Abstract

Fields of a radially polarized petawatt laser beam, represented by a truncated series in the diffraction angle ϵ to order ϵ15 and focused to subwavelength waist radius, are shown to accelerate protons and bare nuclei to several hundred MeV per nucleon over a distance equivalent to a few laser wavelengths.

© 2007 Optical Society of America

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Corrections

Yousef I. Salamin, "Acceleration in vacuum of bare nuclei by tightly focused radially polarized laser light: erratum," Opt. Lett. 33, 1662-1662 (2008)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-33-15-1662

References

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  1. http://www.teslasociety.com/teslafacil.htm.
  2. O. Jäkel, D. Schulz-Ertner, C. P. Karger, P. Heeg, and J. Debus, Nucl. Instrum. Methods Phys. Res. B 241, 717 (2005); http://www.gsi.de/portrait/beschleunigeranlagelowbare.html; http://www.wanjiehospital.com/porton/program.htm.
    [CrossRef]
  3. A. Alves, P. Reichart, R. Siegele, P. N. Johnston, and D. N. Jamieson, Nucl. Instrum. Methods Phys. Res. B 249, 730 (2006).
    [CrossRef]
  4. Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
    [CrossRef]
  5. Y. I. Salamin, Opt. Lett. 32, 90 (2007).
    [CrossRef]
  6. K. T. McDonald, puhep1.princeton.edu/~mcdonald/examples/axicon.pdf.
  7. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).
  8. R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  9. Y. I. Salamin, Opt. Lett. 31, 2619 (2006).
    [CrossRef] [PubMed]
  10. Y. I. Salamin, New J. Phys. 8, 133 (2006).
    [CrossRef]
  11. V. V. Kulagin, V. A. Cherepenin, and H. Suk, Phys. Plasmas 11, 5239 (2004).
    [CrossRef]
  12. M. D. Perry, D. Pennington, B. C. Stuart, G. Tietbohl, J. A. Britten, C. Brown, S. Herman, B. Golick, M. Kartz, J. Miller, H. T. Powell, M. Vergino, and V. Yanovsky, Opt. Lett. 24, 160 (1999).
    [CrossRef]

2007 (1)

2006 (4)

Y. I. Salamin, Opt. Lett. 31, 2619 (2006).
[CrossRef] [PubMed]

Y. I. Salamin, New J. Phys. 8, 133 (2006).
[CrossRef]

A. Alves, P. Reichart, R. Siegele, P. N. Johnston, and D. N. Jamieson, Nucl. Instrum. Methods Phys. Res. B 249, 730 (2006).
[CrossRef]

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
[CrossRef]

2005 (1)

O. Jäkel, D. Schulz-Ertner, C. P. Karger, P. Heeg, and J. Debus, Nucl. Instrum. Methods Phys. Res. B 241, 717 (2005); http://www.gsi.de/portrait/beschleunigeranlagelowbare.html; http://www.wanjiehospital.com/porton/program.htm.
[CrossRef]

2004 (1)

V. V. Kulagin, V. A. Cherepenin, and H. Suk, Phys. Plasmas 11, 5239 (2004).
[CrossRef]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2001 (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).

1999 (1)

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, Appl. Phys. B 72, 109 (2001).

New J. Phys. (1)

Y. I. Salamin, New J. Phys. 8, 133 (2006).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (2)

O. Jäkel, D. Schulz-Ertner, C. P. Karger, P. Heeg, and J. Debus, Nucl. Instrum. Methods Phys. Res. B 241, 717 (2005); http://www.gsi.de/portrait/beschleunigeranlagelowbare.html; http://www.wanjiehospital.com/porton/program.htm.
[CrossRef]

A. Alves, P. Reichart, R. Siegele, P. N. Johnston, and D. N. Jamieson, Nucl. Instrum. Methods Phys. Res. B 249, 730 (2006).
[CrossRef]

Opt. Lett. (3)

Phys. Plasmas (1)

V. V. Kulagin, V. A. Cherepenin, and H. Suk, Phys. Plasmas 11, 5239 (2004).
[CrossRef]

Phys. Rev. A (1)

Y. I. Salamin, Phys. Rev. A 73, 043402 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Other (2)

K. T. McDonald, puhep1.princeton.edu/~mcdonald/examples/axicon.pdf.

http://www.teslasociety.com/teslafacil.htm.

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Figures (3)

Fig. 1
Fig. 1

Energy gain per nucleon of seven different nuclei accelerated by radially polarized laser light of power (a) 1 PW and (b) 10 PW . The wavelength in all cases is λ = 1064 nm , the initial phase ψ 0 = 0 , and Eq. (2) has been integrated from t = 0 to a time t f satisfying the transcendental equation ω t f k z ( t f ) = 20 π . The energy gain is shown versus the laser beam radius at focus for values ranging from w 0 = λ π (which corresponds to ϵ = 1 ) to w 0 = 1.2 λ ( ϵ = 0.265 ) . Initial conditions of rest at the origin of coordinates were assumed.

Fig. 2
Fig. 2

Energy gain per nucleon versus the forward distance of travel along the beam axis, for the nuclei of Fig. 1 and a laser waist radius w 0 = 0.35 λ ( ϵ 0.91 ) . All other parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Energy gain by a proton versus the laser output power for three values of the laser beam radius at focus. Other parameters are the same as in Fig. 1. Shown here also, as curves with symbols, are the corresponding approximate gains calculated from Eq. (9).

Equations (9)

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d p d t = Q [ E + c β × B ] , d E d t = Q c β E ,
d β d t = Q γ M c [ ( E + c β × B ) β ( β E ) ] .
G = ( γ f γ i ) M c 2 ,
E z ( ρ = 0 , ζ , t ) = E 0 { ϵ 2 [ S 2 ] + ϵ 4 [ S 3 2 ] + ϵ 6 [ 3 S 4 8 ] + ϵ 8 [ 3 S 5 8 ] + ϵ 10 [ 15 S 6 32 ] + ϵ 12 [ 45 S 7 64 ] + ϵ 14 [ 315 S 8 256 ] } ,
P = π w 0 2 2 E 0 2 c μ 0 ( ϵ 2 ) 2 [ 1 + 3 ( ϵ 2 ) 2 + 9 ( ϵ 2 ) 4 + 30 ( ϵ 2 ) 6 + 225 2 ( ϵ 2 ) 8 + 12203 32 ( ϵ 2 ) 10 3445 32 ( ϵ 2 ) 12 928671 128 ( ϵ 2 ) 14 ] ,
S n = ( w 0 w ) n sin ( ψ + n ψ G ) , n = 2 , 3 , ,
w = w 0 1 + ζ 2 ,
ψ = ψ 0 + ω t k z , ψ G = tan 1 z z r ,
G [ MeV nucleon ] Z A β ( λ π w 0 ) 2 240 P [ TW ] ,

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