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Modeling of the electrostatic sheath shape on the rear target surface in short-pulse laser-driven proton acceleration



Proton beams, generated in the interaction process of short ultra-intense laser pulses with thin foils, carry imprints of rear side target structures. These intensity patterns, imaged with a particle detector, sometimes show slight deformations. We propose an analytical model to describe these deformations by the spatial shape of a monoenergetic layer of protons in the beginning of free proton propagation. We also present results of simulations, which reproduce the detected structures and allow finally making quantitative conclusions on the shape of the layer. In experiments with electrically conducting targets, the shape is always close to a parabolic one independently on target thickness or laser parameters. Since the protons are pulled by the free electrons, there must be a strong correlation to the electron space charge distribution on the rear side of the illuminated foil. Simulations demonstrate that the deformations in the detected patterns of the proton layers are very sensitive to the initial layer shape. Analyzing spatial structures of the generated proton beams we can indirectly conclude on electron transport phenomena in the overdense part of the target.


Corresponding author

Address correspondence and reprint requests to: Erik Brambrink, Laboratoire LULI, Ecole Polytechnique, Route de Saclay, F-91128 Palaiseau, France. E-mail:


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Allen, M., Patel, P.K., Mackinnon, A., Price, D., Wilks, S. & Morse, E. (2004). Direct experimental evidence of back-surface ion acceleration from laser-irradiated gold foils. Phys. Rev. Lett. 93, 265004.
Borghesi, M., Campbell, D.H., Schiavi, A., Willi, O., Mackinnon, A.J., Hicks, D., Patel, P., Gizzi, L.A., Galimberti, M. & Clarke, R.J. (2002). Laser-produced protons and their applications as a particle probe. Laser Part. Beams 20, 269.
Borghesi, M., Audebert, P., Bulanov, S.V., Cowan, T., Fuchs, J., Gauthier, J.C., Mackinnon, A.J., Patel, P.K., Pretzler, G., Romagnani, L., Schiavi, A., Toncian, T. & Willi, O. (2005). High-intensity laser-plasma interaction studies employing laser-driven proton probes. Laser Part. Beams 23, 291.
Brambrink, E., Roth, M., Karsch, S., Neely, D., Clarke, R., McKanna, P. & Ledingham, K. (2004). Emittance measurement of energetic proton beams generated with a petawatt laser. CLF Ann. Rep.
Breschi, E., Borghesi, M., Campbell, D.H., Galimberti, M., Giulietti, D., Gizzi, L.A., Romagnani, L., Schiavi, A. & Willi, O. (2004). Spectral and angular characterization of laser-produced proton beams from dosimetric measurements. Laser Part. Beams 22, 393.
Clark, E.L., Krushelnick, K.R. Davies, J., Zepf, M., Tatarakis, M., Beg, F.N., Machacek, A., Norreys, P.A., Santala, M.I.K., Watts, I., &Dangor, A.E. (2000). Measurements of energetic proton transport through magnetized plasma from intense laser interactions with solids. Phys. Rev. Lett. 84, 670.
Cowan, T.E., Fuchs, J., Ruhl, H., Kemp, A., Audebert, P., Roth, M., Stephens, R., Barton, I., Blazevic, A., Brambrink, E., Cobble, J., Fernández, J., Gauthier, J.-C., Geissel, M., Hegelich, M., Kaae, J., Karsch, G.P., Le Sage, S., Letzring, M., Manclossi, S., Meyroneinc, A., Newkirk, S., Pépin, H. & Renard-LeGalloudec N. (2004). Ultralow emittance, multi-MeV proton beams from a laser virtual-cathode plasma accelerator. Phys. Rev. Lett. 92, 204801.
Fernandez, J.C., Hegelich, B.M., Cobble, J.A., Flippo, K.A., Letzring, S.A., Johnson, R.P., Gautier, D.C., Shimada, T., Kyrala, G.A., Wang, Y., Wettland, C.J. & Schreiber, J. (2005). Laser-ablation treatment of short-pulse laser targets: Toward an experimental program on energetic-ion interactions with dense plasmas. Laser Part. Beams 23, 267.
Fuchs, J., Cowan, T.E., Audebert, P., Ruhl, H., Gremillet, L., Kemp, A., Allen, M., Blazevic, A., Gauthier, J.-C., Geissel, M., Hegelich, M., Karsch, S., Parks, P., Roth, M., Sentoku, Y., Stephens, R. & Campbell, E.M. (2003). Spatial uniformity of laser-accelerated ultrahigh-current MeV electron propagation in metals and insulators. Phys. Rev. Lett. 91, 255002.
Hatchett, S.P., Brown, C.G., Cowan, T.E., Henry, E.A., Johnson, J.S., Key M.H., Koch, J.A., Langdon, A.B., Lasinski, B.F., Lee, R.W., Mackinnon, A.J., Pennington, D.M., Perry, M.D., Phillips, T.W., Roth M., Sangster T.C., Singh, M.S., Snavely, R.A., Stoyer, M.A., Wilks, S.C., &Yasuike, K. (2000). Electron, photon, and ion beams from the relativistic interaction of Petawatt laser pulses with solid targets. Phys. Plasma 7, 2076.
Hegelich, M., Karsch, S., Pretzler, G., Habs, D., Witte, K., Guenther, W., Allen, M., Blazevic, A., Fuchs, J., Gauthier, J.C., Geissel, M., Audebert, P., Cowan, T. & Roth, M. (2002). MeV ion jets from short-pulse-laser interaction with thin foils. Phys. Rev. Lett. 89, 085002.
Kaluza, M., Schreiber, J., Santala, M.I.K., Tsakiris, G.D., Eidmann, K., Meyer-ter-Vehn, J. & Witte, K.J. (2004). Influence of the laser prepulse on proton acceleration in thin-foil experiments. Phys. Rev. Lett. 93, 045003.
Krushelnick, K., Clark, E.L., Zepf, M., Davies, J.R., Beg, F.N., Machacek, A., Santala, M.I.K., Tatarakis, M., Watts, I., Norreys, P.A. & Dangor, A.E. (2000). Energetic proton production from relativistic laser interaction with high density plasmas. Phys. Plasma 7, 2055.
Mackinnon, A.J., Sentoku, Y., Patel, P.K., Price, D.W., Hatchett, S., Key, M.H., Andersen, C., Snavely, R. & Freeman, R.R. (2002). Enhancement of proton acceleration by hot-electron recirculation in thin foils irradiated by ultraintense laser pulses. Phys. Rev. Lett. 88, 215006.
Maksimchuk, A., Gu, S., Flippo, K., Umstadter, Bychenkov, D., &xxx, Yu. (2000). Forward ion acceleration in thin films driven by a high-intensity laser. Phys. Rev. Lett. 84, 4108.
McLaughlin, W.L., Chen Yun-Dong, Soares, C.G., Miller, A., Van Dyk, G., &Lewis, D.F. (1991). Densitometry of the response of a new radiochromic film dosimeter to gamma radiation and electron beams. Nucl. Instr. Meth. A 302, 165.
Murakami, Y., Kitagawa, Y., Sentoku, Y., Mori, M., Kodama, R., Tanaka, K.A., Mima, K. & Yamanaka, T. (2001). Observation of proton rear emission and possible gigagauss scale magnetic fields from ultra-intense laser illuminated plastic target. Phys. Plasma 8, 4138.
Roth, M., Blazevic, A., Geissel, M., Schlegel, T., Cowan, T.E., Allen, M., Gauthier, J.-C., Audebert, P., Fuchs, J., Meyer-ter-Vehn, J., Hegelich, M., Karsch, S. & Pukhov, A. (2002a). Energetic ions generated by laser pulses: A detailed study on target properties. PRST-AB 5, 061301.
Roth, M., Allen, M., Audebert, P., Blazevic, A., Brambrink, E., Cowan, T.E., Fuchs, J., Gauthier, J.-C., Geißel, M., Hegelich, M., Karsch, S., Meyer-ter-Vehn, J., Ruhl, H., Schlegel, T. & Stephens, R.B. (2002b). The generation of high-quality, intense ion beams by ultra-intense lasers. Plasma Phys. Contr. Fusion B44, 99.
Roth, M., Brambrink, E., Audebert, M., Blazevic, A., Clarke, R., Cobble, J., Cowan, T.E., Fernandez, J., Fuchs, J., Geissel, M., Habs, D., Hegelich, M., Karsch, S., Ledingham, K., Neely, D., Ruhl, H., Schlegel, T. & Schreiber, J. (2005). Laser accelerated ions and electron transport in ultra-intense laser matter interaction. Laser Part. Beams 23, 95.
Snavely, R.A., Key, M.H., Hatchett, S.P., Cowan, T.E., Roth, M., Phillips, T.W., Stoyer, M.A., Henry, E.A., Sangster, T.C., Singh, M.S., Wilks, S.C., MacKinnon, A., Offenberger, A., Pennington, D.M., Yasuike, K., Langdon, A.B., Lasinski, B.F., Johnson, J., Perry, M.D. & Campbell, E.M. (2000). Intense high-energy proton beams from petawatt-laser irradiation of solids. Phys. Rev. Lett. 85, 2945.
Wilks, S.C., Langdon, A.B., Cowan, T.E., Roth, M., Singh, M., Hatchett, S., Key, M.H., Pennington, D., MacKinnon, A. & Snavely, R.A. (2001). Energetic proton generation in ultra-intense laser–solid interactions. Phys. Plasma 8, 542.



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