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Unformatted text preview: associated return current. start to accelerate ions. As a rough estimate, a test ion crossing the sheath would acquire the energy E i $ ZeEs Ls ¼ ZTh ,
resulting in MeV energies and a scaling as I 1=2 if Th ’ E p
given by Eq. (6) holds. Protons from a thin layer of hydrogencontaining impurities on the surface will be in a very favorable condition for acceleration because of both their initial
position, located at the maximum of the ﬁeld, and their
highest charge-to-mass ratio so that they will be more rapid
than heavier ions in following electrons and screening the
sheath ﬁeld. This is the qualitative scenario for TNSA of
protons as introduced by Wilks et al. (2001) to explain their
experimental results on proton acceleration (Hatchett et al.,
2000; Snavely et al., 2000).
The essential features of the TNSA mechanism have been
supported by several experiments and TNSA has become the
reference framework to interpret observations of multi-MeV
protons from the target rear side. Various schemes for beam
optimization and control have been designed on the basis of
TNSA. Detailed discussions of main experimental ﬁndings
are reported in Secs. III.A, III.B, and III.E.
From a theoretical viewpoint, there are two main categories of models which describe TNSA, namely, ‘‘static’’ and
‘‘dynamic’’ models which, depending on the starting assumptions, allow one to provide simpliﬁed analytical descriptions
useful for interpreting experimental data. These models and
related numerical investigations are presented in Sec. III.C.
2. Front surface acceleration Already in the ﬁrst measurements of proton acceleration in
the forward direction, the possibility of a contribution originating at the front surface of the target was conceived (Clark
et al., 2000a; Maksimchuk et al., 2000). As a consequence,
mechanisms leading to ion acceleration in such a region have
also been extensively investigated.
At the front surface, the intense radiation pressure of the laser
pulse pushes an overdense target inward, steepening the density
proﬁle and bending the surface; this process is commonly named
hole boring. The recession velocity vHB of the plasma surface Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . may be estimated by balancing the electromagnetic and mass
momentum ﬂows I=c $ ni ðmi vHB ÞvHB . This corresponds to an
energy per nucleon E i ¼ mp v2 =2 $ I=Ani c. The scaling with
the laser intensity I is more favorable than the I 1=2 scaling for
TNSA and suggests that RPA effects should become more
important for higher intensities. More accurate, relativistic, and
dynamic modeling is presented in Sec. IV.A.1 along with related
Radiation pressure action and hot electron temperature
may also lead to the generation of collisionless shock waves
(Tidman and Krall, 1971) with high Mach number M. Such
waves are associated with the reﬂection of ions from
the shock fron...
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