## 3 Pulsed Ion Beams (Protons and Carbon Ions): Laser-Driven Source Features
### Typical Ion Energy Spectra  
We do not discuss the laser acceleration processes in detail but refer readers to the many papers written on this subject; in particular, two new reviews ([16, 17] [PERSON], [PERSON]). The laser and target parameter regime relevant to the Target Normal Sheath Acceleration (TNSA) scheme [29, 30, 31] (or a variant of it) is the most studied. A conceptual description of this process is now given. A short, high-intensity laser pulse is incident on a thin target of any number of different materials, which invariably has hydrogen-bearing contaminant layers on its surfaces. These targets are characteristically a few microns thick and because of this, the laser pulse is mostly reflected. The laser prepulse ionizes the front surface to form a preplasma of electrons and ions. The subsequent main laser pulse is partially absorbed in this preplasma and accelerates the electrons in the forward direction to relativistic velocities (_i.e._, high temperatures) from the front surface to the back surface. The hot electrons and cool ions at the target back surface generate a charge separation and therefore  
Figure 1: The relative radiation dose deposited as a function of tissue depth for various particle and photon beams. an electrostatic extraction field over a few microns which accelerates back-surface protons and other ions in this field region. The whole process occurs within a vacuum environment. A sketch of the TNSA process is given in Figure 2. Extracting energetic particles from the vacuum then requires transmission through a thin vacuum window. Laser-accelerated ion spectra from thick targets feature a broad energy spread which is much greater than the monochromatic case typical of proton and heavy ion beams produced by conventional accelerators (in this work conventional means not laser-driven). In fact, the energy spread in the TNSA regime can exceed 100% with relatively few ions at the higher energies needed for proton irradiation of deep seated tumors. Moreover, laser driven ion beams at the source (laser target) have a characteristically wide angular divergence (half angle near 10\({}^{\circ}\)-20\({}^{\circ}\)) as well as a short bunch duration (ps) which are very different from conventional accelerator produced beams. Figure 3 shows data taken using picosecond laser pulses provided by the Vulcan laser at the Rutherford Appleton Laboratory (STFC-RAL). The displayed spectral profile is quasi-exponential with a high energy cutoff or maximum value. Laser and target (_i.e.,_ combined source) parameters can determine the maximum proton energy. We note that there are fundamentally very few particles at the cutoff energy and that the cutoff value is likely to be a demonstrably unstable (shot-to-shot) feature of the spectrum. It is not assumed to be an operation energy for a laser-driven accelerator. Instead, its value is in spectral characterization and comparison with simulated prediction. The scaling of the maximum proton energy using long pulse glass lasers (\(\sim\)picosecond pulse duration) is shown in Figure 4 and Figure 5 shows its variation with pulse duration and laser power where it is clearly steeper for shorter pulse durations. The angular divergence of the emitted ion beam behind the target is much smaller than that in front of the target. For a given laser power on target the maximum proton energy increases markedly with pulse duration as revealed in Figure 5. At the time of writing the maximum reported proton energy was about 70 MeV in the TNSA acceleration regime. This is well below the energy necessary for ion beam treatment of deep seated tumors. However, ocular tumors could be treated at this energy. Figure 2: A simple sketch of ion beam generation, and acceleration by the Target Normal Sheath Acceleration (TNSA) mechanism, showing the extreme laminarity of the beams. At this stage the beams are not neutral although quasi-neutrality becomes evident further from the target.