Lecture Notes in Physics

3 Laser-Triggered Nuclear Reactions 27
The mean electron energies obtained by the interaction of a short laser pulse
with solid targets, that is, dense plasmas with a steep density gradient, usually
reach several MeV at laser intensities of 10 19 − 10 20 W/cm 2 . Using prepulses
may lead to an increase of electron energy.
A fraction η of these electrons that are accelerated by the laser–target
interaction enter and traverse the thin solid target. This acceleration of electrons
is the first step to the acceleration of protons and ions by a mechanism
called target normal sheath acceleration (TNSA) [29, 30]: when the electrons
leave the few micrometer thin solid target at the rear surface with an electron
density ne and a temperature kBTe, they leave behind a positively charged
target layer. Thus a high electrostatic space-charge field of the order of
E ≈ kBTe/eλD, λD =(ε0kBTe/e 2 ne) 1/2 , (3.2)
is created, where λD is the Debye-length, with ε0 being the dielectric constant.
The electron density ne = ηNe/(cτLAF) is given by the number of electrons
Ne, which are accelerated during a time span given approximately by the
duration of the laser pulse τL and the focus area AF. c is the speed of light.
η ≈ 10 − 20% is the fraction of energy transferred from the laser pulse energy
into the electrons that are accelerated and transmitted through the target foil.
Therewith from (3.2) it follows that electric fields of about
E = (ηIL)/(ε0c) ≈ 10 12 V/cm (3.3)
can be generated. This high space-charge field causes field ionization of a
few monolayers of rear surface ions, and accelerates them in the direction
of the target normal. Under the poor vacuum conditions during laser-matter
interaction experiments, these first few monolayers consist of hydrocarbon and
water impurities, adsorbed at the target surfaces.
Protons are accelerated first because of their high charge-to-mass ratio.
Typical proton spectra (see Fig. 3.1) show an exponential decay with increasing
energy followed by a sharp cutoff at energies that depend on the square
root of the laser intensity, as can be seen from the above expression for the
field strength. This scaling has been proven experimentally for relativistic
laser intensities as well as by particle-in-cell simulations [24] and an analytical
treatment of the dynamic evolution of the accelerating space-charge field [31].
The cutoff energy as well as the number of acclerated protons depends on
both, the intensity and the energy of the laser pulse. Typically, numbers of
about 10 9 to 10 12 protons with a temperature in the order of hundred keV can
be accelerated [5, 32, 33]. The maximum energies vary between a few MeV
and several tens of MeV. It has been shown in several experiments that the
beam quality of laser-accelerated protons can be superior to proton beams
from classical particle accelerators with respect to low transversal emittance
and a small source size [23]. Only recently it has been demonstrated that even
monoenergetic features in the ion spectra can be generated by structuring the
target surface [35, 47].