Lecture Notes in Physics

3 Laser-Triggered Nuclear Reactions 29
bubble acceleration [45] can therefore act on the plasma electrons over large
distances of hundreds of microns or even a few millimeters.
The electric field strength generated by a laser wake, that is, by a laserexcited
resonant plasma wave is about 100 GV/cm, allowing for the acceleration
of electrons to energies in the order of 100 MeV [18, 19]. When accelerated
in the broken wave (or bubble) regime, electrons may be quasi monoenergetic
[19, 20, 21, 46].
In the following part of this article, electrons will not be considered as
projectiles that induce nuclear reactions. This is due to the fact that even
if electrons are able to trigger nuclear reactions, this effect will not be measurable.
The cross sections of electron-induced reactions are at least two orders
of magnitude smaller than those of photon-induced reactions. Coinstantaneously,
electrons that are incident on a solid target will always produce
bremsstrahlung. Therefore, photon-induced reactions will always be dominant
and electron-induced reactions can be neglected.
3.2.3 Bremsstrahlung
In Sect. 3.3, nuclear reactions induced by laser-generated energetic photons
will be reviewed. In particular, the spectrum of bremsstrahlung generated
by laser–matter interaction will be used. Therefore, in the following the generation
of bremsstrahlung is recalled and the expected photon spectrum is
derived.
Photons with energies of up to several tens or hundreds of MeV are generated
from the stopping of laser-accelerated electrons inside high-Z materials,
such as tantalum, tungsten, or gold. The number of bremsstrahlung photons
per energy interval d(ω) which are generated by a number of Ne electrons
with energy E in a target with number density n is generally given by
dσγ(E)
dnγ(ω) =nNe dx. (3.4)
d(ω)
Therein dσγ(E)/d(ω) is – in photon energy – the differential cross section for
bremsstrahlung generation. The distance dx, which is travelled by the electrons
inside the target material, is given by the stopping power S = −dE/dx.
In a thick target (with respect to the incident electron energy) where the
electrons are stopped completely because of inelastic scattering processes and
radiation losses, the path length for the electrons is given by
x =
E0
ω
dE
, (3.5)
S
where E0 is the initial electron energy. The lower integration limit follows
from the fact that a photon with energy ω can be produced only by an
electron with at least the same energy value. For high electron energies and