Abstract

The interaction between the electrons and the radiation in a free-electron laser leads to a shift and a spread of the electron velocity distribution. The electron dynamics of a two-element system are studied in the small signal region. It is found that the efficiency and gain can be increased through introduction of an adjustable drift distance between two identical wigglers.

© 1980 Optical Society of America

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References

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  1. D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
    [CrossRef]
  2. L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
    [CrossRef]
  3. H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
    [CrossRef]
  4. W. B. Colson, Ph.D. Thesis, Stanford University (1977).
  5. A. Yariv, C. Shih, Opt. Commun. 24, 233 (1978).
    [CrossRef]
  6. C. Shih, A. Yariv, Tenth International Quantum Electronics Conference, Atlanta, Georgia, May 29, 1978.
  7. F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.
  8. We have considered using a magnet system in the drift space. However, it is found that the velocity dependence of the magnet is a second-order effect that is too small to affect the first-order bunching effect.
  9. D. L. Webster, J. Appl. Phys. 10, 501 (1939).
    [CrossRef]
  10. J. M. J. Madey, Nuovo Cim. 50B, 64 (1979).
    [CrossRef]
  11. If σmax is defined as the maximum allowable width of electron distribution, where the gain drops by a certain factor, it is found that σmax does not depend on parameters strongly near zeros of Δ.

1979 (1)

J. M. J. Madey, Nuovo Cim. 50B, 64 (1979).
[CrossRef]

1978 (1)

A. Yariv, C. Shih, Opt. Commun. 24, 233 (1978).
[CrossRef]

1977 (2)

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
[CrossRef]

1976 (1)

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

1939 (1)

D. L. Webster, J. Appl. Phys. 10, 501 (1939).
[CrossRef]

Al Abawi, H.

H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
[CrossRef]

Colson, W. B.

W. B. Colson, Ph.D. Thesis, Stanford University (1977).

Deacon, D. A. G.

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

Elias, L. R.

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Fairbank, W. M.

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Hopf, F. A.

H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
[CrossRef]

F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.

Madey, J. M. J.

J. M. J. Madey, Nuovo Cim. 50B, 64 (1979).
[CrossRef]

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Meystre, P.

H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
[CrossRef]

F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.

Moore, G. T.

F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.

Ramian, G. J.

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

Schwettman, H. A.

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Scully, M. O.

F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.

Shih, C.

A. Yariv, C. Shih, Opt. Commun. 24, 233 (1978).
[CrossRef]

C. Shih, A. Yariv, Tenth International Quantum Electronics Conference, Atlanta, Georgia, May 29, 1978.

Smith, T. I.

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Webster, D. L.

D. L. Webster, J. Appl. Phys. 10, 501 (1939).
[CrossRef]

Yariv, A.

A. Yariv, C. Shih, Opt. Commun. 24, 233 (1978).
[CrossRef]

C. Shih, A. Yariv, Tenth International Quantum Electronics Conference, Atlanta, Georgia, May 29, 1978.

J. Appl. Phys. (1)

D. L. Webster, J. Appl. Phys. 10, 501 (1939).
[CrossRef]

Nuovo Cim. (1)

J. M. J. Madey, Nuovo Cim. 50B, 64 (1979).
[CrossRef]

Opt. Commun. (1)

A. Yariv, C. Shih, Opt. Commun. 24, 233 (1978).
[CrossRef]

Phys. Rev. A (1)

H. Al Abawi, F. A. Hopf, P. Meystre, Phys. Rev. A 16, 666 (1977).
[CrossRef]

Phys. Rev. Lett. (2)

D. A. G. Deacon, L. R. Elias, J. M. J. Madey, G. J. Ramian, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 38, 892 (1977).
[CrossRef]

L. R. Elias, W. M. Fairbank, J. M. J. Madey, H. A. Schwettman, T. I. Smith, Phys. Rev. Lett. 36, 717 (1976).
[CrossRef]

Other (5)

W. B. Colson, Ph.D. Thesis, Stanford University (1977).

C. Shih, A. Yariv, Tenth International Quantum Electronics Conference, Atlanta, Georgia, May 29, 1978.

F. A. Hopf, P. Meystre, G. T. Moore, M. O. Scully, in Physics of Quantum Electronics, S. F. Jacobs, M. Sargent, M. O. Scully, eds. (Addison Wesley, Reading, Mass., 1978), Vol. 5.

We have considered using a magnet system in the drift space. However, it is found that the velocity dependence of the magnet is a second-order effect that is too small to affect the first-order bunching effect.

If σmax is defined as the maximum allowable width of electron distribution, where the gain drops by a certain factor, it is found that σmax does not depend on parameters strongly near zeros of Δ.

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Figures (1)

Fig. 1
Fig. 1

A two-element free-electron laser.

Tables (1)

Tables Icon

Table 1 Gain Enhancement of a Two-Element Devicea

Equations (11)

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v = v + Δ v = v + c 2 ω L { η ( 1 - cos ζ ζ sin ϕ + sin ζ ζ cos ϕ ) - η 2 [ 1 - cos ζ - ζ 2 sin ζ ζ 3 + sin ζ - ζ 2 ζ 3 sin ( 2 ϕ - ζ ) ] } ,
Δ v = Δ + 2 σ cos θ ,
Δ max = ( Δ / σ 2 ) σ max 2 .
σ = 2 c 2 η ω L ζ [ ( 1 - cos ζ ) ( 1 + cos α ) ] - 1 / 2 , Δ = - c 2 η 2 ω L [ f ( ζ ) ( 2 + L D L ) sin α + g ( ζ ) ( 1 + cos α ) ] ,
α = ω L D ( 1 c - 1 v ) + ζ , f ( ζ ) = ( 1 - cos ζ ) / ζ 2 , g ( ζ ) = ( 2 - 2 cos ζ - ζ sin ζ ) / ζ 3 .
Δ = - c 2 η 2 ω L ( 1 + L D 2 L ) and σ = c 2 η ω L
α = - δ L D λ γ 2 .
Δ L D = 2 λ γ 2 .
Δ v ϕ = 1 2 v [ Δ v 2 ϕ ] ,
Δ Δ v ϕ = σ σ v .
R = ω L 2 c 2 [ ( 2 + L e L ) tan α 2 + ( 2 ζ - cot ζ 2 ) ] .

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