Abstract

We report the development and initial implementation of what we believe to be a new rapid- spatial-scan millimeter-wave interferometer for plasma density measurements. The fast scan is effected by electronic frequency sweeping of a wideband (180280  GHz) backward-wave oscillator whose output is focused onto a fixed blazed diffraction grating. The system, which augments the rotating-grating scanned multiview H-1 heliac interferometer, can sweep the plasma cross section in a period of less than 1 ms with a beam diameter in the plasma of 20  mm and phase noise of the order of 0.01  rad.

© 2006 Optical Society of America

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References

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  1. A. J. H. Donné, "High spatial resolution interferometry and polarimetry in hot plasmas," Rev. Sci. Instrum. 66, 3407-3423 (1995).
    [Crossref]
  2. H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
    [Crossref]
  3. K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
    [Crossref]
  4. Y. Jiang and D. Brower, "Horizontal-view interferometer on TEXT-Upgrade," Rev. Sci. Instrum. 66, 852-854 (1995).
    [Crossref]
  5. J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
    [Crossref]
  6. J. Howard, "Novel scanning interferometer for two-dimensional plasma density measurements," Rev. Sci. Instrum. 61, 1086-1094 (1990).
    [Crossref]
  7. G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
    [Crossref]
  8. ELVA-1, 46 Robezu, LV-1004, Riga, Latvia.
  9. I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge U. Press, 1987).
  10. G. Warr and J. Howard, "A three-dimensional Gaussian-beam ray-tracing program for designing interferometer/polarimeter plasma diagnostics," Rev. Sci. Instrum. 72, 2305-2309 (2001).
    [Crossref]
  11. L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
    [Crossref]
  12. D. Véron, "Submillimeter interferometry of high density plasmas," in Infrared and Millimeter Waves, K.Button, ed. (Academic, 1979), Vol. 2, pp. 69-135.

2001 (1)

G. Warr and J. Howard, "A three-dimensional Gaussian-beam ray-tracing program for designing interferometer/polarimeter plasma diagnostics," Rev. Sci. Instrum. 72, 2305-2309 (2001).
[Crossref]

1999 (2)

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
[Crossref]

1997 (3)

H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
[Crossref]

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

1995 (2)

A. J. H. Donné, "High spatial resolution interferometry and polarimetry in hot plasmas," Rev. Sci. Instrum. 66, 3407-3423 (1995).
[Crossref]

Y. Jiang and D. Brower, "Horizontal-view interferometer on TEXT-Upgrade," Rev. Sci. Instrum. 66, 852-854 (1995).
[Crossref]

1990 (1)

J. Howard, "Novel scanning interferometer for two-dimensional plasma density measurements," Rev. Sci. Instrum. 61, 1086-1094 (1990).
[Crossref]

Blackwell, B. D.

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

Brower, D.

Y. Jiang and D. Brower, "Horizontal-view interferometer on TEXT-Upgrade," Rev. Sci. Instrum. 66, 852-854 (1995).
[Crossref]

Donné, A. J. H.

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

A. J. H. Donné, "High spatial resolution interferometry and polarimetry in hot plasmas," Rev. Sci. Instrum. 66, 3407-3423 (1995).
[Crossref]

Geist, T.

H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
[Crossref]

Hartfuss, H. J.

H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
[Crossref]

Hirsch, M.

H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
[Crossref]

Howard, J.

G. Warr and J. Howard, "A three-dimensional Gaussian-beam ray-tracing program for designing interferometer/polarimeter plasma diagnostics," Rev. Sci. Instrum. 72, 2305-2309 (2001).
[Crossref]

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

J. Howard, "Novel scanning interferometer for two-dimensional plasma density measurements," Rev. Sci. Instrum. 61, 1086-1094 (1990).
[Crossref]

Hutchinson, I. H.

I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge U. Press, 1987).

Ito, Y.

K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
[Crossref]

Jiang, Y.

Y. Jiang and D. Brower, "Horizontal-view interferometer on TEXT-Upgrade," Rev. Sci. Instrum. 66, 852-854 (1995).
[Crossref]

Karelse, F. A.

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

Kawahata, K.

K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
[Crossref]

Nguyen, X.

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

Peebles, W. A.

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

Porte, L.

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

Rettig, C. L.

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

Rommers, J. H.

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

Tanaka, K.

K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
[Crossref]

Véron, D.

D. Véron, "Submillimeter interferometry of high density plasmas," in Infrared and Millimeter Waves, K.Button, ed. (Academic, 1979), Vol. 2, pp. 69-135.

Wach, J.

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

Warr, G.

G. Warr and J. Howard, "A three-dimensional Gaussian-beam ray-tracing program for designing interferometer/polarimeter plasma diagnostics," Rev. Sci. Instrum. 72, 2305-2309 (2001).
[Crossref]

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

Fusion Eng. Des. (1)

G. Warr, B. D. Blackwell, J. Wach, and J. Howard, "First results from the three view far-infrared interferometer for the H-1 heliac," Fusion Eng. Des. 34-35, 387-391 (1997).
[Crossref]

Plasma Phys. Controlled Fusion (1)

H. J. Hartfuss, T. Geist, and M. Hirsch, "Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry," Plasma Phys. Controlled Fusion 39, 1693-1769 (1997).
[Crossref]

Rev. Sci. Instrum. (7)

K. Kawahata, K. Tanaka, and Y. Ito, "Far infrared laser interfereometer system on the large helical device," Rev. Sci. Instrum. 70, 707-709 (1999).
[Crossref]

Y. Jiang and D. Brower, "Horizontal-view interferometer on TEXT-Upgrade," Rev. Sci. Instrum. 66, 852-854 (1995).
[Crossref]

J. H. Rommers, A. J. H. Donné, F. A. Karelse, and J. Howard, "The multichannel triple-laser interferometer/polarimeter system at RTP," Rev. Sci. Instrum. 68, 1217-1226 (1997).
[Crossref]

J. Howard, "Novel scanning interferometer for two-dimensional plasma density measurements," Rev. Sci. Instrum. 61, 1086-1094 (1990).
[Crossref]

G. Warr and J. Howard, "A three-dimensional Gaussian-beam ray-tracing program for designing interferometer/polarimeter plasma diagnostics," Rev. Sci. Instrum. 72, 2305-2309 (2001).
[Crossref]

L. Porte, C. L. Rettig, W. A. Peebles, and X. Nguyen, "Design and operation of a low cost, reliable millimeter-wave interferometer," Rev. Sci. Instrum. 70, 1082-1084 (1999).
[Crossref]

A. J. H. Donné, "High spatial resolution interferometry and polarimetry in hot plasmas," Rev. Sci. Instrum. 66, 3407-3423 (1995).
[Crossref]

Other (3)

D. Véron, "Submillimeter interferometry of high density plasmas," in Infrared and Millimeter Waves, K.Button, ed. (Academic, 1979), Vol. 2, pp. 69-135.

ELVA-1, 46 Robezu, LV-1004, Riga, Latvia.

I. H. Hutchinson, Principles of Plasma Diagnostics (Cambridge U. Press, 1987).

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Figures (8)

Fig. 1
Fig. 1

(Color online) A 3D Gaussian beam ray trace model of the H-1 scanning interferometer optical system. Laser radiation incident on the rotating grating is sequentially diffracted through a fan of angles. The beam is collected by monolithic optics mounted on a vertical table, directed into the plasma, and returned back along the incident path to processing optics mounted on a horizontal optical table. The grating is illuminated at three positions to allow plasma probing in three directions, two diagonal and one horizontal. The radiation enters the vacuum tank (not shown) via the indicated vacuum port windows.

Fig. 2
Fig. 2

(Color online) Raw interferometer projection data for a discharge exhibiting a large scale global instability. Each image shows the temporal evolution (horizontal axis) of the phase shift (radians) for the two diagonal sweeps of the plasma (vertically juxtaposed in the figure).

Fig. 3
Fig. 3

(Color online) Schematic of the benchtop interferometer. Test phase objects are placed in the region indicated by the plasma outline. When the wavelength is electronically tuned, the diffraction grating generates a spatial sweep across the plasma region. The optics are arranged so that longer wavelengths probe the plasma edge regions.

Fig. 4
Fig. 4

(Color online) (a) Interferogram for the full 220 270   GHz sweep using a 100 Hz linear ramp. (b) Detail of the interferogram during the first 2 ms. Note the varying IF frequency and noisy amplitude due to multipath effects. (c) Power spectrum of the signal in (a). In this instance, approximately 400 waves∕sweep give an IF signal peaked near 40 kHz.

Fig. 5
Fig. 5

(Color online) (a) Interferogram shown in Fig. 4(a) following amplitude normalization and phase regularization as described in the text. (b) Power spectrum of (a). (c) Note the narrowing power spectrum of the signal in (a). In this instance, approximately 400 waves∕sweep give an IF signal peaked near 40 kHz.

Fig. 6
Fig. 6

(Color online) (a) Superimposed phase images of a Mylar strip of width 30 mm translated across the ELSI field of view. (b) Phase images of Mylar strips of widths 5, 10, 20, and 40   mm . The convolution of a Gaussian and a rectangular function (superimposed) compares satisfactorily with the measurements and indicates a spatial resolution of 20   mm .

Fig. 7
Fig. 7

(Color online) Two representations of demodulated interferometric phase data for a typical 0.5 T minority-heated hydrogen discharge in the standard-magnetic-configuration H-1 heliac. (a) Demodulated line average density presented as a raw time series. The multiple stripes correspond to successive sweeps of the BWO beam across the plasma. In (b) the data have been arranged into an array format indexed according to sweep start time and beam position in the plasma.

Fig. 8
Fig. 8

Line average plasma density evolution displayed in a single plot as a superposition of successive sweeps. The time between sweeps is 2   ms .

Equations (10)

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S ( t ) = I ( t ) [ 1 + ζ ( t ) cos ϕ ( t ) ] ,
φ = 2 π ν c 0 L μ ( ν , t ) d l ,
μ = ( 1 ν pe 2 ν 2 ) 1 / 2 ,
ν pe = ( n e e 2 4 π 2 m e ϵ 0 ) 1 / 2
φ P ( t ) = r e λ 0 L p n e d l ,
sin   α + sin   β = m λ d .
f 1 F = 1 2 π d ϕ d t = τ d ν d τ = τ d ν d V d V d t .
N = Δ ν Δ L c ,
R = m π cos   β ¯ w 0 d Δ f f .
α max = sin - 1 ( n 0 / n c ) 9 × 10 16 n 0 λ 2 ,

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