Abstract

It is shown that the current distribution in a typical Tokamak plasma can be measured by a light scattering technique. The direction of the total magnetic field is measured accurately enough that the magnitude of the small poloidal component can be found. The field direction is measured by observing the scattered frequency spectrum of CO2 laser light. The usual Gaussian spectrum becomes modulated at the electron cyclotron frequency when the difference between the incident and scattered wave vectors is nearly perpendicular to the magnetic field. The harmonics can be superimposed with a Fabry-Perot interferometer and their collective width resolved as the scattering direction is changed. The SNR is high only when the detector is shielded against background radiation.

© 1974 Optical Society of America

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References

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  1. F. W. Perkins, Bull. Am. Phys. Soc. 11, 1418 (1970); also Princeton Plasma Physics Laboratory MATT-818.
  2. R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
    [CrossRef]
  3. R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
    [CrossRef]
  4. F. C. Jobes, R. L. Hickok, Nucl. Fusion 10, 195 (1970).
    [CrossRef]
  5. M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.
  6. J. Sheffield, Plasma Phys. 14, 385 (1972).
    [CrossRef]
  7. D. Dimock et al., Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1971), Vol. 1, p. 451.
  8. T. Laaspeere, J. Geophys. Res. 65, 3955 (1960).
    [CrossRef]
  9. D. E. Evans, P. Carolan, Phys. Rev. Lett. 25, 1605 (1970).
    [CrossRef]
  10. L. Kellerer, in 4th European Conference on Controlled Fusion and Plasma Physics (Comitata Nazionale per l’Energia Nucleare, Rome, 1970), p. 125.
  11. Lumonics Research Ltd., Ottawa, Ont.
  12. Santa Barbara Research Center, Goleta, California.
  13. D. W. Kruse, L. D. Mc Glauchlin, R. B. Mc Quistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 365.
  14. K. Chen, Ph.D. Thesis, Massachusetts Institute of Technology (1972).

1972 (2)

R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
[CrossRef]

J. Sheffield, Plasma Phys. 14, 385 (1972).
[CrossRef]

1971 (1)

R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
[CrossRef]

1970 (4)

F. W. Perkins, Bull. Am. Phys. Soc. 11, 1418 (1970); also Princeton Plasma Physics Laboratory MATT-818.

F. C. Jobes, R. L. Hickok, Nucl. Fusion 10, 195 (1970).
[CrossRef]

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

D. E. Evans, P. Carolan, Phys. Rev. Lett. 25, 1605 (1970).
[CrossRef]

1960 (1)

T. Laaspeere, J. Geophys. Res. 65, 3955 (1960).
[CrossRef]

Cano, R.

R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
[CrossRef]

R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
[CrossRef]

Carolan, P.

D. E. Evans, P. Carolan, Phys. Rev. Lett. 25, 1605 (1970).
[CrossRef]

Chen, K.

K. Chen, Ph.D. Thesis, Massachusetts Institute of Technology (1972).

Clarke, J. F.

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

Dimock, D.

D. Dimock et al., Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1971), Vol. 1, p. 451.

Etievant, C.

R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
[CrossRef]

Evans, D. E.

D. E. Evans, P. Carolan, Phys. Rev. Lett. 25, 1605 (1970).
[CrossRef]

Fidone, I.

R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
[CrossRef]

Hickok, R. L.

F. C. Jobes, R. L. Hickok, Nucl. Fusion 10, 195 (1970).
[CrossRef]

Hosea, J.

R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
[CrossRef]

Jobes, F. C.

F. C. Jobes, R. L. Hickok, Nucl. Fusion 10, 195 (1970).
[CrossRef]

Kellerer, L.

L. Kellerer, in 4th European Conference on Controlled Fusion and Plasma Physics (Comitata Nazionale per l’Energia Nucleare, Rome, 1970), p. 125.

Kelley, G. G.

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

Kruse, D. W.

D. W. Kruse, L. D. Mc Glauchlin, R. B. Mc Quistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 365.

Laaspeere, T.

T. Laaspeere, J. Geophys. Res. 65, 3955 (1960).
[CrossRef]

Lubin, M.

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

Mc Glauchlin, L. D.

D. W. Kruse, L. D. Mc Glauchlin, R. B. Mc Quistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 365.

Mc Quistan, R. B.

D. W. Kruse, L. D. Mc Glauchlin, R. B. Mc Quistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 365.

Murakami, M.

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

Perkins, F. W.

F. W. Perkins, Bull. Am. Phys. Soc. 11, 1418 (1970); also Princeton Plasma Physics Laboratory MATT-818.

Schwartz, M. J.

R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
[CrossRef]

Sheffield, J.

J. Sheffield, Plasma Phys. 14, 385 (1972).
[CrossRef]

Bull. Am. Phys. Soc. (2)

F. W. Perkins, Bull. Am. Phys. Soc. 11, 1418 (1970); also Princeton Plasma Physics Laboratory MATT-818.

M. Murakami, J. F. Clarke, G. G. Kelley, M. Lubin, Bull. Am. Phys. Soc. 11, 1411 (1970); also Oak Ridge National Laboratory ORNL-TM-3093.

J. Geophys. Res. (1)

T. Laaspeere, J. Geophys. Res. 65, 3955 (1960).
[CrossRef]

Nucl. Fusion (1)

F. C. Jobes, R. L. Hickok, Nucl. Fusion 10, 195 (1970).
[CrossRef]

Phys. Rev. Lett. (3)

D. E. Evans, P. Carolan, Phys. Rev. Lett. 25, 1605 (1970).
[CrossRef]

R. Cano, I. Fidone, M. J. Schwartz, Phys. Rev. Lett. 27, 783 (1971).
[CrossRef]

R. Cano, C. Etievant, J. Hosea, Phys. Rev. Lett. 29, 1302 (1972).
[CrossRef]

Plasma Phys. (1)

J. Sheffield, Plasma Phys. 14, 385 (1972).
[CrossRef]

Other (6)

D. Dimock et al., Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1971), Vol. 1, p. 451.

L. Kellerer, in 4th European Conference on Controlled Fusion and Plasma Physics (Comitata Nazionale per l’Energia Nucleare, Rome, 1970), p. 125.

Lumonics Research Ltd., Ottawa, Ont.

Santa Barbara Research Center, Goleta, California.

D. W. Kruse, L. D. Mc Glauchlin, R. B. Mc Quistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 365.

K. Chen, Ph.D. Thesis, Massachusetts Institute of Technology (1972).

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Figures (11)

Fig. 1
Fig. 1

Scattered spectrum for αc ≫ 1 when kTe = 1.0 keV, θs = 90°.

Fig. 2
Fig. 2

Shape of a single harmonic for kTe = 1.0 keV, B = 30 kG, and θs= 90°. The scale has been normalized to unity when ϕ = π/2.

Fig. 3
Fig. 3

Scattering geometry for θs = 90°.

Fig. 4
Fig. 4

Scattering system on a Tokamak.

Fig. 5
Fig. 5

The output of the Fabry-Perot interferometer f ( ϕ ) = ω 1 / e ω 1 / e T F - P S ( k , ω ) d ω vs ϕ , taking the integration in all cases to the 1/e points of a 1.0-keV Gaussian. The fixed parameters are θs = 90°, B = 30 kG, and F = 6.

Fig. 6
Fig. 6

The output of the Fabry-Perot interferometer for the first scattered harmonic f 1 ( ϕ ) = 0.5 ω C 1.5 ω C T F - P S ( k , ω ) d ω vs ϕ for the conditions kTe = 1.0 keV, B = 30 kG, and F = 6. The effect of a small change in the field ΔB/B is shown. f1(ϕ) has been normalized to 0.84 for convenient comparison to the other figures.

Fig. 7
Fig. 7

Detector and equivalent circuit.

Fig. 8
Fig. 8

Room temperature background radiation spectrum PB and detector responsivity |R.

Fig. 9
Fig. 9

Side view of optical scheme for a single channel system.

Fig. 10
Fig. 10

Output of Fabry-Perot interferometer f ( ϕ ) = ω 1 / e ω 1 / e T F - P S ( k , ω ) d ω vs ϕ , where kTe = 1.0 keV, B = 30 kG, and F = 6. The effect of rays that differ from the normal by Δθi is shown.

Fig. 11
Fig. 11

Top view of optical scheme for a multiple detector system.

Equations (21)

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S ( k , ω ) = α c π 1 / 2 ω c exp ( - z ) n = - n = I n ( z ) exp ( - α c 2 ) [ ( ω / ω c ) - n ] 2 ,
- S ( k , ω ) d ω = 1 .
T F - P = 1 / ( 1 + { [ ( 4 ρ ) / ( 1 - ρ ) 2 ] sin 2 [ ω s ( t / c ) cos θ i ] } ) ,
B B t [ 1 + 1 / 2 ( B p 2 / B t 2 ) ] .
f ( ϕ ) = - ω 1 / e ω 1 / e T F - P ( ω ) S ( k , ω ) d ω
Δ N s = N i n e r 0 2 L Δ Ω ,
Δ V L = V 0 R L ( R L + R D ) [ ( R L + R D ) 2 + ω 2 C s 2 R L 2 R D 2 ] 1 / 2 ( Δ R D Δ ϕ ) Δ ϕ ,
Δ V L = R L R D 2 V 0 ( 1 + ω 2 C s 2 R L 2 ) 1 / 2 ( Δ R D Δ ϕ ) Δ ϕ .
R L = ( 1 / ω i ) ( Δ V L / Δ ϕ ) .
R L = 2 ( R L / R D ) { R / [ ( 1 + ω 2 C s 2 R L 2 ) 1 / 2 ] } .
R L = 2 ( R L / R D ) R .
Δ P s = Δ N s T f ( ϕ ) ( ω i / τ )
Δ V s = R L Δ P s = 2 { [ Δ N s T f ( ϕ ) ] / τ } ω i R L .
Δ P N = [ ( A D 1 / 2 ) / ( D * 10 μ m ) ] ( Δ ω / 2 π ) 1 / 2 ,
( S N ) B = Δ P s Δ P N = Δ N s T f ( ϕ ) h ω i D * 10 μ m ( 2 π A D τ ) 1 / 2 .
Δ V J = [ ( 2 / π ) K T R L Δ ω ] 1 / 2 { 1 / [ ( 1 + ω 2 R L 2 C s 2 ) 1 / 2 ] } ,
Δ V J = ( k T / π C s ) 1 / 2
R = ( R D / ω i ) { e G η / [ ( 1 + ω 2 τ R 2 ) 1 / 2 ] } ,
f ( ϕ ) = ω 1 / e ω 1 / e T F - P S ( k , ω ) d ω vs ϕ ,
f 1 ( ϕ ) = 0.5 ω C 1.5 ω C T F - P S ( k , ω ) d ω vs ϕ
f ( ϕ ) = ω 1 / e ω 1 / e T F - P S ( k , ω ) d ω vs ϕ ,

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