And ion acceleration involving collective and self

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Unformatted text preview: llective and self-organization effects, is apparent. Unfolding such dynamics requires the use of self-consistent electromagnetic (EM), kinetic simulations. To this aim, the particle-in-cell (PIC) method (see Sec. II.D) is by far the most commonly used approach. Large-scale, multidimensional PIC simulations running on parallel supercomputers are an effective support for the design and interpretation of laser-plasma acceleration experiments, although fully ‘‘realistic’’ simulations in three spatial dimensions and for actual laser and target parameters are most of the time still beyond computational capabilities. These limitations further motivate the development of complementary, reduced simulation models. These issues are further discussed in Secs. II.D and III.C.4. A comprehensive description of laser-plasma dynamics is far beyond the scope of this work and can be found in recent books and reviews (Gibbon, 2005b; Mourou, Tajima, and Bulanov, 2006; Mulser and Bauer, 2010). In Secs. II.A and II.B we describe only a few basic issues of relevance to the understanding of ion acceleration mechanisms. The main mechanisms are first introduced in a compact form in Sec. II.C, leaving a detailed discussion to the following Secs. III and IV. II. LASER ION ACCELERATION IN A NUTSHELL A. Laser interaction with overdense matter In this work we mostly refer to ion acceleration occurring in the interaction with solid targets, where the electron density ne greatly exceeds the so-called critical or cutoff density, nc ¼   me !2  À2 ¼ 1:1 Â 1021 cmÀ3 : 1 m 4e2 (1) The condition ne ¼ nc is equivalent to !p ¼ !, where !p ¼ ð4ne e2 =me Þ1=2 and ! ¼ 2c= are the plasma and laser frequencies, respectively. Since the linear refractive index of the plasma is n ¼ ð1 À !2 =!2 Þ1=2 ¼ ð1 À ne =nc Þ1=2 , in the p ne > nc ‘‘overdense’’ region n has imaginary values and the laser pulse cannot propagate. All the laser-plasma interaction occurs either in the ‘‘underdense’’ region where ne < nc or near the ‘‘critical’’ surface at which ne ’ nc . Relativistic effects make the refractive index nonlinear. Qualitatively speaking, the relativistic refractive index Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 describing the propagation of a plane wave with vector potential A ¼ Aðx; tÞ is obtained from the linear expression by replacing the electron mass with the quantity me , where the relativistic factor is given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2) ¼ 1 þ h a2 i ¼ 1 þ a 2 = 2 ; 0 where a ¼ eA=me c2 , and the angular brackets denote an average over the oscillation period. The parameter a0 is the commonly used ‘‘dimensionless’’ amplitude related to the laser intensity I by1 a0 ¼ 0:85  I2 m  1018 W cmÀ2 1=2 ; (3) where we used I ¼ chE2 i=4 to relate the electric field E ¼ Àð1=cÞ@A=@t to the laser intensity I ....
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This document was uploaded on 09/28/2013.

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