Abstract

Radial electron density profiles of a toroidal belt pinch plasma have been obtained by a single measurement. Collimated ruby laser light, incident on the plasma, is focused to a diffraction-limited spot (100 μm). The technique, a variation of the dark-ground microscope, involves masking the center of the plasma diffraction pattern with a thin wire. Undiffracted light is blocked by a thin wire, whereas light diffracted by the plasma is spread beyond the wire and onto a photoplate. The resulting interference generates a high-contrast fringe pattern whose intensity varies as 1 − cosΔϕ, where Δϕ is the phase shift induced by the plasma. The fringes are recorded on Polaroid-type 46L transparency film. Using this technique, radial density profiles of the plasma produced in the Columbia Torus I belt pinch have been measured. The plasma minor cross section is elliptical with 2a ∼ 2 cm, 2b ∼ 30 cm, and 〈n(0)〉 ∼ 3 × 1016/cm3. Average densities as low as 2 × 1015/cm3 have been measured.

© 1982 Optical Society of America

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References

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  1. U. Ascoli-Bartoli, Plasma Physics (IAEA, Vienna, 1965), p. 287;Lecture Presented to the Seminar on Plasma Physics Organized by and Held at the International Center of Theoretical Physics, Trieste.
  2. F. C. Jahoda, G. A. Sawyer, in Plasma Physics, H. Griem, R. Lovberg, Eds. (Academic, New York, 1971), Vol. 9B, p. 9.
  3. R. Lovberg, IEEE Trans. Nucl. Sci. NS-11, 191 (1964).
  4. G. Dodel, W. Kunz, Appl. Opt. 14, 2537 (1975).
    [CrossRef] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 419.
  6. H. J. Shafer, Master's Thesis, Princeton U. (1948).
  7. S. F. Paul, Ph.D. Thesis, Columbia U. (1981);Plasma Physics Laboratory Report 83.
  8. H. J. Shafer, J. Soc. Motion Pic. Eng. 53, 524 (1949).
  9. P. G. Weber, Plasma Phys. 53, 550 (1980).
  10. W. J. Smith, in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Chap. 2, p. 2–30.
  11. K. Bockasten, J. Opt. Soc. Am. 51, 943 (1961).
    [CrossRef]
  12. E. Silver, W. Roney, IEEE Trans. Plasma Sci. PS-8, 231 (1980).
    [CrossRef]
  13. J. Glasser, J. Chapelle, J. C. Boettner, Appl. Opt. 17, 3750 (1978).
    [CrossRef] [PubMed]
  14. IMSL, Inc., IMSL Library, Reference Manual (1980), subroutine name—ISSCU.
  15. F. L. Sandel, K. L. Wong, Bull. Am. Phys. Soc. 21, 1152A (1976).
  16. H. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
    [CrossRef]

1980

P. G. Weber, Plasma Phys. 53, 550 (1980).

E. Silver, W. Roney, IEEE Trans. Plasma Sci. PS-8, 231 (1980).
[CrossRef]

IMSL, Inc., IMSL Library, Reference Manual (1980), subroutine name—ISSCU.

1978

1976

F. L. Sandel, K. L. Wong, Bull. Am. Phys. Soc. 21, 1152A (1976).

1975

1967

H. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

1964

R. Lovberg, IEEE Trans. Nucl. Sci. NS-11, 191 (1964).

1961

1949

H. J. Shafer, J. Soc. Motion Pic. Eng. 53, 524 (1949).

Ascoli-Bartoli, U.

U. Ascoli-Bartoli, Plasma Physics (IAEA, Vienna, 1965), p. 287;Lecture Presented to the Seminar on Plasma Physics Organized by and Held at the International Center of Theoretical Physics, Trieste.

Bockasten, K.

Boettner, J. C.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 419.

Chapelle, J.

Dodel, G.

Glasser, J.

Jahoda, F. C.

F. C. Jahoda, G. A. Sawyer, in Plasma Physics, H. Griem, R. Lovberg, Eds. (Academic, New York, 1971), Vol. 9B, p. 9.

Kunz, W.

Lovberg, R.

R. Lovberg, IEEE Trans. Nucl. Sci. NS-11, 191 (1964).

Paul, S. F.

S. F. Paul, Ph.D. Thesis, Columbia U. (1981);Plasma Physics Laboratory Report 83.

Presby, H.

H. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

Roney, W.

E. Silver, W. Roney, IEEE Trans. Plasma Sci. PS-8, 231 (1980).
[CrossRef]

Sandel, F. L.

F. L. Sandel, K. L. Wong, Bull. Am. Phys. Soc. 21, 1152A (1976).

Sawyer, G. A.

F. C. Jahoda, G. A. Sawyer, in Plasma Physics, H. Griem, R. Lovberg, Eds. (Academic, New York, 1971), Vol. 9B, p. 9.

Shafer, H. J.

H. J. Shafer, J. Soc. Motion Pic. Eng. 53, 524 (1949).

H. J. Shafer, Master's Thesis, Princeton U. (1948).

Silver, E.

E. Silver, W. Roney, IEEE Trans. Plasma Sci. PS-8, 231 (1980).
[CrossRef]

Smith, W. J.

W. J. Smith, in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Chap. 2, p. 2–30.

Weber, P. G.

P. G. Weber, Plasma Phys. 53, 550 (1980).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 419.

Wong, K. L.

F. L. Sandel, K. L. Wong, Bull. Am. Phys. Soc. 21, 1152A (1976).

Appl. Opt.

Bull. Am. Phys. Soc.

F. L. Sandel, K. L. Wong, Bull. Am. Phys. Soc. 21, 1152A (1976).

IEEE Trans. Nucl. Sci.

R. Lovberg, IEEE Trans. Nucl. Sci. NS-11, 191 (1964).

IEEE Trans. Plasma Sci.

E. Silver, W. Roney, IEEE Trans. Plasma Sci. PS-8, 231 (1980).
[CrossRef]

IMSL Library, Reference Manual

IMSL, Inc., IMSL Library, Reference Manual (1980), subroutine name—ISSCU.

J. Opt. Soc. Am.

J. Soc. Motion Pic. Eng.

H. J. Shafer, J. Soc. Motion Pic. Eng. 53, 524 (1949).

Plasma Phys.

P. G. Weber, Plasma Phys. 53, 550 (1980).

Rev. Sci. Instrum.

H. Presby, Rev. Sci. Instrum. 38, 1563 (1967).
[CrossRef]

Other

W. J. Smith, in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Chap. 2, p. 2–30.

U. Ascoli-Bartoli, Plasma Physics (IAEA, Vienna, 1965), p. 287;Lecture Presented to the Seminar on Plasma Physics Organized by and Held at the International Center of Theoretical Physics, Trieste.

F. C. Jahoda, G. A. Sawyer, in Plasma Physics, H. Griem, R. Lovberg, Eds. (Academic, New York, 1971), Vol. 9B, p. 9.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965), p. 419.

H. J. Shafer, Master's Thesis, Princeton U. (1948).

S. F. Paul, Ph.D. Thesis, Columbia U. (1981);Plasma Physics Laboratory Report 83.

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Figures (11)

Fig. 1
Fig. 1

Image formation as double diffraction process. Higher orders are represented by S+ and S and the central order by S0. The darker ray indicates that most of the energy is carried in the central order.

Fig. 2
Fig. 2

Schematic of Torus I showing the vacuum chamber, plasma dimensions, and optical access.

Fig. 3
Fig. 3

Scale diagram showing the optical apparatus and its position with respect to the torus.

Fig. 4
Fig. 4

Reproductions of transparency representing a radial slice of the vacuum chamber. The center of the racetrack corresponds to the toroidal axis. The actual length of the slit is 10 cm. The outer radius is on the right-hand side, and the inner radius is on the left.

Fig. 5
Fig. 5

Digitized transmission readings of Fig. 4. The plasma region is magnified. The radial position is measured in centimeters from the toroidal axis.

Fig. 6
Fig. 6

Phase shift is plotted in the solid line as a function of distance (normalized to the plasma width) from the center of the plasma profile. The smoothed spline approximation to the phase shift is shown by the dashed line.

Fig. 7
Fig. 7

Refractive index, plotted as a function of distance (normalized to the plasma width) from the center of the plasma, is represented by the solid line and is read on the right ordinate. The plasma density is represented by the dashed line and is read on the left ordinate in units of 1017 cm−3.

Fig. 8
Fig. 8

Evolution of electron density profile. The density (scale peaks at 1.6 × 1017/cm3) is read vs distance in centimeters from the toroidal axis. The negative direction refers to the outside wall. Figures represent plasma density at the midplane of the Torus.

Fig. 9
Fig. 9

Plasma at the instant of implosion.

Fig. 10
Fig. 10

Schlieren photograph of the plasma.

Fig. 11
Fig. 11

Most applicable optical density diagnostic is placed in parameter space whose components are phase shift and relative size. Δϕ is read on the horizontal axis, and a/A is read on the vertical axis.

Equations (13)

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U ( ξ ) = C 1 F dxf ( x ) exp ( ikx ξ / f ) ,
V ( x ) = C 2 F d ξ U ( ξ ) exp ( ik x ξ / D ) .
V ( x ) = C F F dxd ξ f ( x ) exp [ ik ( x / D + x / f ) ξ ] ,
Δ ϕ = 2 π / λ L ( μ 1 ) dl ,
μ = 1 ½ ω p e 2 / ω 2 ,
ω pe = ( 4 π n e e 2 / m e ) 1 / 2 = 5.6 × 10 4 n e sec 1 ,
V ( x ) = + ξ 1 dxd ξ f ( x ) exp [ ik ( x + x ) ξ / f ] + + ξ 1 dxd ξ f ( x ) exp [ ik ( x + x ) ξ / f ] ,
+ ξ 1 + ξ 1 dxd ξ f ( x ) exp [ ik ( x + x ) ξ / f ] ,
V ( x ) = + + dxd ξ f ( x ) exp [ ik ( x + x ) ξ / f ] + ξ 1 + ξ 1 dxd ξ f ( x ) exp [ ik ( x + x ) ξ / f ] .
V ( x ) = π f ( x ) + dtf ( t + x ) sin ( k ξ 1 t / f ) t .
V ( x ) = 2 π f / k × [ f ( x ) 1 ] .
I ( x ) = | V ( x ) | 2 | exp [ i Δ ϕ ( x ) ] 1 | 2 = 2 { 1 cos [ Δ ϕ ( x ) ] } .
μ ( r ) 1 = λ / 2 π ( 1 / π ) r R Δ ϕ ( x ) dx x 2 r 2 ,

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