Abstract

Simulations based on the coupled relativistic equations of motion show that protons stemming from laser-plasma processes can be efficiently post-accelerated employing single and crossed pulsed laser beams focused to spot radii on the order of the laser wavelength. We demonstrate that the crossed beams produce quasi-monoenergetic accelerated protons with kinetic energies exceeding 200 MeV, small energy spreads of about 1% and high densities as required for hadron cancer therapy. To our knowledge, this is the first scheme allowing for this important application based on an all-optical set-up.

© 2010 OSA

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2009 (2)

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

2008 (1)

Y. I. Salamin, Z. Harman, and C. H. Keitel, “Direct high-power laser acceleration of ions for medical applications,” Phys. Rev. Lett. 100, 155004 (2008).
[CrossRef] [PubMed]

2007 (4)

E. Gerstner, “Laser physics: extreme light,” Nature 446, 16–18 (2007).
[CrossRef] [PubMed]

Y. I. Salamin, “Fields of a Gaussian beam beyond paraxial approximation,” Appl. Phys. B 86, 319–326 (2007).
[CrossRef]

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

J. Badziak, “Laser-driven generation of fast particles,” Opto-Electr. Review 15, 1–12 (2007).
[CrossRef]

2006 (3)

M. Dunne, “Laser-driven particle accelerators,” Science 312, 374–376 (2006).
[CrossRef] [PubMed]

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

2005 (1)

Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

2004 (1)

2003 (2)

J. A. van Kan, A. A. Bettiol, and F. Watt, “Three-dimensional nanolithography using proton beam writing,” Appl. Phys. Lett. 83, 1629–1631 (2003).
[CrossRef]

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300, 1107–1111 (2003).
[CrossRef] [PubMed]

2002 (1)

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

2001 (3)

O. Jäkel, M. Krämer, C. P. Karger, and J. Debus, “Treatment planning for heavy ion radiotherapy: clinical implementation and application,” Phys. Med. Biol. 46, 1101–1116 (2001).
[CrossRef] [PubMed]

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

G. V. Stupakov and M. S. Zolotorev, “Ponderomotive laser acceleration and focusing in vacuum for generation of attosecond electron bunches,” Phys. Rev. Lett. 86, 5274–5277 (2001).
[CrossRef] [PubMed]

2000 (1)

Y. I. Salamin and C. H. Keitel, “Subcycle high electron acceleration by crossed laser beams,” Appl. Phys. Lett. 77, 1082–1084 (2000).
[CrossRef]

1999 (1)

J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
[CrossRef]

1995 (2)

C. M. Haaland, “Laser electron acceleration in vacuum,” Opt. Commun. 114, 280–284 (1995).
[CrossRef]

E. Esarey, P. Sprangle, and J. Krall, “Laser acceleration of electrons in vacuum,” Phys. Rev. E 52, 5443–5453 (1995).
[CrossRef]

1986 (1)

X. Jaén, J. Llosa, and A. Molina, “A reduction of order two for infinite-order Lagrangians,” Phys. Rev. D 34, 2302–2311 (1986).
[CrossRef]

Ahmad, I.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Aleonard, M.-M.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Amthor, K.-U.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Antici, P.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Apolonski, A.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Audebert, P.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Badziak, J.

J. Badziak, “Laser-driven generation of fast particles,” Opto-Electr. Review 15, 1–12 (2007).
[CrossRef]

Bahk, S.-W.

Bettiol, A. A.

J. A. van Kan, A. A. Bettiol, and F. Watt, “Three-dimensional nanolithography using proton beam writing,” Appl. Phys. Lett. 83, 1629–1631 (2003).
[CrossRef]

Borghesi, M.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Brambrink, E.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Burgy, F.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Campbell, H.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Cecchetti, C. A.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Chambaret, J.-P.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Chemin, J.-F.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Chen, Z.

Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

Chvykov, V.

Clarke, R. J.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Combs, S. E.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

d’Humières, E.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Dangor, A. E.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Debus, J.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

O. Jäkel, M. Krämer, C. P. Karger, and J. Debus, “Treatment planning for heavy ion radiotherapy: clinical implementation and application,” Phys. Med. Biol. 46, 1101–1116 (2001).
[CrossRef] [PubMed]

Dunne, M.

M. Dunne, “Laser-driven particle accelerators,” Science 312, 374–376 (2006).
[CrossRef] [PubMed]

Esarey, E.

E. Esarey, P. Sprangle, and J. Krall, “Laser acceleration of electrons in vacuum,” Phys. Rev. E 52, 5443–5453 (1995).
[CrossRef]

Esirkepov, T.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Feng, L.

J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
[CrossRef]

Fritzler, S.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Fuchs, J.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Fülöp, J. A.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Gerstner, E.

E. Gerstner, “Laser physics: extreme light,” Nature 446, 16–18 (2007).
[CrossRef] [PubMed]

Haaland, C. M.

C. M. Haaland, “Laser electron acceleration in vacuum,” Opt. Commun. 114, 280–284 (1995).
[CrossRef]

Haberer, T.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Harman, Z.

Y. I. Salamin, Z. Harman, and C. H. Keitel, “Direct high-power laser acceleration of ions for medical applications,” Phys. Rev. Lett. 100, 155004 (2008).
[CrossRef] [PubMed]

Hatchett, S.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Hein, J.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Henig, A.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Ho, Y. K.

Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
[CrossRef]

Hörlein, R.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Hua, J. F.

Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

Huber, P. E.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Jäckel, O.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1999), 3rd ed.

Jaekel, O.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Jaén, X.

X. Jaén, J. Llosa, and A. Molina, “A reduction of order two for infinite-order Lagrangians,” Phys. Rev. D 34, 2302–2311 (1986).
[CrossRef]

Jäkel, O.

O. Jäkel, M. Krämer, C. P. Karger, and J. Debus, “Treatment planning for heavy ion radiotherapy: clinical implementation and application,” Phys. Med. Biol. 46, 1101–1116 (2001).
[CrossRef] [PubMed]

Kalintchenko, G.

Kaluza, M.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Karger, C. P.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

O. Jäkel, M. Krämer, C. P. Karger, and J. Debus, “Treatment planning for heavy ion radiotherapy: clinical implementation and application,” Phys. Med. Biol. 46, 1101–1116 (2001).
[CrossRef] [PubMed]

Karsch, S.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Keitel, C. H.

Y. I. Salamin, Z. Harman, and C. H. Keitel, “Direct high-power laser acceleration of ions for medical applications,” Phys. Rev. Lett. 100, 155004 (2008).
[CrossRef] [PubMed]

Y. I. Salamin and C. H. Keitel, “Subcycle high electron acceleration by crossed laser beams,” Appl. Phys. Lett. 77, 1082–1084 (2000).
[CrossRef]

Key, M. H.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Klingebiel, S.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Kong, Q.

J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
[CrossRef]

Krall, J.

E. Esarey, P. Sprangle, and J. Krall, “Laser acceleration of electrons in vacuum,” Phys. Rev. E 52, 5443–5453 (1995).
[CrossRef]

Krämer, M.

O. Jäkel, M. Krämer, C. P. Karger, and J. Debus, “Treatment planning for heavy ion radiotherapy: clinical implementation and application,” Phys. Med. Biol. 46, 1101–1116 (2001).
[CrossRef] [PubMed]

Krausz, F.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Kruber, S.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Krushelnick, K.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Ledingham, K. W. D.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300, 1107–1111 (2003).
[CrossRef] [PubMed]

Lefebvre, E.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Liesfeld, B.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Lindau, F.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Llosa, J.

X. Jaén, J. Llosa, and A. Molina, “A reduction of order two for infinite-order Lagrangians,” Phys. Rev. D 34, 2302–2311 (1986).
[CrossRef]

Lundh, O.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Mackinnon, A. J.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Major, Z.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Maksimchuk, A.

Malka, G.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Malka, V.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Manclossi, M.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Mangles, S. P. D.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

McCanny, T.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

McKenna, P.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300, 1107–1111 (2003).
[CrossRef] [PubMed]

Meyroneinc, S.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Molina, A.

X. Jaén, J. Llosa, and A. Molina, “A reduction of order two for infinite-order Lagrangians,” Phys. Rev. D 34, 2302–2311 (1986).
[CrossRef]

Mora, P.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Mourou, G. A.

Münter, M. W.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Najmudin, Z.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Neely, D.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Nikoghosyan, A.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Osterhoff, J.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Patel, P. K.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Pépin, H.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Pervak, V.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Pfotenhauer, S.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Pittman, M.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Planchon, T. A.

Popp, A.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Robson, L.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Rousseau, J.-P.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Rousseau, P.

Salamin, Y. I.

Y. I. Salamin, Z. Harman, and C. H. Keitel, “Direct high-power laser acceleration of ions for medical applications,” Phys. Rev. Lett. 100, 155004 (2008).
[CrossRef] [PubMed]

Y. I. Salamin, “Fields of a Gaussian beam beyond paraxial approximation,” Appl. Phys. B 86, 319–326 (2007).
[CrossRef]

Y. I. Salamin and C. H. Keitel, “Subcycle high electron acceleration by crossed laser beams,” Appl. Phys. Lett. 77, 1082–1084 (2000).
[CrossRef]

Sauerbrey, R.

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Scheid, W.

J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
[CrossRef]

Scheurer, J.-N.

V. Malka, S. Fritzler, E. Lefebvre, M.-M. Aleonard, F. Burgy, J.-P. Chambaret, J.-F. Chemin, K. Krushelnick, G. Malka, S. P. D. Mangles, Z. Najmudin, M. Pittman, J.-P. Rousseau, J.-N. Scheurer, B. Walton, and A. E. Dangor, “Electron acceleration by a wake field forced by an intense ultrashort laser pulse,” Science 298, 1596–1600 (2002).
[CrossRef] [PubMed]

Schiavi, A.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

Schreiber, J.

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

Schulz-Ertner, D.

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

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H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Siebold, M.

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Simpson, P. T.

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

Singhal, R. P.

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300, 1107–1111 (2003).
[CrossRef] [PubMed]

Snavely, R.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

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E. Esarey, P. Sprangle, and J. Krall, “Laser acceleration of electrons in vacuum,” Phys. Rev. E 52, 5443–5453 (1995).
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G. V. Stupakov and M. S. Zolotorev, “Ponderomotive laser acceleration and focusing in vacuum for generation of attosecond electron bunches,” Phys. Rev. Lett. 86, 5274–5277 (2001).
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J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
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J. A. van Kan, A. A. Bettiol, and F. Watt, “Three-dimensional nanolithography using proton beam writing,” Appl. Phys. Lett. 83, 1629–1631 (2003).
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L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
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Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

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J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
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Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
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Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

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J. A. van Kan, A. A. Bettiol, and F. Watt, “Three-dimensional nanolithography using proton beam writing,” Appl. Phys. Lett. 83, 1629–1631 (2003).
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Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

Wilks, S. C.

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

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A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
[CrossRef] [PubMed]

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Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

Yan, Z.

Z. Yan, Y. K. Ho, P. X. Wang, J. F. Hua, Z. Chen, and L. Wu, “Accurate description of ultra-short tightly focused Gaussian laser pulses and vacuum laser acceleration,” Appl. Phys. B 81, 813–819 (2005).
[CrossRef]

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J. X. Wang, Y. K. Ho, L. Feng, Q. Kong, P. X. Wang, Z. S. Yuan, and W. Scheid, “High-intensity laser-induced electron acceleration in vacuum,” Phys. Rev. E 60, 7473–7478 (1999).
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L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
[CrossRef]

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H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
[CrossRef] [PubMed]

Zolotorev, M. S.

G. V. Stupakov and M. S. Zolotorev, “Ponderomotive laser acceleration and focusing in vacuum for generation of attosecond electron bunches,” Phys. Rev. Lett. 86, 5274–5277 (2001).
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Y. I. Salamin, “Fields of a Gaussian beam beyond paraxial approximation,” Appl. Phys. B 86, 319–326 (2007).
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[CrossRef]

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J. A. van Kan, A. A. Bettiol, and F. Watt, “Three-dimensional nanolithography using proton beam writing,” Appl. Phys. Lett. 83, 1629–1631 (2003).
[CrossRef]

Y. I. Salamin and C. H. Keitel, “Subcycle high electron acceleration by crossed laser beams,” Appl. Phys. Lett. 77, 1082–1084 (2000).
[CrossRef]

Cancer (1)

S. E. Combs, A. Nikoghosyan, O. Jaekel, C. P. Karger, T. Haberer, M. W. Münter, P. E. Huber, J. Debus, and D. Schulz-Ertner, “Carbon ion radiotherapy for pediatric patients and young adults treated for tumors of the skull base,” Cancer 115, 1348–1355 (2009).
[CrossRef] [PubMed]

Nature (2)

H. Schwoerer, S. Pfotenhauer, O. Jäckel, K.-U. Amthor, B. Liesfeld, W. Ziegler, R. Sauerbrey, K. W. D. Ledingham, and T. Esirkepov, “Laser-plasma acceleration of quasi-monoenergetic protons from microstructured targets,” Nature 439, 445–448 (2006).
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Nature Physics (2)

J. Fuchs, P. Antici, E. d’Humières, E. Lefebvre, M. Borghesi, E. Brambrink, C. A. Cecchetti, M. Kaluza, V. Malka, M. Manclossi, S. Meyroneinc, P. Mora, J. Schreiber, T. Toncian, H. Pépin, and P. Audebert, “Laser-driven proton scaling laws and new paths towards energy increase,” Nature Physics 2, 48–54 (2006).
[CrossRef]

L. Robson, P. T. Simpson, R. J. Clarke, K. W. D. Ledingham, F. Lindau, O. Lundh, T. McCanny, P. Mora, D. Neely, C.-G. Wahlström, M. Zepf, and P. McKenna, “Scaling of proton acceleration driven by petawatt-laser-plasma interactions,” Nature Physics 3, 58–62 (2007).
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[CrossRef]

E. Esarey, P. Sprangle, and J. Krall, “Laser acceleration of electrons in vacuum,” Phys. Rev. E 52, 5443–5453 (1995).
[CrossRef]

Phys. Rev. Lett. (3)

A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, “Effect of plasma scale length on multi-MeV proton production by intense laser pulses,” Phys. Rev. Lett. 86, 1769–1772 (2001).
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[CrossRef] [PubMed]

K. W. D. Ledingham, P. McKenna, and R. P. Singhal, “Applications for nuclear phenomena generated by ultra-intense lasers,” Science 300, 1107–1111 (2003).
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The Review of Laser Engineering (1)

Z. Major, S. Trushin, I. Ahmad, M. Siebold, C. Wandt, S. Klingebiel, T.-J. Wang, J. A. Fülöp, A. Henig, S. Kruber, R. Weingartner, A. Popp, J. Osterhoff, R. Hörlein, J. Hein, V. Pervak, A. Apolonski, F. Krausz, and S. Karsch, “Basic concepts and current status of the petawatt field synthesizer – a new approach to ultrahigh field generation,” The Review of Laser Engineering 37, 431–436 (2009).

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Figures (3)

Fig. 1
Fig. 1

(Color online) (a) The protons, produced by laser-plasma interaction, are injected with the angle θi with respect to the propagation direction of a pulsed beam through its focus. The laser field polarization is denoted by E and the propagation direction is given by k. The protons are ejected out of the focus in the polarization direction E. (b) Here, the protons are injected through the intersection point of two pulsed beams with crossing half-angle θ. The laser field polarizations are denoted by E1 and E2 and their propagation directions are given by k1 and k2. The protons are ejected in direction of the resulting electric field E.

Fig. 2
Fig. 2

(Color online) (a) Intensity profile of two crossed Gaussian beams in the propagation plane y = 0. For visualization purpose the crossing-half angle is set to θ = 35°. The brighter areas correspond to higher field intensities. (b) Vector field plot of the polarization plane z = 0 at t = 0.2 fs for the single beam scheme (blue arrows) with power P and crossed beam scheme (red arrows) with power P/2 for each beam. The constructive interference of the crossed beams results in a higher electric field strength in the intersection volume. The background of the graph shows a density map of the electric field strength |E| of two crossed beams in the polarization plane.

Fig. 3
Fig. 3

Kinetic energy K for one proton initially being at rest and located at x = z = λ/30 and y = 0. The initial time is ti = 0 (dashed line) and ti = −10Δt (full line). The single proton dynamics is compared at same laser parameters.

Tables (1)

Tables Icon

Table 1 Average particle kinetic energy and its percentual spread for different laser system parameters. Ni = ni · Vfocus is the number of ions one can accelerate as one bunch with n i S LPA 10 21 cm 3 and n i TNSA 10 19 cm 3 is the ion density of the source used and Vfocus denotes the volume initially containing all ions. The crossing half-angle is θ = 3°. The optimal particle injection angle for the single beam set-up is θi = 3° for the S-LPA source and θi = 50° in case of the TNSA source, respectively. For two crossed beams the particles are injected with an angle θc with respect to the symmetry axis (z-axis) of the laser beam configuration. In case of the S-LPA source we have θc = 0° and for the TNSA source θc = 50°.

Equations (5)

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

E exp ( ( t z / c ) 2 2 Δ t 2 ) E , B exp ( ( t z / c ) 2 2 Δ t 2 ) B ,
d p j d t = q ( E ( r j ) + E j int . + c β j × ( B ( r j ) + B j int . ) ) , d j d t = qc β j ( E ( r j ) + E j int . ) .
ϕ j k = q 4 π ɛ 0 1 | r j r k | ,
A j k = q 8 π ɛ 0 c 2 | r j k | ( v k + r j k ( v k r j k ) | r j k | ) ,
E x = ( E 1 x + E 2 x ) cos θ + ( E 1 z E 2 z ) sin θ , E y = E 1 y + E 2 y , E z = ( E 1 x + E 2 x ) sin θ + ( E 1 z + E 2 z ) cos θ , B x = ( B 1 z B 2 z ) sin θ , B y = B 1 y + B 2 y , B z = ( B 1 z + B 2 z ) cos θ .

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