Abstract

The dynamics of the plasma ions in the wake fields of short, ultraintense laser pulses in underdense plasmas are investigated analytically and numerically. Owing to the large ion-to-electron mass ratio, the motion of plasma ions in such wake fields has often been assumed to be neglectable. It is shown that when the laser intensity exceeds 1020Wcm2, the ion motion can no longer be ignored. In this case, ion momentum peaks appear behind the laser pulse, which correspond with the ion density peaks. The laser-excited wake field appears to be effective for ion acceleration, in particular to ions with high-charge numbers. The dependence of ion acceleration on the laser intensity, pulse width, and background plasma density is discussed.

© 2006 Optical Society of America

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  1. M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
    [CrossRef]
  2. M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
    [CrossRef]
  3. M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
    [CrossRef]
  4. V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
    [CrossRef]
  5. P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
    [CrossRef]
  6. R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
    [CrossRef] [PubMed]
  7. M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
    [CrossRef]
  8. H. Homeyer, "High energy ions for materials analysis, materials modification and medical applications," Nucl. Instrum. Methods Phys. Res. B 139, 58-64 (1998).
    [CrossRef]
  9. F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
    [CrossRef]
  10. S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

2004 (1)

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

2003 (1)

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

2001 (1)

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

2000 (1)

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

1999 (3)

V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
[CrossRef]

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

1998 (1)

H. Homeyer, "High energy ions for materials analysis, materials modification and medical applications," Nucl. Instrum. Methods Phys. Res. B 139, 58-64 (1998).
[CrossRef]

1996 (1)

M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
[CrossRef]

1994 (1)

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Allott, R.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Atzeni, S.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Beg, F. N.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Borghesi, M.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Bulanov, S.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Bulanov, S. V.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Bychenkov, V. Yu.

V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
[CrossRef]

Califano, F.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Campbell, D. H.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Campbell, E. M.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Cao, L. H.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Chen, Z. Y.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Clark, E.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Clarke, R. J.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Creswell, A.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Dangor, A. E.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Dudnikova, G. I.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Esirkepov, T.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Esirkepov, T. Zh.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Fang, X.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Feit, M. D.

M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
[CrossRef]

Fujita, H.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Galimberti, M.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Garrison, J. C.

M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
[CrossRef]

Gizzi, L. A.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Glinsky, M. E.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Graham, P.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Haines, M. G.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Hammer, J.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Homeyer, H.

H. Homeyer, "High energy ions for materials analysis, materials modification and medical applications," Nucl. Instrum. Methods Phys. Res. B 139, 58-64 (1998).
[CrossRef]

Honrubia, J.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Kamenets, F. F.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Kato, Y.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Kennedy, B.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Khoroshkov, V.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Kitagawa, Y.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Kodama, R.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Kruer, W. L.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Krushelnick, K.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Ledingham, K. W. D.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Lin, Y.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Lisikina, T. V.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Lu, P. X.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Machacek, A.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Mackinnon, A. J.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Magill, J.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Mason, R. J.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Matsushita, T.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

McCanny, T.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Mima, K.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Naumova, N. M.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Neely, D.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Nishihara, K.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Norreys, P. A.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Pegoraro, F.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Perry, M. D.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Rubenchik, A. M.

M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
[CrossRef]

Ruhl, H.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Sanderson, D. C. W.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Santala, M.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Schiavi, A.

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Sentoku, Y.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Singhal, R. P.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Tabak, M.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Tajima, T.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Takahashi, K.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Tanaka, K. A.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Tatarakis, M.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Temporal, M.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Tikhonchuk, V. T.

V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
[CrossRef]

Tolokonnikov, S. V.

V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
[CrossRef]

Vshivkov, V. A.

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

Wark, J. S.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Watts, I.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Wilks, S. C.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Willi, O.

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Woodworth, J.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

Xu, Z. Z.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Yamanaka, T.

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Yu, M. Y.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Yu, W.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

Zepf, M.

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Zhang, J.

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

JETP (1)

V. Yu. Bychenkov, V. T. Tikhonchuk, and S. V. Tolokonnikov, "Nuclear reactions triggered by laser-accelerated high-energy ions," JETP 88, 1137-1142 (1999).
[CrossRef]

Laser Part. Beams (1)

F. Pegoraro, S. Atzeni, M. Borghesi, S. Bulanov, T. Esirkepov, J. Honrubia, Y. Kato, V. Khoroshkov, K. Nishihara, T. Tajima, M. Temporal, and O. Willi, "Production of ion beams in high-power laser-plasma interactions and their applications," Laser Part. Beams 22, 19-24 (2004).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (1)

H. Homeyer, "High energy ions for materials analysis, materials modification and medical applications," Nucl. Instrum. Methods Phys. Res. B 139, 58-64 (1998).
[CrossRef]

Phys. Plasmas (3)

M. Y. Yu, W. Yu, Z. Y. Chen, J. Zhang, Y. Lin, L. H. Cao, P. X. Lu, and Z. Z. Xu, "Electron acceleration by an intense short-pulse laser in underdense plasma," Phys. Plasmas 10, 2468-2474 (2003).
[CrossRef]

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Perry, and R. J. Mason, "Ignition and high gain with ultrapowerful lasers," Phys. Plasmas 1, 1626-1634 (1994).
[CrossRef]

P. A. Norreys, M. Santala, E. Clark, M. Zepf, I. Watts, F. N. Beg, K. Krushelnick, M. Tatarakis, A. E. Dangor, X. Fang, P. Graham, T. McCanny, R. P. Singhal, K. W. D. Ledingham, A. Creswell, D. C. W. Sanderson, J. Magill, A. Machacek, J. S. Wark, R. Allott, B. Kennedy, and D. Neely, "Observation of a highly directional gamma-ray beam from ultrashort, ultraintense laser pulse interactions with solids," Phys. Plasmas 6, 2150-2156 (1999).
[CrossRef]

Phys. Rev. E (1)

M. D. Feit, J. C. Garrison, and A. M. Rubenchik, "Short pulse laser propagation in underdense plasmas," Phys. Rev. E 53, 1068-1083 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

R. Kodama, K. A. Tanaka, Y. Sentoku, T. Matsushita, K. Takahashi, H. Fujita, Y. Kitagawa, Y. Kato, T. Yamanaka, and K. Mima, "Long-scale jet formation with specularly reflected light in ultraintense laser-plasma interactions," Phys. Rev. Lett. 84, 674-677 (2000).
[CrossRef] [PubMed]

Plasma Phys. Controlled Fusion (1)

M. Borghesi, A. Schiavi, D. H. Campbell, M. G. Haines, O. Willi, A. J. Mackinnon, L. A. Gizzi, M. Galimberti, R. J. Clarke, and H. Ruhl, "Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies," Plasma Phys. Controlled Fusion 43, A267-A276 (2001).
[CrossRef]

Plasma Phys. Rep. (1)

S. V. Bulanov, V. A. Vshivkov, G. I. Dudnikova, T. Zh. Esirkepov, F. Califano, F. F. Kamenets, T. V. Lisikina, N. M. Naumova, and F. Pegoraro, "Interaction of petawatt laser pulses with underdense plasmas," Plasma Phys. Rep. 25, 701-714 (1999).

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Figures (10)

Fig. 1
Fig. 1

(a) Evolution of the normalized vector (a, dashed line) and scalar (φ, solid line) potentials, the normalized longitudinal electron momentum ( p e m e c , solid line), the normalized longitudinal proton momentum ( p i m e c , dotted line), the electron density ( n e n 0 ) and the proton density ( n i n 0 ) for n 0 = 10 3 , d = 10 λ , and a = 10 . (b) The longitudinal electron and proton momenta normalized by m e c obtained by 1D PIC simulation with the laser and plasma parameters as in (a).

Fig. 2
Fig. 2

Evolution of the normalized vector and scalar potentials, the longitudinal electron and proton momenta, and the electron and ion densities for n 0 = 10 4 , d = 10 λ , and a = 25 .

Fig. 3
Fig. 3

Maximum normalized scalar potentials ( φ ) in the wake versus the laser strength a with and without consideration the ion motion, respectively. Here n 0 = 10 4 and d = 10 λ .

Fig. 4
Fig. 4

Maximum proton kinetic energy ϵ i max and density n i max n 0 as functions of the laser strength a 0 for d = 10 λ and n 0 = 10 4 .

Fig. 5
Fig. 5

FWHM in space for proton kinetic energy and density as functions of the laser strength a 0 for d = 10 λ and n 0 = 10 4 , and the FWHM is normalized by laser wavelength λ.

Fig. 6
Fig. 6

Maximum proton kinetic energy and density as functions of the background electron density n 0 for a 0 = 25 and d = 10 λ .

Fig. 7
Fig. 7

Dependence of the optimum plasma density n 0 n c on laser pulse width d λ for a 0 = 25 .

Fig. 8
Fig. 8

Maximum kinetic energy and density of the Xe ions as a function of laser strength a 0 for d = 10 λ and n 0 = 10 4 , i.e., same as in Fig. 4.

Fig. 9
Fig. 9

Maximum kinetic energy and density of the Xe ions as a function of the background electron density n 0 for a 0 = 25 and d = 10 λ .

Fig. 10
Fig. 10

2D spatial distribution of the longitudinal proton momentum in a hydrogen plasma obtained by 2D PIC simulation for a 0 = 10 , d = 10 λ , n 0 = 10 3 , and the laser spot size w = 10 λ . Here only ions with momenta larger than 0.13 m e c in the absolute value are plotted.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

r e u e = a , t ( γ e v e ) = z ( φ γ e ) , ( γ e v e ) 2 = γ e 2 1 a 2 ,
r i u i = μ a , t ( γ i v i ) = z ( μ φ + γ i ) ,
( γ i v i ) 2 = γ i 2 1 μ 2 a 2 ,
a = a 0 exp ( ζ 2 2 L 2 ) cos ζ ,
γ e v e = γ e φ 1 , n e n e v e = n 0 ,
γ i v i = γ i + μ φ 1 , n i n i v i = n 0 Z ,
ξ ξ φ = n e Z n i = n 0 [ γ e ( φ + 1 ) γ i ( 1 μ φ ) ] ,
p i = ( m i m e ) γ i v i , ϵ i = ( m i m e ) ( γ i 1 ) ,

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