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Unformatted text preview: ’ vHB implies that ‘‘reﬂected’’ ions directed into
the bulk will have a velocity $2vHB , i.e., twice the surface recession
velocity, as the fastest ions generated by the piston action in HB
acceleration (see Sec. IV.A.1). This similarity may explain why HB
and CSA are often confused in the literature. 778 Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . strongly relativistic limit a0 ) 1 the condition to obtain
supersonic shocks driven by radiation pressure (M > 1) can
be written as 2a0 > ne =nc . The reﬂected ions may get
further acceleration by the transient sheath ﬁeld at the rear
surface as in TNSA, eventually producing a plateau in the ion
spectrum. A similar signature was observed experimentally
by Zepf et al. (2003) and thus interpreted as evidence of the
front side contribution to ion acceleration, in contrast to pure
TNSA at the rear side of the target. Under particular conditions, the staged CSA-TNSA acceleration might produce
the highest energy component in the ion spectrum as observed
in simulation studies (d’Humieres et al., 2005; Chen et al.,
2007) which, however, also suggest lower efﬁciency and
brilliance with respect to pure TNSA.
Recently, CSA has been indicated as the mechanism
responsible for monoenergetic acceleration of protons up
to 22 MeV (see Fig. 28) in the interaction of CO2 laser
pulses with hydrogen gas jets at intensities up to 6:5 Â
1016 W cmÀ2 corresponding to a0 ¼ 2:5 (Haberberger
et al., 2012). The particular temporal structure of the laser
pulse, i.e., a 100 ps train of 3 ps pulses, was found to be
essential for the acceleration mechanism, since no spectral
peaks were observed for a smooth, not modulated pulse.
Comparison with PIC simulations suggested that the multiple pulses lead to efﬁcient generation of suprathermal
electrons, and that this process (rather than radiation pressure) drives the shocks which eventually accelerate protons.
Simulations also suggest that the process could scale in order
to produce 200 MeV protons at 1018 W cmÀ2 that may be
foreseeable with future CO2 laser development. Such a
scheme based on gas lasers and gas jet target would have
the advantage of high-repetition rate operation, but the
efﬁciency per shot might be low with respect to other
approaches: in the experiment of Haberberger et al. (2012)
the number of ions ($ 2:5 Â 105 ) in the narrow spectral peak
at ’ 22 MeV for a 60 J pulse energy implies a conversion
efﬁciency of $10À8 .
In addition to collisionless shocks, the standard ﬂuid theory
also predicts solitons (Tidman and Krall, 1971) propagating
at the velocity vsol with 1 < vsol =cs & 1:6. These solitons are
characterized by ZeÈmax < mi v2 =2 and are thus transparent
to background ions ‘‘by construction.’’ However, the generation of electrostatic solitons may lead to ion acceleration in
some circumstances, e.g., when the soliton breaks in the...
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