Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T12:04:42.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling of ion energies in the relativistic-induced transparency regime

Published online by Cambridge University Press:  14 October 2015

D. Jung ,
B.J. Albright ,
L. Yin ,
D.C. Gautier ,
B. Dromey ,
R. Shah ,
S. Palaniyappan ,
S. Letzring ,
H.-C. Wu  and
T. Shimada
...Show all authors
D. Jung*
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Centre for Plasma Physics (CPP), Queen's University Belfast, Belfast BT7 1NN, UK
B.J. Albright
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
L. Yin
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
D.C. Gautier
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
B. Dromey
Affiliation:
Centre for Plasma Physics (CPP), Queen's University Belfast, Belfast BT7 1NN, UK
R. Shah
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
S. Palaniyappan
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
S. Letzring
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
H.-C. Wu
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
T. Shimada
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
R.P. Johnson
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
D. Habs
Affiliation:
Department für Physik, Ludwig-Maximilians-Universität München, D-85748 Garching, Germany
M. Roth
Affiliation:
Department für Physik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
J.C. Fernández
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
B.M. Hegelich
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
*
Address correspondence and reprint requests to: D. Jung, Centre for Plasma Physics (CPP), Queen's University Belfast, Belfast BT7 1NN, UK. E-mail: daniel.jung@outlook.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimental data are presented showing maximum carbon C6+ ion energies obtained from nm-scaled targets in the relativistic transparent regime for laser intensities between 9 × 1019 and 2 × 1021 W/cm2. When combined with two-dimensional particle-in-cell simulations, these results show a steep linear scaling for carbon ions with the normalized laser amplitude a0 ($a_0 \propto \sqrt ( I)$). The results are in good agreement with a semi-analytic model that allows one to calculate the optimum thickness and the maximum ion energies as functions of a0 and the laser pulse duration τλ for ion acceleration in the relativistic-induced transparency regime. Following our results, ion energies exceeding 100 MeV/amu may be accessible with currently available laser systems.

Keywords

Laser-driven accelerationLaser–plasma interactionsLaser-produced plasmaParticle-in-cell methodPlasma simulation
Type
Research Article
Information
Laser and Particle Beams , Volume 33 , Issue 4 , December 2015 , pp. 695 - 703
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Albright, B.J., Yin, L., Bowers, K.J., Hegelich, B.M., Flippo, K.A., Kwan, T.J.T. & Fernandez, J.C. (2007). Relativistic Buneman instability in the laser breakout afterburner. Phys. Plasmas 140, 094502.CrossRefGoogle Scholar
Applied Diamond, Inc. [online] http://www.usapplieddiamond.com/Google Scholar
Batha, S.H., Aragonez, R., Archuleta, F.L., Archuleta, T.N., Benage, J.F., Cobble, J.A., Cowan, J.S., Fatherley, V.E., Flippo, K.A., Gautier, D.C., Gonzales, R.P., Greenfield, S.R., Hegelich, B.M., Hurry, T.R., Johnson, R.P., Kline, J.L., Letzring, S.A., Loomis, E.N., Lopez, F.E., Luo, S.N., Montgomery, D.S., Oertel, J.A., Paisley, D.L., Reid, S.M., Sanchez, P.G., Seifter, A., Shimada, T. & Workman, J.B. (2008). Trident high-energy-density facility experimental capabilities and diagnostics. Rev. Sci. Instrum. 790, 10F305. doi: 10.1063/1.2972020.CrossRefGoogle Scholar
Borghesi, M., Mackinnon, A.J., Campbell, D.H., Hicks, D.G., Kar, S., Patel, P.K., Price, D., Romagnani, L., Schiavi, A. & Willi, O. (2004). Multi-MeV proton source investigations in ultraintense laser–foil interactions. Phys. Rev. Lett. 92, 055003. doi: 10.1103/PhysRevLett.92.055003.CrossRefGoogle ScholarPubMed
Bowers, K.J., Albright, B.J., Yin, L., Bergen, B. & Kwan, T.J.T. (2008). Ultrahigh performance three-dimensional electromagnetic relativistic kinetic plasma simulation. Phys. Plasmas 150, 055703. doi: 10.1063/1.2840133.CrossRefGoogle Scholar
Buneman, O. (1959). Dissipation of currents in ionized media. Phys. Rev. 115, 503–517. doi: 10.1103/PhysRev.115.503.CrossRefGoogle Scholar
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, S., Le Sage, G.P., Letzring, S., Manclossi, M., Meyroneinc, S., Newkirk, A., Pépin, H. & Renard-LeGalloudec, N. (2004). Ultralow emittance, multi-MeV proton beams from a laser virtual-cathode plasma accelerator. Phys. Rev. Lett. 920, 204801. doi: 10.1103/PhysRevLett.92.204801.CrossRefGoogle Scholar
Dollar, F., Zulick, C., Thomas, A.G.R., Chvykov, V., Davis, J., Kalinchenko, G., Matsuoka, T., McGuffey, C., Petrov, G.M., Willingale, L., Yanovsky, V., Maksimchuk, A. & Krushelnick, K. (2012). Finite spot effects on radiation pressure acceleration from intense high-contrast laser interactions with thin targets. Phys. Rev. Lett. 108, 175005. doi: 10.1103/PhysRevLett.108.175005.CrossRefGoogle ScholarPubMed
Esirkepov, T., Borghesi, M., Bulanov, S.V., Mourou, G. & Tajima, T. (2004). Highly efficient relativistic-ion generation in the laser-piston regime. Phys. Rev. Lett. 920, 175003. doi: 10.1103/PhysRevLett.92.175003.CrossRefGoogle Scholar
Esirkepov, T., Yamagiwa, M. & Tajima, T. (2006). Laser ion-acceleration scaling laws seen in multiparametric particle-in-cell simulations. Phys. Rev. Lett. 96, 105001. doi: 10.1103/PhysRevLett.96.105001.CrossRefGoogle ScholarPubMed
Fleischer, R.L., Price, P.B. & Walker, R.M. (1965). Ion explosion spike mechanism for formation of charged-particle tracks in solids. J. Appl. Phys. 360, 3645–3652. doi: 10.1063/1.1703059.CrossRefGoogle Scholar
Fuchs, J., Antici, P., d'Humieres, E., Lefebvre, E., Borghesi, M., Brambrink, E., Cecchetti, C.A., Kaluza, M., Malka, V., Manclossi, M., Meyroneinc, S., Mora, P., Schreiber, J., Toncian, T., Pepin, H. & Audebert, P. (2006). Laser-driven proton scaling laws and new paths towards energy increase. Nat. Phys. 20, 48–54. doi: 10.1038/nphys199.CrossRefGoogle Scholar
Gaillard, S.A., Kluge, T., Flippo, K.A., Bussmann, M., Gall, B., Lockard, T., Geissel, M., Offermann, D.T., Schollmeier, M., Sentoku, Y. & Cowan, T.E. (2011). Increased laser-accelerated proton energies via direct laser-light-pressure acceleration of electrons in microcone targets. Phys. Plasmas 180, 056710. ISSN 1070664X. doi: 10.1063/1.3575624.CrossRefGoogle Scholar
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. Plasmas 70, 2076–2082. doi: 10.1063/1.874030.CrossRefGoogle Scholar
Hegelich, B.M., Albright, B.J., Cobble, J., Flippo, K., Letzring, S., Paffett, M., Ruhl, H., Schreiber, J., Schulze, R.K. & Fernandez, J.C. (2006). Laser acceleration of quasi-monoenergetic MeV ion beams. Nature 4390, 441–444. doi: 10.1038/nature04400.CrossRefGoogle Scholar
Hegelich, B.M., Jung, D., Albright, B.J., Cheung, M., Dromey, B., Gautier, D.C., Hamilton, C., Letzring, S., Munchhausen, R., Palaniyappan, S., Shah, R., Wu, H.-C., Yin, L. & Fernández, J.C. (2013). 160 MeV laser-accelerated protons from CH2 nano-targets for proton cancer therapy. ArXiv e-prints.Google Scholar
Hegelich, B.M., Jung, D., Albright, B.J., Fernandez, J.C., Gautier, D.C., Huang, C., Kwan, T.J., Letzring, S., Palaniyappan, S., Shah, R.C., Wu, H.-C., Yin, L., Henig, A., Hrlein, R., Kiefer, D., Schreiber, J., Yan, X.Q., Tajima, T., Habs, D., Dromey, B. & Honrubia, J.J. (2011). Experimental demonstration of particle energy, conversion efficiency and spectral shape required for ion-based fast ignition. Nucl. Fusion 510, 083011. doi: 10.1088/0029-5515/51/8/083011.CrossRefGoogle Scholar
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. 890, 085002. doi: 10.1103/PhysRevLett.89.085002.CrossRefGoogle Scholar
Henig, A., Kiefer, D., Markey, K., Gautier, D.C., Flippo, K.A., Letzring, S., Johnson, R.P., Shimada, T., Yin, L., Albright, B.J., Bowers, K.J., Fernández, J.C., Rykovanov, S.G., Wu, H.-C., Zepf, M., Jung, D., Liechtenstein, V.Kh., Schreiber, J., Habs, D. & Hegelich, B.M. (2009 a). Enhanced laser-driven ion acceleration in the relativistic transparency regime. Phys. Rev. Lett. 1030, 045002. doi: 10.1103/PhysRevLett.103.045002.CrossRefGoogle Scholar
Henig, A., Steinke, S., Schnürer, M., Sokollik, T., Hörlein, R., Kiefer, D., Jung, D., Schreiber, J., Hegelich, B.M., Yan, X.Q., Meyer-ter Vehn, J., Tajima, T., Nickles, P.V., Sandner, W. & Habs, D. (2009 b). Radiation-pressure acceleration of ion beams driven by circularly polarized laser pulses. Phys. Rev. Lett. 1030, 245003. doi: 10.1103/PhysRevLett.103.245003.CrossRefGoogle Scholar
Jung, D., Albright, B.J., Yin, L., Gautier, D.C., Shah, R., Palaniyappan, S., Letzring, S., Dromey, B., Wu, H.-C., Shimada, T., Johnson, R.P., Roth, M., Fernandez, J.C., Habs, D. & Hegelich, B.M. (2013 a). Beam profiles of proton and carbon ions in the relativistic transparency regime. New J. Phys. 150, 123035. doi: 10.1088/1367-2630/15/12/123035.CrossRefGoogle Scholar
Jung, D., Falk, K., Guler, N., Deppert, O., Devlin, M., Favalli, A., Fernandez, J.C., Gautier, D.C., Geissel, M., Haight, R., Hamilton, C.E., Hegelich, B.M., Johnson, R.P., Merrill, F., Schaumann, G., Schoenberg, K., Schollmeier, M., Shimada, T., Taddeucci, T., Tybo, J.L., Wender, S.A., Wilde, C.H., Wurden, G.A. & Roth, M. (2013 b). Characterization of a novel, short pulse laser-driven neutron source. Phys. Plasmas 200, 056706. doi: 10.1063/1.4804640.CrossRefGoogle Scholar
Jung, D., Hrlein, R., Gautier, D.C., Letzring, S., Kiefer, D., Allinger, K., Albright, B.J., Shah, R., Palaniyappan, S., Yin, L., Fernndez, J.C., Habs, D. & Hegelich, B.M. (2011). A novel high resolution ion wide angle spectrometer. Rev. Sci. Instrum. 820, 043301. ISSN 00346748. doi: 10.1063/1.3575581.CrossRefGoogle Scholar
Jung, D., Senje, L., McCormack, O., Yin, L., Albright, B.J., Letzring, S., Gautier, D.C., Dromey, B., Toncian, T., Fernandez, J.C., Zepf, M. & Hegelich, B.M. (2015). On the analysis of inhomogeneous magnetic field spectrometer for laser-driven ion acceleration. Rev. Sci. Instrum. 860, 033303. doi: 10.1063/1.4914845.CrossRefGoogle Scholar
Jung, D., Yin, L., Albright, B.J., Gautier, D.C., Letzring, S., Dromey, B., Yeung, M., Hörlein, R., Shah, R., Palaniyappan, S., Allinger, K., Schreiber, J., Bowers, K.J., Wu, H-C., Fernandez, J.C., Habs, D. & Hegelich, B.M. (2013 c). Efficient carbon ion beam generation from laser-driven volume acceleration. New J. Phys. 150, 023007. doi: 10.1088/1367-2630/15/2/023007.CrossRefGoogle Scholar
Jung, D., Yin, L., Gautier, D.C., Wu, H.-C., Letzring, S., Dromey, B., Shah, R., Palaniyappan, S., Shimada, T., Johnson, R.P., Schreiber, J., Habs, D., Fernández, J.C., Hegelich, B.M. & Albright, B.J. (2013 d). Laser-driven 1 GeV carbon ions from preheated diamond targets in the break-out afterburner regime. Phys. Plasmas 200, 083103. doi: 10.1063/1.4817287.CrossRefGoogle Scholar
Kar, S., Kakolee, K.F., Qiao, B., Macchi, A., Cerchez, M., Doria, D., Geissler, M., McKenna, P., Neely, D., Osterholz, J., Prasad, R., Quinn, K., Ramakrishna, B., Sarri, G., Willi, O., Yuan, X.Y., Zepf, M. & Borghesi, M. (2012). Ion acceleration in multispecies targets driven by intense laser radiation pressure. Phys. Rev. Lett. 109, 185006. doi: 10.1103/PhysRevLett.109.185006.CrossRefGoogle ScholarPubMed
Klimo, O., Psikal, J., Limpouch, J. & Tikhonchuk, V.T. (2008). Monoenergetic ion beams from ultrathin foils irradiated by ultrahigh-contrast circularly polarized laser pulses. Phys. Rev. ST Accel. Beams 110, 031301. doi: 10.1103/PhysRevSTAB.11.031301.CrossRefGoogle Scholar
Macchi, A., Veghini, S., Liseykina, T.V. & Pegoraro, F. (2010). Radiation pressure acceleration of ultrathin foils. New J. Phys. 120, 045013. doi: 10.1088/1367-2630/12/4/045013.CrossRefGoogle Scholar
Macchi, A., Veghini, S. & Pegoraro, F. (2009). “Light sail” acceleration reexamined. Phys. Rev. Lett. 1030, 085003. doi: 10.1103/PhysRevLett.103.085003.CrossRefGoogle Scholar
Mako, F. & Tajima, T. (1984). Collective ion acceleration by a reflexing electron beam: Model and scaling. Phys. Fluids 270, 1815–1820. doi: 10.1063/1.864794.CrossRefGoogle Scholar
Mancic, A., Fuchs, J., Antici, P., Gaillard, S.A. & Audebert, P. (2008). Absolute calibration of photostimulable image plate detectors used as (0.5-20 MeV) high-energy proton detectors. Rev. Sci. Instrum. 790, 073301. doi: 10.1063/1.2949388.CrossRefGoogle Scholar
Naumova, N., Schlegel, T., Tikhonchuk, V.T., Labaune, C., Sokolov, I.V. & Mourou, G. (2009). Hole boring in a dt pellet and fast-ion ignition with ultraintense laser pulses. Phys. Rev. Lett. 102, 025002. doi: 10.1103/PhysRevLett.102.025002.CrossRefGoogle Scholar
Palaniyappan, S., Hegelich, B.M., Wu, H.-C., Jung, D., Gautier, D.C., Yin, L., Albright, B.J., Johnson, R.P., Shimada, T., Letzring, S., Offermann, D.T., Ren, J., Huang, C., Hörlein, R., Dromey, B., Fernandez, J.C. & Shah, R.C. (2012). Dynamics of relativistic transparency and optical shuttering in expanding overdense plasmas. Nat. Phys. 8, 763–769. doi: 10.1038/nphys2390.CrossRefGoogle Scholar
Paterson, I.J., Clarke, R.J., Woolsey, N.C. & Gregori, G. (2008). Image plate response for conditions relevant to laser–plasma interaction experiments. Meas. Sci. Technol. 190, 095301. doi: 10.1088/0957-0233/19/9/095301.CrossRefGoogle Scholar
Reitzel, K.J. & Morales, G.J. (1998). Dynamics of narrow electron streams in magnetized plasmas. Phys. Plasmas 50, 3806–3815. doi: 10.1063/1.873099.CrossRefGoogle Scholar
Robinson, A.P.L., Gibbon, P., Zepf, M., Kar, S., Evans, R.G. & Bellei, C. (2009). Relativistically correct hole-boring and ion acceleration by circularly polarized laser pulses. Plasma Phys. Controll. Fusion 510, 024004. doi: 10.1088/0741-3335/51/2/024004.CrossRefGoogle Scholar
Robson, L., Simpson, P.T., Clarke, R.J., Ledingham, K.W.D., Lindau, F., Lundh, O., McCanny, T., Mora, P., Neely, D., Wahlstrom, C.-G., Zepf, M. & McKenna, P. (2007). Scaling of proton acceleration driven by petawatt–laser–plasma interactions. Nat. Phys. 30, 58–62. doi: 10.1038/nphys476.CrossRefGoogle Scholar
Roth, M., Cowan, T.E., Key, M.H., Hatchett, S.P., Brown, C., Fountain, W., Johnson, J., Pennington, D.M., Snavely, R.A., Wilks, S.C., Yasuike, K., Ruhl, H., Pegoraro, F., Bulanov, S.V., Campbell, E.M., Perry, M.D. & Powell, H. (2001). Fast ignition by intense laser-accelerated proton beams. Phys. Rev. Lett. 860, 436–439. doi: 10.1103/PhysRevLett.86.436.CrossRefGoogle Scholar
Roth, M., Jung, D., Falk, K., Guler, N., Deppert, O., Devlin, M., Favalli, A., Fernandez, J., Gautier, D., Geissel, M., Haight, R., Hamilton, C.E., Hegelich, B.M., Johnson, R.P., Merrill, F., Schaumann, G., Schoenberg, K., Schollmeier, M., Shimada, T., Taddeucci, T., Tybo, J.L., Wagner, F., Wender, S.A., Wilde, C.H. & Wurden, G.A. (2013). Bright laser-driven neutron source based on the relativistic transparency of solids. Phys. Rev. Lett. 110, 044802. doi: 10.1103/PhysRevLett.110.044802.CrossRefGoogle ScholarPubMed
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. 850, 2945–2948. doi: 10.1103/PhysRevLett.85.2945.CrossRefGoogle Scholar
Steinke, S., Henig, A., Schnrer, M., Sokollik, T., Nickles, P.V., Jung, D., Kiefer, D., Hrlein, R., Schreiber, J., Tajima, T., Yan, X.Q., Hegelich, M., Meyer-ter Vehn, J., Sandner, W. & Habs, D. (2010). Efficient ion acceleration by collective laser-driven electron dynamics with ultra-thin foil targets. Laser Part. Beams 280, 215–221. doi: 10.1017/S0263034610000157.CrossRefGoogle Scholar
Tabak, M., Hammer, J., Glinsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. (1994). Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 10, 1626–1634. doi: 10.1063/1.870664.CrossRefGoogle Scholar
Tajima, T., Habs, D. & Yan, X. (2009). Laser acceleration of ions for radiation therapy. Rev. Accel. Sci. Tech. 2, 201–228. doi: 10.1142/S1793626809000296.CrossRefGoogle Scholar
Vshivkov, V.A., Naumova, N.M., Pegoraro, F. & Bulanov, S.V. (1998). Nonlinear electrodynamics of the interaction of ultra-intense laser pulses with a thin foil. Phys. Plasmas 50, 2727–2741. doi: 10.1063/1.872961.CrossRefGoogle Scholar
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. Plasmas 80, 542–549. ISSN 1070664X. doi: 10.1063/1.1333697.CrossRefGoogle Scholar
Yan, X., Tajima, T., Hegelich, M., Yin, L. & Habs, D. (2010). Theory of laser ion acceleration from a foil target of nanometer thickness. Appl. Phys. B: Lasers Opt. 98, 711–721. ISSN 0946-2171. doi: 10.1007/s00340-009-3707-5.CrossRefGoogle Scholar
Yan, X.Q., Lin, C., Sheng, Z.M., Guo, Z.Y., Liu, B.C., Lu, Y.R., Fang, J.X. & Chen, J.E. (2008). Generating high-current monoenergetic proton beams by a circularly polarized laser pulse in the phase-stable acceleration regime. Phys. Rev. Lett. 1000, 135003. doi: 10.1103/PhysRevLett.100.135003.CrossRefGoogle Scholar
Yin, L., Albright, B.J., Bowers, K.J., Jung, D., Fernández, J.C. & Hegelich, B.M. (2011 a). Three-dimensional dynamics of breakout afterburner ion acceleration using high-contrast short-pulse laser and nanoscale targets. Phys. Rev. Lett. 1070, 045003. doi: 10.1103/PhysRevLett.107.045003.CrossRefGoogle Scholar
Yin, L., Albright, B.J., Hegelich, B.M., Bowers, K.J., Flippo, K.A., Kwan, T.J.T. & Fernandez, J.C. (2007). Monoenergetic and GeV ion acceleration from the laser breakout afterburner using ultrathin targets. Phys. Plasmas 140, 056706. doi: 10.1063/1.2436857.CrossRefGoogle Scholar
Yin, L., Albright, B.J., Jung, D., Shah, R.C., Palaniyappan, S., Bowers, K.J., Henig, A., Fernndez, J.C. & Hegelich, B.M. (2011 b). Break-out afterburner ion acceleration in the longer laser pulse length regime. Phys. Plasmas 180, 063103. doi: 10.1063/1.3596555.CrossRefGoogle Scholar