Abstract

A novel method of determining both the Doppler and Stark shifts in a single measurement of spectral lines emitted by the arc-heated flow from a plasma jet has been successfully demonstrated. The method uses a spherical mirror arranged with its optical axis coincident with the optical axis of a Fabry-Perot interferometer and with its center of curvature at the center line of the flow. The common optical axis lies at an angle to the flow. With this system, both red- and blue-shifted line profiles are recorded in the same spectral scan. If conditions are such that the red- and blue-shifted profiles are not resolvable, the blue-shifted component is chopped so that the recorded signal consists of the envelopes of both the red-shifted profile and the superimposed red- and blue-shifted profiles. The wavelength difference between the blue- and red-shifted line profiles is exactly twice the Doppler shift integrated along a line of sight through the flow and is independent of a Stark shift. The Stark shift is given by the wavelength difference between the absolute line center and the midpoint of the red- and blue-shifted lines. Abel inversion of integrated line shift data has yielded radial velocity profiles to an accuracy of ±3% in a supersonic, arc-heated argon flow.

© 1972 Optical Society of America

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References

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  1. W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
    [CrossRef]
  2. B. Ahlborn, R. N. Morris, J. Quant. Spectrosc. Rad. Transfer 9, 1519 (1969).
    [CrossRef]
  3. R. W. Porter, SIAM Rev. 6, 228 (1964).
    [CrossRef]
  4. D. P. Aeschliman, D. L. Evans, Paper 71-589, AIAA 4th Fluid and Plasmadynamics Conference, 21–23 June 1971, Palo Alto, California.
  5. M. A. Biondi, Rev. Sci. Instrum. 27, 36 (1956).
    [CrossRef]

1969 (1)

B. Ahlborn, R. N. Morris, J. Quant. Spectrosc. Rad. Transfer 9, 1519 (1969).
[CrossRef]

1967 (1)

W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
[CrossRef]

1964 (1)

R. W. Porter, SIAM Rev. 6, 228 (1964).
[CrossRef]

1956 (1)

M. A. Biondi, Rev. Sci. Instrum. 27, 36 (1956).
[CrossRef]

Aeschliman, D. P.

D. P. Aeschliman, D. L. Evans, Paper 71-589, AIAA 4th Fluid and Plasmadynamics Conference, 21–23 June 1971, Palo Alto, California.

Ahlborn, B.

B. Ahlborn, R. N. Morris, J. Quant. Spectrosc. Rad. Transfer 9, 1519 (1969).
[CrossRef]

Beth, M.-U.

W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
[CrossRef]

Biondi, M. A.

M. A. Biondi, Rev. Sci. Instrum. 27, 36 (1956).
[CrossRef]

Bohn, W. L.

W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
[CrossRef]

Evans, D. L.

D. P. Aeschliman, D. L. Evans, Paper 71-589, AIAA 4th Fluid and Plasmadynamics Conference, 21–23 June 1971, Palo Alto, California.

Morris, R. N.

B. Ahlborn, R. N. Morris, J. Quant. Spectrosc. Rad. Transfer 9, 1519 (1969).
[CrossRef]

Nedder, G.

W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
[CrossRef]

Porter, R. W.

R. W. Porter, SIAM Rev. 6, 228 (1964).
[CrossRef]

J. Quant. Spectrosc. Rad. Transfer (2)

W. L. Bohn, M.-U. Beth, G. Nedder, J. Quant. Spectrosc. Rad. Transfer 7, 661 (1967).
[CrossRef]

B. Ahlborn, R. N. Morris, J. Quant. Spectrosc. Rad. Transfer 9, 1519 (1969).
[CrossRef]

Rev. Sci. Instrum. (1)

M. A. Biondi, Rev. Sci. Instrum. 27, 36 (1956).
[CrossRef]

SIAM Rev. (1)

R. W. Porter, SIAM Rev. 6, 228 (1964).
[CrossRef]

Other (1)

D. P. Aeschliman, D. L. Evans, Paper 71-589, AIAA 4th Fluid and Plasmadynamics Conference, 21–23 June 1971, Palo Alto, California.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of 160-kW plasma jet and optical system used for spectral line profile measurement.

Fig. 2
Fig. 2

Strip-chart record of doublet from a cw He–Ne gas laser.

Fig. 3
Fig. 3

Superposed red- and blue-shifted 4159-Å Ar I line profiles integrated along a line of sight through jet axis. Viewing angle is 57°.

Fig. 4
Fig. 4

Strip-chart record of chopped signal reflected from spherical mirror, integrated along a line of sight, for case of unresolved lines. Upper envelope (a) is superposed red- and blue-shifted profile; lower envelope (b) is pure red-shifted profile. Solid line (c) is resultant blue-shifted profile, and (d) is the pressure inside the interferometer.

Fig. 5
Fig. 5

Integrated 4159-Å Ar I line intensity λ0(y), Doppler line shift Δλ(y), and H(y) lateral profiles for supersonic arc-heated flow 2.8 cm from the exit of a plasma jet operated at 30-kW input power. Plasma jet stagnation pressure = 103 Torr; chamber pressure = 10 Torr.

Fig. 6
Fig. 6

Radial distributions of Doppler line shift Δλ(r), velocity v(r), and normalized emission coefficient λ0(r) for test conditions of Fig. 5.

Tables (1)

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Table I Fabry-Perot Interferometer Characteristics

Equations (7)

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λ 0 ( y ) = 0 ( λ , y ) d λ .
λ 0 ( y ) = FSR ( λ , y ) d λ .
λ 0 ( r ) = - sin θ π r R d y ( y 2 - r 2 ) 1 2 y [ ( λ , y ) d λ ] = - sin θ π r R d y ( y 2 - r 2 ) 1 2 y [ λ 0 ( y ) ] ,
H ( y ) = 2 sin θ y R Δ λ ( r ) λ 0 ( r ) r d r ( r 2 - y 2 ) 1 2 ,
H ( r ) = Δ λ ( r ) λ 0 ( r ) = - sin θ π r R d y ( y 2 - r 2 ) 1 2 y H ( y ) .
Δ λ ( r ) = H ( r ) / [ λ 0 ( r ) ] .
v ( r ) = [ c Δ λ ( r ) ] / ( λ 0 cos θ ) .

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