Abstract

Many applications of flashtubes require a detailed knowledge of the current pulse profile in time. We have extended the standard theory of Markiewicz and Emmett to include the effects of the flashtube self-inductance and time derivatives of the flashtube self-inductance. These effects are important at early times when the discharge is spatially confined. Calculations show that these effects yield corrections to the flashtube and pulse-forming network model equations which are proportional to the square of the length of the flashtube and inversely proportional to the discharge radius. Growth of the flashtube discharge is treated with a model based on the total energy input to the flashtube. Considerably improved correspondence between the theory and experimental pulse profiles is obtained, particularly for large flashtubes and short times within the pulse.

© 1983 Optical Society of America

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References

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  1. J. P. Markiewicz, J. L. Emmett, IEEE J. Quantum Electron. QE-2, 707 (1966).
    [CrossRef]
  2. J. H. Goncz, J. Appl. Phys. 36, 742 (1965).
    [CrossRef]
  3. J. F. Holzrichter, J. L. Emmett, Appl. Opt. 8, 1459 (1969).
    [CrossRef] [PubMed]
  4. D. C. Brown, T-S. N. Nee, IEEE Trans. Electron. Dev. ED-24, 1285 (1977).
    [CrossRef]
  5. R. H. Dishington, W. R. Hook, R. P. Hilberg, Appl. Opt. 13, 2300 (1974).
    [CrossRef] [PubMed]
  6. J. T. Lue, D. Y. Song, J. Appl. Phys. 51, 4626 (1980).
    [CrossRef]
  7. B. P. Newell, “Spectral Radiance and Efficiency of Pulsed Xenon Short Arcs,” EG&G Tech. Rep. B-4370 (1972).

1980 (1)

J. T. Lue, D. Y. Song, J. Appl. Phys. 51, 4626 (1980).
[CrossRef]

1977 (1)

D. C. Brown, T-S. N. Nee, IEEE Trans. Electron. Dev. ED-24, 1285 (1977).
[CrossRef]

1974 (1)

1969 (1)

1966 (1)

J. P. Markiewicz, J. L. Emmett, IEEE J. Quantum Electron. QE-2, 707 (1966).
[CrossRef]

1965 (1)

J. H. Goncz, J. Appl. Phys. 36, 742 (1965).
[CrossRef]

Brown, D. C.

D. C. Brown, T-S. N. Nee, IEEE Trans. Electron. Dev. ED-24, 1285 (1977).
[CrossRef]

Dishington, R. H.

Emmett, J. L.

J. F. Holzrichter, J. L. Emmett, Appl. Opt. 8, 1459 (1969).
[CrossRef] [PubMed]

J. P. Markiewicz, J. L. Emmett, IEEE J. Quantum Electron. QE-2, 707 (1966).
[CrossRef]

Goncz, J. H.

J. H. Goncz, J. Appl. Phys. 36, 742 (1965).
[CrossRef]

Hilberg, R. P.

Holzrichter, J. F.

Hook, W. R.

Lue, J. T.

J. T. Lue, D. Y. Song, J. Appl. Phys. 51, 4626 (1980).
[CrossRef]

Markiewicz, J. P.

J. P. Markiewicz, J. L. Emmett, IEEE J. Quantum Electron. QE-2, 707 (1966).
[CrossRef]

Nee, T-S. N.

D. C. Brown, T-S. N. Nee, IEEE Trans. Electron. Dev. ED-24, 1285 (1977).
[CrossRef]

Newell, B. P.

B. P. Newell, “Spectral Radiance and Efficiency of Pulsed Xenon Short Arcs,” EG&G Tech. Rep. B-4370 (1972).

Song, D. Y.

J. T. Lue, D. Y. Song, J. Appl. Phys. 51, 4626 (1980).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

J. P. Markiewicz, J. L. Emmett, IEEE J. Quantum Electron. QE-2, 707 (1966).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

D. C. Brown, T-S. N. Nee, IEEE Trans. Electron. Dev. ED-24, 1285 (1977).
[CrossRef]

J. Appl. Phys. (2)

J. H. Goncz, J. Appl. Phys. 36, 742 (1965).
[CrossRef]

J. T. Lue, D. Y. Song, J. Appl. Phys. 51, 4626 (1980).
[CrossRef]

Other (1)

B. P. Newell, “Spectral Radiance and Efficiency of Pulsed Xenon Short Arcs,” EG&G Tech. Rep. B-4370 (1972).

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Figures (8)

Fig. 1
Fig. 1

Flashtube current as a function of time for Case 1 (see Tables I and II). The experimental data are indicated by a solid curve, the extended ME theory wiith self-inductance effects included is indicated by a dashed curve, and the results of ME theory without self-inductance effects are given by the dot–dash curve.

Fig. 2
Fig. 2

Case 2 (see Fig. 1 caption for explanation).

Fig. 3
Fig. 3

Case 3 (see Fig. 1 caption for explanation).

Fig. 4
Fig. 4

Case 4 (see Fig. 1 caption for explanation).

Fig. 5
Fig. 5

Case 5 (see Fig. 1 caption for explanation).

Fig. 6
Fig. 6

Case 6 (see Fig. 1 caption for explanation).

Fig. 7
Fig. 7

Case 7 (see Fig. 1 caption for explanation).

Fig. 8
Fig. 8

Case 8 (see Fig. 1 caption for explanation).

Equations (30)

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γ ( J ) = 1.13 / J 1 / 2 Ω - cm ,
V = ± K 0 i 1 / 2 .
K 0 = k l / d ,
L d i / d t ± K 0 i 1 / 2 + 1 / C 0 t i d t = V 0 ,
Z 0 = L / C ,             I = i Z 0 / V 0 ,             τ = t / T , T = L C ,             α = K 0 / ( V 0 Z 0 ) 1 / 2 .
d I / d τ ± α I 1 / 2 + 0 τ I d τ = 1.
[ L + L a ( t ) ] d i d t + i d d t [ L a ( t ) ] ± K 0 i 1 / 2 + 1 C 0 t i d t = V 0 ,
[ 1 + L a ( t ) L ] d I d τ + I d d τ [ L a ( t ) L ] ± α I 1 / 2 + β I + 0 τ I d τ = 1.
[ 1 + L a ( 0 ) L ] d I d τ = 1.
L a ( 0 ) > L a ( t )
d I d τ | τ = 0 < 1.
L ^ L a ( 0 ) / L 0.5 ,
L a ( t ) D L 2 r a ( t ) .
r a ( t ) 0.75 [ ( t ) / l ] 0.6 ,
( t ) = 0 t i 2 R l d t ,
R l = k l d i 1 / 2 ,
( t ) = k l d 0 t i 3 / 2 d t .
R l ( t ) = k l 2 r a ( t ) i 3 / 2 .
r a ( t ) = 3 4 [ k 0 t i ( t ) 3 / 2 r a ( t ) d t ] 0.6 .
d r a d t = [ 3 4 r a ( t ) ] 5 / 3 ( 0.6 ) k i ( t ) 3 / 2 ,
d ( L a / L ) d t = - ( 0.6 ) ( 3 4 ) 5 / 3 l 2 k L [ r a ( t ) ] - 11 / 3 i ( t ) 3 / 2 .
J ( r ) = { J = i / π r a 2 , r r a , 0 r > r a .
L a i 2 = 1 c 2 d 3 x d 3 x J ( x ) · J ( x ) x - x = 1 c 2 d 3 x d 3 x J 2 ( r ) x - x ,
L a = 2 π r a 4 c 2 0 l d z 0 l d z 0 2 π d θ 0 r a r d r × 0 r a r d r 1 [ r 2 + r 2 - 2 r r cos θ + ( z - z ) 2 ] 1 / 2 .
K 0 ( r , r ) = 2 0 π d α 1 ( r 2 + r 2 - 2 r r cos α ) 1 / 2 = 2 r + r K ( 2 r r r + r ) ,
[ r 2 + r 2 - 2 r r cos θ ( z - z ) 2 ] - 1 / 2 ( r 2 + r 2 - 2 r r cos θ ) - 1 / 2 + [ ( z - z ) 2 / 2 ] [ d 2 / d ( z - z ) 2 ] × [ r 2 + r 2 - 2 r r cos θ + ( z - z ) 2 ] - 1 / 2 z = z = 0 .
[ r 2 + r 2 - 2 r r cos θ + ( z - z ) 2 ] - 1 / 2 ( r 2 + r 2 - 2 r r cos θ ) - 1 / 2 - [ ( z - z ) 2 / 2 ] ( r 2 + r 2 - 2 r r cos θ ) - 3 / 2 .
L a 4 l 2 π r a 4 c 2 0 r a d r 0 r a d r ( r r r + r ) K ( 2 r r r + r ) .
L a 4 l 2 π r a c 2 0 1 d x 0 1 d x ( x x x + x ) K ( 2 x x x + x ) .
L a = D l 2 / r a .

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