Clinical trials using accelerated heavy charged‐particle beams for treating cancer and other diseases have been performed for nearly four decades. Recently there have been worldwide efforts to construct hospital‐based medically dedicated proton or light‐ion accelerator facilities. To make such accelerated heavy charged‐particle beams clinically useful, specialized instruments must be developed to modify the physical characteristics of the particle beams in order to optimize their biological and clinical effects. This article reviews the beam modifying devices and associated dosimetric equipment developed specifically for controlling and monitoring the clinical beams.

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Instrumentation for Treatment of Cancer Using Proton and Light-Ion Beams

The knowledge of proton depth-dose curves, or “Bragg curves,” is a fundamental prerequisite for dose calculations in radiotherapy planning, among other applications. In various cases it is desirable to have an analytical representation of the Bragg curve, rather than using measured or numerically calculated data. This work provides an analytical approximation of the Bragg curve in closed form. The underlying model is valid for proton energies between about 10 and 200 MeV. Its main four constituents are: (i) a power-law relationship describing the range-energy dependency; (ii) a linear model for the fluence reduction due to nonelastic nuclear interactions, assuming local deposition of a fraction of the released energy; (iii) a Gaussian approximation of the range straggling distribution; and (iv) a representation of the energy spectrum of poly-energetic beams by a Gaussian with a linear “tail.” Based on these assumptions the Bragg curve can be described in closed form using a simple combination of Gaussians and parabolic cylinder functions. The resulting expression can be fitted to measurements within the measurement error. Very good agreement is also found with numerically calculated Bragg curves.

An analytical approximation of the Bragg curve for therapeutic proton beams

Range modulators for protons and heavy ions

Passage of Heavy Particles through Matter

In order to interpret cosmogenic radionuclides in extraterrestrial matter one has to differentiate between p- and α-induced reactions with solar (SCR) and with galactic (GCR) cosmic rays. Our earlier studies have shown that for a satisfactory description of GCR-interactions with dense matter rather few but characteristic high energy cross sections are required. In contrast, for the low and medium energy SCR-production a detailed knowledge of the respective nuclear reactions is needed. In the present study, excitation functions are presented for 39 p-induced reactions on Ni, Fe, Mn, Cr and Ti, which contribute to SCR-produced radionuclides (44≤A≤59) at energies up to 200 MeV. The excitation functions are based mainly on our own cross section measurements, partly on hybrid model predictions and to a lesser extent on experimental data from other authors. Based on these excitation functions, depth profiles for the proton induced SCR-production of46Sc,44Ti,48V,51Cr,52Mn,53Mn,54Mn,55Fe,56Co,57Co,58Co,60Co and59Ni from the 5 major targets mentioned before in extraterrestrial matter are calculated, assuming normal lunar surface conditions. Typical rigidities were adopted for the solar proton fluxes, ranging from 50 to 150 MV, which cover the rigidity values commonly observed in solar flares. In order to derive depth dependent p-fluxes from calculations of the energy loss of incoming particles, rather large differences in the respective chemical compositions had to be considered. The theoretical profiles are compared with experimental data from lunar samples, and several cosmochemical applications are discussed. They range from the study of single solar flare events by short-lived radioisotopes to the investigation of supposed long-term variations of the solar flare activity on a large times-cale of millions of years. The latter is possible by comparing the production rates of very long-lived nuclides (as for example53Mn with T=3,8·106 y) with that of short- or medium-lived nuclides. In this respect, the particular importance of44Ti (T-47.3 y) for measuring today's mean solar flare activity is pointed out. In general, the depth dependent production rates established in this work enable one to estimate the SCR-contributions to cosmogenic radionuclides from the respective target elements, thus providing a basis for a better understanding of the solar cosmic ray interaction with extraterrestrial matter.

Robert R. Wilson

Papers

Range, Straggling, and Multiple Scattering of Fast Protons

Proton-Proton Scattering at 14.5 Mev