Abstract

In the study of laser-driven electron acceleration, it has become customary to work within the framework of paraxial wave optics. Using an exact solution to the Helmholtz equation as well as its paraxial counterpart, we perform numerical simulations of electron acceleration with a high-power TM01 beam. For beam waist sizes at which the paraxial approximation was previously recognized valid, we highlight significant differences in the angular divergence and energy distribution of the electron bunches produced by the exact and the paraxial solutions. Our results demonstrate that extra care has to be taken when working under the paraxial approximation in the context of electron acceleration with radially polarized laser beams.

© 2013 Optical Society of America

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2012 (2)

V. Marceau, A. April, and M. Piché, Opt. Lett. 37, 2442 (2012).
[CrossRef]

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

2011 (1)

K. P. Singh and M. Kumar, Phys. Rev. ST—Accel. Beams 14, 030401 (2011).
[CrossRef]

2010 (3)

2008 (3)

K. Nakajima, Nat. Phys. 4, 92 (2008).
[CrossRef]

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

A. April, Opt. Lett. 33, 1563 (2008).
[CrossRef]

2007 (3)

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 104, 18409 (2007).
[CrossRef]

Y. I. Salamin, Opt. Lett. 32, 90 (2007).
[CrossRef]

2006 (2)

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

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

2005 (1)

C. Varin, M. Piché, and M. A. Porras, Phys. Rev. E 71, 026603 (2005).
[CrossRef]

1999 (1)

April, A.

Baum, P.

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 104, 18409 (2007).
[CrossRef]

Brunetti, E.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Budde, F.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Debus, A.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Fortin, P.-L.

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Fourmaux, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Gallacher, J. G.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Haupt, K.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Jäckel, O.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Jaroszynski, D. A.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Karmakar, A.

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Kärtner, F. X.

Kieffer, J.-C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Kumar, M.

K. P. Singh and M. Kumar, Phys. Rev. ST—Accel. Beams 14, 030401 (2011).
[CrossRef]

Légaré, F.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

MacLean, J.-P.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Marceau, V.

Nakajima, K.

K. Nakajima, Nat. Phys. 4, 92 (2008).
[CrossRef]

Payeur, S.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Pfotenhauer, S.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Piché, M.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

V. Marceau, A. April, and M. Piché, Opt. Lett. 37, 2442 (2012).
[CrossRef]

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

C. Varin, M. Piché, and M. A. Porras, Phys. Rev. E 71, 026603 (2005).
[CrossRef]

Porras, M. A.

C. Varin, M. Piché, and M. A. Porras, Phys. Rev. E 71, 026603 (2005).
[CrossRef]

Pukhov, A.

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Rohwer, E.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Saghafi, S.

Salamin, Y. I.

Y. I. Salamin, Opt. Lett. 32, 90 (2007).
[CrossRef]

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

Schlenvoigt, H.-P.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Schmidt, B. E.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Schwoerer, H.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Shanks, R. P.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Sheppard, C. J. R.

Singh, K. P.

K. P. Singh and M. Kumar, Phys. Rev. ST—Accel. Beams 14, 030401 (2011).
[CrossRef]

Tchervenkov, C.

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

Varin, C.

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

C. Varin, M. Piché, and M. A. Porras, Phys. Rev. E 71, 026603 (2005).
[CrossRef]

Wiggins, S. M.

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Wong, L. J.

Zewail, A. H.

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 104, 18409 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

S. Payeur, S. Fourmaux, B. E. Schmidt, J.-P. MacLean, C. Tchervenkov, F. Légaré, M. Piché, and J.-C. Kieffer, Appl. Phys. Lett. 101, 041105 (2012).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. B (1)

P.-L. Fortin, M. Piché, and C. Varin, J. Phys. B 43, 025401 (2010).
[CrossRef]

Laser Part. Beams (1)

A. Karmakar and A. Pukhov, Laser Part. Beams 25, 371 (2007).
[CrossRef]

Nat. Phys. (2)

K. Nakajima, Nat. Phys. 4, 92 (2008).
[CrossRef]

H.-P. Schlenvoigt, K. Haupt, A. Debus, F. Budde, O. Jäckel, S. Pfotenhauer, H. Schwoerer, E. Rohwer, J. G. Gallacher, E. Brunetti, R. P. Shanks, S. M. Wiggins, and D. A. Jaroszynski, Nat. Phys. 4, 130 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. E (2)

C. Varin, M. Piché, and M. A. Porras, Phys. Rev. E 71, 026603 (2005).
[CrossRef]

C. Varin and M. Piché, Phys. Rev. E 74, 045602(R) (2006).
[CrossRef]

Phys. Rev. ST—Accel. Beams (1)

K. P. Singh and M. Kumar, Phys. Rev. ST—Accel. Beams 14, 030401 (2011).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

P. Baum and A. H. Zewail, Proc. Natl. Acad. Sci. USA 104, 18409 (2007).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Electron bunch accelerated by a TM01 pulsed beam with P=1015W, k0a=500, ξ0=14.21, ϕ0=π. The simulation was performed with: (i) the exact fields [Eqs. (1)–(3)], (ii) the paraxial fields [Eqs. (8) and (9)], and (iii) the corrected paraxial fields [Eqs. (5)–(7) up to O(δ3)]. (a) Bunch snapshot; (b) and (c) close-up view of the front end; (d) energy gain distribution; and (e) average energy gain versus final radial coordinate. The electrons are initially at rest outside the laser pulse in the (r,z) plane and distributed randomly according to a Gaussian distribution centered at the origin with σr=σz=λ0/10. The results are computed 15 ps after the passage of the beam at z=0. Only N=200 electrons are shown in (a)–(c), while N=50,000 different initial conditions were used to obtain the results in (d) and (e).

Fig. 2.
Fig. 2.

Normalized amplitude of (a) eEz and (b) e(ErcBϕ) at t=0 (exact fields). During subcycle acceleration, electrons spend most of their time between a maximum of eEz and the minimum located behind [an example is shown by the rectangle in (a) and (b)]. In this phase configuration, electrons travel at vzc and feel, according to (b), a radial force directed outward. Parameters are the same as in Fig. 1.

Equations (11)

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E˜r=jE0ek0aj2(k0R˜)sinθ˜cosθ˜
E˜z=23jE0ek0a[j0(k0R˜)+j2(k0R˜)P2(cosθ˜)]
B˜ϕ=B0ek0aj1(k0R˜)sinθ˜.
P=P0[2k0asinh(2k0a)cosh(2k0a)+12k02a2],
E˜r=12E0[ρf2δ3/2(3jρf3+3ρ3f4j2ρ5f5)δ5/2+O(δ7/2)]exp(jΨ)
E˜z=jE0[(f2jρ2f3)δ2(jf3+5ρ2f47j2ρ4f5ρ6f62)δ3+O(δ4)]exp(jΨ)
B˜ϕ=12B0[ρf2δ3/2(jρf3+2ρ3f4j2ρ5f5)δ5/2+O(δ7/2)]exp(jΨ),
E˜r(0)=12E0ρf2δ3/2exp(jΨ)=cBϕ(0)
E˜z(0)=jE0(f2jρ2f3)δ2exp(jΨ).
drdt=v,dvdt=eγme[E+v×Bvc2(v·E)],
dvrdte(ErvzBϕ)γme.

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