## 4 Rationale of Proton Beam Therapy  
Although at the time of diagnosis, about 50% of cancers have not yet metastasized, cancer remains a major cause of death nowadays [32, 33]. In cases where it is possible to intervene clinically, tumours can be treated with therapies as surgery, chemotherapy, and radiotherapy, often used in combination; despite this, in only 80% of cases, medical treatments are successful in completely removing the tumours or inclutivating them [34]. Hadron therapy is an increasingly diffused radiation treatment modality that uses beams of accelerated charged particles as a tool for tumours treatments [35]. Conventional radiotherapy, which uses high-energy photons, is mainly useful for the treatment of superficial tumours due to the release of energy in matter with an exponentially decreasing trend with depth [36]. Furthermore, at equal doses, photons are radiobiologically less effective than particle beams, especially those heavy as carbon ones. The greater ballistic accuracy in the dose delivered to the tumour volume and the higher radiobiological effectiveness, considering the carbon ions, are the main clinically relevant advantages of hadron therapy in respect of the conventional radiotherapy. The first property is directly related to the type of energy deposition along and around the path of ion beams in the matter, described by the well-known Bragg curve. It results in a greater sparing of normal tissue and/or organs at risk compared to photons. The second propriety, on the other hand, depends on the different response of the tumour cells to ionizing radiations of different quality; in general  
Figure 3: Comparison of the calculated SR brilliance of a 3 GeV SR source (red), a Globar (black), and an ideal bending magnet SR diffraction limited source (blue). Reprinted with permission from Reference [5]. term, in fact, the biological effectiveness, that is, the ability to suppress more cells at an equal amount of dose, increases as the number Z of the particles used increase. Indeed, significant progress in the treatment of deep-seated and/or radioresistant tumours have been achieved using mainly protons and carbon ions particle therapy. The possible use of beams with lower or higher atomic number (Z) particles, such as helium, lithium or oxygen, [37], in the clinic, is currently a main subject of study. When charged particles interact with matter, the continuum of the ionization events produced by ions (the track structure) is related to the particles' energy, and for a given energy, to Z. It is important to evidence that even at equal/similar linear energy transfer (LET) values (a parameter used to describe the local energy deposition from particles in the matter), particles with different Z can cause qualitatively and quantitatively different biological effects owing to secondary ionization events, consequently to their track structure. For these reasons, it would be useful to evaluate the damage level along the whole path of the charged particle beam in order to determine the relative biological effectiveness (RBE) changes along the entire Bragg curve. Obviously, experimental studies are mainly concentrated into the spread-out Bragg peak (SOBP) region (Figure 4), which can be seen as a \"broadened\" peak that is obtained, during therapies, as a convolution of multiple mono-energetic Bragg curves, modulating the particle beam energy to uniformly contour the tumoral region. The main physical motivation of the use of hadrons in tumour therapy is the high value obtainable for the ratio between the energy deposited in the SOBP and the one delivered at the beam entrance/plateau region, which can reach the order of two or even three for carbon ions.