Abstract

Using two different empirical density profiles for the end region of a theta-pinch plasma, one with a maximum density on the axis (radiation-dispersing profile) the other with a pronounced axial minimum (radiation-trapping profile), the trajectory of the CO2 laser beam (10.6 μm) focused axially on such a plasma was studied numerically. This calculation is used to evaluate the optical influence of the plasma, since the maximum power density in the focal plane can be reduced by several orders of magnitude owing to the presence of the plasma. This influence can be substantial even for very subcritical electron densities (ne ≪ 1019 cm−3). In cases of large dispersion, the characteristics of a multifocal lens capable of producing perfect focusing are found, and it is shown that the solution is not unique. The radial distribution of the laser beam power density is also calculated and shows numerous irregularities and discontinuities due to the nonuniform beam dispersion.

© 1977 Optical Society of America

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References

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  1. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Permagon, Oxford, 1964).
  2. J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964).
  3. T. H. Stix, Theory of Plasma Waves (McGraw-Hill, New York, 1962).
  4. P. D. Rockett, in IEEE 2nd International Conference Plasma Science, Ann Arbor, Mich. (1975).
  5. L. C. Steinhauer, H. G. Ahlstrom, Phys. Fluids 14, 1109 (1971).
    [CrossRef]
  6. R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
    [CrossRef]
  7. A. L. Hoffman, Appl. Phys. Lett. 23, 693 (1973).
    [CrossRef]
  8. G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
    [CrossRef]
  9. R. A. Hess, H. R. Griem, Phys. Fluids 18, 1056 (1975).
    [CrossRef]
  10. D. V. Giovanielli, R. P. Godwin, Am. J. Phys. 43, 808 (1975).
    [CrossRef]
  11. S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
    [CrossRef]

1975 (3)

R. A. Hess, H. R. Griem, Phys. Fluids 18, 1056 (1975).
[CrossRef]

D. V. Giovanielli, R. P. Godwin, Am. J. Phys. 43, 808 (1975).
[CrossRef]

S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
[CrossRef]

1974 (2)

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

1973 (1)

A. L. Hoffman, Appl. Phys. Lett. 23, 693 (1973).
[CrossRef]

1971 (1)

L. C. Steinhauer, H. G. Ahlstrom, Phys. Fluids 14, 1109 (1971).
[CrossRef]

Ahlstrom, H. G.

L. C. Steinhauer, H. G. Ahlstrom, Phys. Fluids 14, 1109 (1971).
[CrossRef]

Bengtson, R. D.

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

Decoste, R.

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

Engelhart, A. G.

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

Eninger, J. E.

S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
[CrossRef]

Fuchs, V.

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Permagon, Oxford, 1964).

Giovanielli, D. V.

D. V. Giovanielli, R. P. Godwin, Am. J. Phys. 43, 808 (1975).
[CrossRef]

Godwin, R. P.

D. V. Giovanielli, R. P. Godwin, Am. J. Phys. 43, 808 (1975).
[CrossRef]

Griem, H. R.

R. A. Hess, H. R. Griem, Phys. Fluids 18, 1056 (1975).
[CrossRef]

Hagler, M. O.

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

Hess, R. A.

R. A. Hess, H. R. Griem, Phys. Fluids 18, 1056 (1975).
[CrossRef]

Hoffman, A. L.

A. L. Hoffman, Appl. Phys. Lett. 23, 693 (1973).
[CrossRef]

Kelso, J. M.

J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964).

Kristiansen, J.

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

Mani, S. A.

S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
[CrossRef]

Molen, G. M.

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

Neufeld, C. R.

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

Rockett, P. D.

P. D. Rockett, in IEEE 2nd International Conference Plasma Science, Ann Arbor, Mich. (1975).

Steinhauer, L. C.

L. C. Steinhauer, H. G. Ahlstrom, Phys. Fluids 14, 1109 (1971).
[CrossRef]

Stix, T. H.

T. H. Stix, Theory of Plasma Waves (McGraw-Hill, New York, 1962).

Wallace, J.

S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
[CrossRef]

Am. J. Phys. (1)

D. V. Giovanielli, R. P. Godwin, Am. J. Phys. 43, 808 (1975).
[CrossRef]

Appl. Phys. Lett. (2)

A. L. Hoffman, Appl. Phys. Lett. 23, 693 (1973).
[CrossRef]

G. M. Molen, J. Kristiansen, M. O. Hagler, R. D. Bengtson, Appl. Phys. Lett. 24, 583 (1974).
[CrossRef]

J. Appl. Phys. (1)

R. Decoste, A. G. Engelhart, V. Fuchs, C. R. Neufeld, J. Appl. Phys. 45, 1127 (1974).
[CrossRef]

Nucl. Fusion (1)

S. A. Mani, J. E. Eninger, J. Wallace, Nucl. Fusion 15, 371 (1975).
[CrossRef]

Phys. Fluids (2)

L. C. Steinhauer, H. G. Ahlstrom, Phys. Fluids 14, 1109 (1971).
[CrossRef]

R. A. Hess, H. R. Griem, Phys. Fluids 18, 1056 (1975).
[CrossRef]

Other (4)

V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Permagon, Oxford, 1964).

J. M. Kelso, Radio Ray Propagation in the Ionosphere (McGraw-Hill, New York, 1964).

T. H. Stix, Theory of Plasma Waves (McGraw-Hill, New York, 1962).

P. D. Rockett, in IEEE 2nd International Conference Plasma Science, Ann Arbor, Mich. (1975).

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Figures (7)

Fig. 1
Fig. 1

Empirical description of the plasma electron density profile in cylindrical geometry.

Fig. 2
Fig. 2

Radiation-dispersing plasma profile (incoming beam): (a) constant electron density lines in the plasma (from 0.9 to 0.1 times 3 × 1017 cm−3) and half of the incoming laser beam trajectory; (b) distribution of the beam rays in the plasma (curve ○), ponderation factor for each ray (curve +), and radial power density distribution of the laser radiation (curve ×).

Fig. 3
Fig. 3

Radiation-dispersing plasma profile (outcoming beam): (a) constant electron density lines in the plasma (from 0.9 to 0.1 times 3 × 1017 cm−3) and half the outgoing point source beam trajectory; (b) distribution of the beam rays in the plasma (curve ○), ponderation factor for each ray (curve +), and radial radiation power density distribution (curve ×).

Fig. 4
Fig. 4

Radiation-trapping plasma profile (incoming beam): (a) constant electron density lines in the plasma (from 0.9 to 0.1 times 3 × 1017 cm−3) and half of the incoming laser beam trajectory; (b) distribution of the beam rays in the plasma (curve ○), ponderation factor for each ray (curve +), and radial radiation power density distribution (curve ×).

Fig. 5
Fig. 5

Radiation-trapping plasma profile (outgoing beam): (a) constant electron density lines in the plasma (from 0.9 to 0.1 times 3 × 1017 cm−3) and half of the outgoing point source beam trajectory; (b) distribution of the beam rays in the plasma (curve ○), ponderation factor for each ray (curve +), and radial radiation power density distribution (curve ×).

Fig. 6
Fig. 6

Radiation-dispersing plasma profile. Multifocal lens characteristics for z = 5L.

Fig. 7
Fig. 7

Radiation-trapping plasma profile. Multifocal lens characteristics for z = 5L.

Tables (1)

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Table I Chosen Values for the Emperical Parameters Describing the Theta-Pinch Plasma of Decostea

Equations (10)

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d θ = [ dl × n ( r , z ) ] · K n ( r , z ) .
n ( r , z ) = [ 1 - ( 80.5 ) 10 6 f L 2 n e ( r , z ) ] 1 / 2 cgs .
[ n e ( r , z ) ] / ( n e o ) = Q ( z ) R [ r , a o , d ( z ) ] ,
Q ( z ) = 1 + exp [ ( - L ) / P ] 1 + exp [ z - L ) / P ] ,
R [ r , a o , d ( z ) ] = exp - [ r - d ( z ) a o ] 2 + exp - [ r + d ( z ) a o ] 2 2 R n ,
d ( z ) = d o - 2 g a o [ ½ - Q ( z ) ] exp ( L / P ) ,
D o = 2 ( a o + d o ) .
d ( L ) ~ d o + a o g .
θ i = tan - 1 [ ( r i ) / f ] .
f ( r ) = r / [ tan θ ( r ) ] .

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