Abstract

The application of an optical method for density measurements in cylindrical plasmas is described. The angular deviation of a probing light beam sent through a plasma is proportional to the maximum of the density in the plasma column. The deviation does not depend on the plasma dimensions; however, it is influenced to a certain degree by the density profile. The method is successfully applied to the investigation of a dense plasma focus with a time resolution of 2 nsec and a spatial resolution (in axial direction) of 2 mm.

© 1978 Optical Society of America

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References

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  1. F. Keilmann, Plasma Phys. 14, 111 (1972).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).
  3. H. Salzmann, “On the Use of Schlieren Optics for Rotationally Symmetric High Density Gradient Plasmas,” Report LGI 68/25, Laboratori Gas Ionizzati, Frascati, Roma (1968).
  4. H. Wolter, “Schlieren-, Phasenkontrast- und Lichtschnittver-fahren,” in Handbuch der Physik, S. Flügge, Ed. (1956), Vol. 24.
    [CrossRef]
  5. H. Schmidt, B. Nahrath, B. Rückle, “Time and Space Resolved Measurements of Density and X-ray Emission of the NESSI Plasma Focus,”in Proceedings of Seventh European Conference on Controlled Fusion and Plasma Physics, Lausanne, September 1975, Vol. 1 (Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérate de Lausanne, Switzerland, 1975), p. 57.
  6. B. Rückle, “Elektronendichtemessungen am Plasmafokus,”Internal Report IPF 76-1, Institut für Plasmaforschung, Stuttgart (1976).
  7. G. Decker et al., “Dynamics of 120 and 20 kV Plasma Focus Devices with Respect to Density and Current Distribution, Neutron and X-ray Emission,”IAEA-CN-35/E18-1 (b)Berchtesgaden, October1976;Plasma Physics and Controlled Nuclear Fusion Research, Vol. 3 (IAEA, Vienna, 1977), p. 441.
  8. H. Schmidt, Plasma Phys., to be published.

1972

F. Keilmann, Plasma Phys. 14, 111 (1972).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Decker, G.

G. Decker et al., “Dynamics of 120 and 20 kV Plasma Focus Devices with Respect to Density and Current Distribution, Neutron and X-ray Emission,”IAEA-CN-35/E18-1 (b)Berchtesgaden, October1976;Plasma Physics and Controlled Nuclear Fusion Research, Vol. 3 (IAEA, Vienna, 1977), p. 441.

Keilmann, F.

F. Keilmann, Plasma Phys. 14, 111 (1972).
[CrossRef]

Nahrath, B.

H. Schmidt, B. Nahrath, B. Rückle, “Time and Space Resolved Measurements of Density and X-ray Emission of the NESSI Plasma Focus,”in Proceedings of Seventh European Conference on Controlled Fusion and Plasma Physics, Lausanne, September 1975, Vol. 1 (Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérate de Lausanne, Switzerland, 1975), p. 57.

Rückle, B.

H. Schmidt, B. Nahrath, B. Rückle, “Time and Space Resolved Measurements of Density and X-ray Emission of the NESSI Plasma Focus,”in Proceedings of Seventh European Conference on Controlled Fusion and Plasma Physics, Lausanne, September 1975, Vol. 1 (Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérate de Lausanne, Switzerland, 1975), p. 57.

B. Rückle, “Elektronendichtemessungen am Plasmafokus,”Internal Report IPF 76-1, Institut für Plasmaforschung, Stuttgart (1976).

Salzmann, H.

H. Salzmann, “On the Use of Schlieren Optics for Rotationally Symmetric High Density Gradient Plasmas,” Report LGI 68/25, Laboratori Gas Ionizzati, Frascati, Roma (1968).

Schmidt, H.

H. Schmidt, B. Nahrath, B. Rückle, “Time and Space Resolved Measurements of Density and X-ray Emission of the NESSI Plasma Focus,”in Proceedings of Seventh European Conference on Controlled Fusion and Plasma Physics, Lausanne, September 1975, Vol. 1 (Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérate de Lausanne, Switzerland, 1975), p. 57.

H. Schmidt, Plasma Phys., to be published.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Wolter, H.

H. Wolter, “Schlieren-, Phasenkontrast- und Lichtschnittver-fahren,” in Handbuch der Physik, S. Flügge, Ed. (1956), Vol. 24.
[CrossRef]

Plasma Phys.

F. Keilmann, Plasma Phys. 14, 111 (1972).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

H. Salzmann, “On the Use of Schlieren Optics for Rotationally Symmetric High Density Gradient Plasmas,” Report LGI 68/25, Laboratori Gas Ionizzati, Frascati, Roma (1968).

H. Wolter, “Schlieren-, Phasenkontrast- und Lichtschnittver-fahren,” in Handbuch der Physik, S. Flügge, Ed. (1956), Vol. 24.
[CrossRef]

H. Schmidt, B. Nahrath, B. Rückle, “Time and Space Resolved Measurements of Density and X-ray Emission of the NESSI Plasma Focus,”in Proceedings of Seventh European Conference on Controlled Fusion and Plasma Physics, Lausanne, September 1975, Vol. 1 (Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Fédérate de Lausanne, Switzerland, 1975), p. 57.

B. Rückle, “Elektronendichtemessungen am Plasmafokus,”Internal Report IPF 76-1, Institut für Plasmaforschung, Stuttgart (1976).

G. Decker et al., “Dynamics of 120 and 20 kV Plasma Focus Devices with Respect to Density and Current Distribution, Neutron and X-ray Emission,”IAEA-CN-35/E18-1 (b)Berchtesgaden, October1976;Plasma Physics and Controlled Nuclear Fusion Research, Vol. 3 (IAEA, Vienna, 1977), p. 441.

H. Schmidt, Plasma Phys., to be published.

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Figures (7)

Fig. 1
Fig. 1

Beam deviation in a plasma of rotational symmetry.

Fig. 2
Fig. 2

Density profiles as described in Table I.

Fig. 3
Fig. 3

Deviation angle profiles for the density profiles of Fig. 2.

Fig. 4
Fig. 4

Deviation angle and spatial distance of interfering rays.

Fig. 5
Fig. 5

Experimental setup for beam deviation measurements at four axial positions in the plasma focus.

Fig. 6
Fig. 6

Streak photograph of the beam deviations at four axial positions during a single discharge of the plasma focus. A N2 laser is used as a time mark.

Fig. 7
Fig. 7

Evaluation of Fig. 6. Temporal development of maximum electron density at four axial positions during a single plasma focus discharge. Dashed line corresponds to interruptions in the beams indicating the occurrence of instabilities.

Tables (2)

Tables Icon

Table I Influence of the Density Profile on the Maximum Deviation Angle

Tables Icon

Table II Comparison of Relevant Data for Plasma Focus and Carbon Arc

Equations (18)

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| n x | < < n λ ,
dr d ψ = r p [ n 2 ( r ) r 2 p 2 ] 1 / 2 ,
n = ( 1 N e N c ) 1 / 2 ,
α ( p R ) = N ̂ e N c 0 [ ( r 0 / R ) 2 ( p / R ) 2 ] 1 / 2 f ( p R , y R ) ( p R ) d ( y R ) ,
α max = C 1 N ̂ e N c ,
φ ( p R ) = 2 π λ 0 N ̂ e N c R [ ( r 0 / R ) 2 ( p / R ) 2 ] 1 / 2 0 f ( p R , y R ) d ( y R ) .
φ max = C 2 2 π λ 0 N ̂ e N c R ,
C 2 = max [ [ ( r 0 / R ) 2 ( p / R ) 2 ] 1 / 2 0 f ( p R , y R ) d ( y R ) ] .
Q = φ max 2 π = C 2 C 1 α max λ 0 R ,
Δ β = α max Q 1 .
λ 0 Δ u < α max Q 1 .
λ 0 R Q 1 Q l < α max Q 1 .
λ 0 < C 3 N ̂ e R N c ,
N c = 4 π 2 c 2 0 m e e 2 1 λ 0 2 , λ 0 > 4 π 2 c 2 0 m e e 2 C 3 1 N ̂ e R ,
Ω < Δ β 2 ,
Ω < C 1 2 C 2 Q Q 1 λ 0 R .
N ̂ e ( cm 3 )
Δ β = α max Q 1 ( mrad )

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