
Curves
r(inches) I
5
Key
A: 8: C’
1 0.08 A&C
I 20
I
I
IO T (“KxlO-‘I
INTENSITY-COORDINATE INTENSITY-TEMPERATURE RADIAL TEMPERATURE FIG.
I 0.12
15 Curve
B PROFILE RELATION DISTRIBUTION
1.
relation for the 4158.6 A line of atomic argon is graphed in curve B. Curve C results from the elimination of the intensity parameter between curves A and B and it represents the radial temperature distribution.
The spectroscopic
measurement
of temperature in transparent argon plasmas
299
In determining the intensity-co-ordinate relation for the plasma, it should be noted that the observed intensity is an average intensity distribution, produced by the thermal gradient existing along the axis of observation. If the plasma is radially symmetric this average intensity distribution may be inverted analytically to a radial distribution of intensity (such as that shown in curve A) by a Volterra-type integral of the form R
Here, r is the radial distance from the azimuthal axis of symmetry of the plasma stream; y is the horizontal co-ordinate perpendicular to the flow, and R is the maximum value which r may assume. This integral equation has been solved numerically by NESTOR and OLSEN@). Observations made at the Gas Dynamics Laboratory indicate that arc heating of gases in a plasma jet generally produces a radially-symmetric high temperature plasma. The last criterion, namely that the plasma be non-self-absorbing, is necessary in order to ensure that the true radiant intensity of the plasma is being measured. To determine if the plasma stream produced by the arc jet is optically thin, a 9 in. parabolic mirror of the type used in schlieren systems was employed in conjuction with the monochrometer. The mirror was placed along the optical axis of the spectrometer at the opposite side of the plasma and at a distance equal to twice the focal length of the mirror. This resulted in the reflected image of the plasma being focused upon the plasma with a magnification of one. It was found from relative intensity measurements that the intensity of the plasma and its image were consistently 95 per cent greater than the intensity of the plasma alone. This measurement provided the evidence that the plasma under consideration was optically thin. On the basis of the aforementioned observations it can be suggested that the method of Fowler-Milne may be used to advantage in determining the temperature of laboratorytype plasma arcs commonly used in studies of hypersonics and magneto-gasdynamic power generation. REFERENCES
I. 2. 3. 4.
W. J. PEARCE,Plasma Jet Temperature Study, WADC Technical Report 59-346, (1960). R. H. FOWLER and E. A. MILNE, Mon. Not. Roy. Astr. Sot. 83,403 (1923); 84,499 (1924). R. W. LARENZ, Concerning a Method for the Measurement of Very High Temperatures in Nearly Transparent Arc Columns, NASA TT F-54, 1960. C. F. KNOPP, C. F. GOT~SCHLICH and A. B. CAMBEL, A Spectroscopic Technique for the Measurement of Temperature in Transparent Plasmas AF OSR-1100, April, (1961). K. T. COMPTON,Phys. Rev., 22, 432 (1923). 0. H. NESTORand H. N. OLSEN, S.Z.A.M. Rev 2 (1960).