Aspects of Fast-Ion Dosimetry

Abstract

A first step in the dosimetry of fast-ion beams is the determination of accurate Bragg (ionization) functions. Bragg functions for several substances have been measured and calculated for 3480 MeV carbon ions. In the measurements, the ions first traverse an absorber in which the energy is reduced to either 1900 or 1200 MeV, then a "range gauge" followed by a thin ionization chamber. Functions are calculated with an analytical method using convolutions of straggling functions. This approach gives results without the stochastic variations implicit in Monte Carlo methods. The comparison of measured and calculated functions shows how reliable the calculations are. An important part of the calculations is the determination of the total range of the ions. The range can be determined from the Bragg function. The measured range is given by the sum of the thickness of the absorber and the residual range measured with the range gauge. For water, the range is about 150 mm, and the precision of the measurements is +/-0.05 mm. Because the ion energy at the surface of the absorber fluctuates with time, measurements with water are used to define this energy. Thus the ranges (or average stopping powers) in absorbers are obtained relative to those in water. Measured ranges R(m) are compared with ranges R(0) calculated with a current version of the Bethe theory. For light absorbers (atomic number Z < 20), differences between R(m) and R(0) are less than +/-0.3 mm; for Z > 20 differences are between 0 and +/-0.6 mm. This agreement between calculated and measured ranges confirms the value I = 80 eV for water measured earlier for protons. The ionization by nuclear fragments is obtained from the difference between measured and calculated ionization functions, and has little influence on the ranges of the primary ions.

Energy‐range relation and mean energy variation in therapeutic particle beams

“…A simplified and improved scaling law for target mixtures and compounds was obtained when the mean charge to mass ratio was calculated according to Z A / M A = ͚ i N i ͑Z i / M i ͒ / ͚ i N i . This resulted in better agreement between the universal range relation and experimental data 12,21 than the common Bragg rule. The analytical mean energy expression, illustrated in Figs.…”

“…and carbon21 ions of different energies in low atomic number materials, such as lucite ͑PMMA͒, polyethylene, polypropylene, polycarbonate, and teflon ͑Fig.2 and Table IV͒. In Fig.…”

Calculated depth-dose distributions for H+ and He+ beams in liquid water

“…From the ELF the mean excitation energy I can be calculated [22], for which we obtain 79.4 eV for liquid water. Other values available in the literature are 75 ± 3 eV [23,24], 79.7 ± 2 eV [25,26], 77 eV [27], and 81.8 eV [28], 80.7 eV [29] and 82.4 eV [30] (depending on the database used for oxygen's K-shell optical oscillator strength), 78.4 ± 1 eV [31] and 80.8 ± 2 [32]. As can be seen, a value of $80 eV for the mean excitation energy of liquid water prevails over the effective value of 67.2 eV used [33] for recent stopping data tables of liquid water [34].…”

Basics of particle therapy I: physics

“…In the interaction, evaporated nucleons (changing the characteristics of the nucleons) and light clusters are produced. The importance of the fragments depends upon how it affects the absorbed dose distribution in linear energy transfer (LET) which in turn depends upon the nature of the medium, ion type and its energy [20]. Further, these effects increase as a function of the beam energy.…”