Target-normal Sheath Acceleration (TNSA) Mechanism

The ion acceleration discussed so far takes place in the laser focus, and is a direct consequence of the ponderomotive displacement of electrons from their original location. It does not depend on where these electrons are moving, but only on the space charge fields set up by this electron removal. In contrast to that, there is another way of accelerating ions, which depends on the buildup of a large density of these displaced electrons in a region separated from the laser field. The process was first suggested by Wilks et al. [33] after the discovery of collimated beams of high energy protons normal to the rear surface of planar and wedge-shaped targets by several groups ([18, 34, 35]. It was named Target-Normal Sheath Acceleration (TNSA) by its inventor, and is now widely accepted by the laser-plasma commu- nity, although there still remains some controversy about its role under different experimental conditions. I will quickly describe the basic mechanism of TNSA in the following paragraph.

Electrons accelerated by the laser (mainly ponderomotively) penetrate the target in forward direction. The first electrons can escape into vacuum, but in doing so they charge up the target, analog to the estimate given in equations 2.18, 2.19. The charging up of the target prevents further electrons from escaping, so that the hot electrons are bound inside and around the target. The hot electrons can be considered as a separate electron population in the target, with only little interaction with the cold background electrons. One consequence of this presence of a hot electron population is that its density does not apruptly drop to zero at the target (rear) boundary. It rather extends into vacuum at a typical scalelength of about one Debye-length, forming a so-called ”Debye-Sheath” of hot electrons at the target rear surface.

λD = s

kT 0

ne2 . (2.27)

Here T is the temperature of the hot electron component, and n is the density of these electrons at the target rear surface. For typical conditions found at e.g. the LULI laser or the Livermore Petawatt laser, λD is on the order of 1µm. Note that the Debye-Sheath mainly forms at the target rear surface, because the electron momentum is forward directed as dictated by the laser fields. Only if the electrons bounce back in the electrostatic field of the sheath, they can also reach the front surface and set up a second, but weaker sheath there, too. The situation now rep- resents an excess of negative charge in the sheath opposing an excess of positive charge in the bulk of the target, similar to a plate capacitor. In Fig. 2.3 the situ-

ation is depicted schematically for two different times, the left side corresponding to the arrival of the first electrons at the rear surface, and the right side showing the beginning of the ion movement. The electron sheath extending into vacuum

Figure 2.3: Schematics of laser intensity (red), ion density (pink) and hot electron density (blue) for two different times.

acts as a virtual cathode, which can ionize and accelerate target atoms off the rear surface. The electric fields strength caused by this charge imbalance amounts to

Estat ≈kThot/eλD (2.28)

which is on the order of 1 TV/m for typical experimental conditions (Thot ≈1−2 MeV). This field is of the same order of magnitude as the primary laser fields, and therefore is sufficiently strong to ionize light atoms up to He-like electron configu- rations. As the field rises with increasing electron density and temperature in the rising edge of the laser pulse, it subsequently ionizes atoms up to charge states allowed by barrier suppression ionization threshold in a matter of femtoseconds. As soon as the field strength at the back surface of the target reaches the thresh- old for single ionization, the free electrons available now are pinning the field at the rear surface to exactly the ionization value, because for each further increase in field strength a new charge pair is generated, which compensates for the field increase. Thus, only in regions behind the rear surface, the field can increase further and ionize the accelerated singly charged ions up to higher charge states. This means that at the rear surface, a sequence of spatially separated field steps is formed, ionizing the ions up to the maximum charge state. For more detail, the reader should refer to [33, 36, 37]. The scaling of the maximum ion energy and temperature is not well understood up to now. For a given ion species (i.e. mass and charge state) it is highly dependent on the other species accelerated as well. Especially protons with their high charge-to-mass ratio can severely inhibit the acceleration efficiency for all other species [36]. The precise process of field inhibi- tion by protons is still work under progress and subject to a number of theoretical and experimental studies.

We have now discussed the two main mechanisms responsible for ion accelera- tion. These processes represent the first step to efficient neutron production, since they provide the high energy ions needed for triggering the necessary nuclear re- actions. As a next step, different nuclear reactions suitable for neutron generation will be presented.

Neutron Generation and

Detection

3.1

Neutron Generation

In the experiments presented in this work, neutrons are not ”generated” from vacuum, but are, of course, only freed from a bound state, the atomic nucleus. Free neutrons are not stable, but undergo a weak decay with a half-life of _∼614 s into a proton, an electron and an electron-antineutrino. Thus it is not feasible to prepare an ensemble of neutrons without this nuclear binding energy in order to make neutrons from this ensemble readily available. The only viable road to neutron production is to free them from the nuclear potential. The mean energy with which a neutron is bound to the nucleus amounts to _∼8 MeV. This amount of energy has hence to be spent to free it. On the other hand, this binding energy ensures the stability of the bound neutron. The large value of this binding energy is prohibitive for simply trying to kick the neutron out of the nucleus, if efficient neutron production is desired. Indeed, there are various other types of neutron generation reactions as well.