Monte-Carlo calculations of radial dose and restricted-let for protons in water

Abstract

A new Monte-Carlo code for event-by-event simulation of the transport of energetic non-relativistic protons (approximately 0.5-10 MeV) and all their secondary electrons (down to 1 Ry) in both the vapour and liquid phases of water is presented. A unified particle-water inelastic model for both phases of water has been developed based on experimental optical data and elements of the Bethe theory. The model applies to both electrons and heavy-charged particles and is particularly suitable for extension to other media of biological relevance (organic polymers, DNA, etc.). Condensed-phase effects are included in the liquid version (MC4L) by means of the dielectric functions which, essentially, substitute the oscillator-strength used in the vapour version (MC4V). The results in the form of radial dose distributions and spatially restricted linear energy transfer are presented and compared with the literature.

Radial doses around energetic ion tracks and the onset of shock waves on the nanoscale

“…The δ-electron contribution to the radial dose is shown by dash-dotted lines in Figures 2 and 3. As can be seen the δ-electrons account for the large radii tail of the radial dose which compares fairly well with the experimental data for tissue equivalent gas for 1-MeV protons [28] as well as with the results of different Monte Carlo simulations and models for 1-MeV protons and 2-MeV/u carbon ions [29][30][31][32]. The integral of the radial dose coming from δ-electrons is shown in Figure 3 by dash-dotted lines and accounts for an important fraction of the total energy deposited by the ion.…”

“…Since in the diffusion description all the electrons are treated as if they had the average energies of 45 eV (first generation) or 15 eV (second generation), it cannot include the large radii tail of the radial dose arising from the energetic δ-electrons. This tail is clearly seen for 1-MeV protons and 2-MeV/u carbon ions in Figure 2, where experimental data for tissue-equivalent gas [28] and results from different Monte Carlo simulations and models [29][30][31][32] are depicted. In the following analysis we will account for the δ-electron contribution by making use of a spatially restricted LET equation [22].…”

“…Figure 1 shows the time evolution of the radial dose of a carbon ion in the Bragg peak region (T = 200 keV/u). It takes approximately ∼50 fs for all the electrons of the [29][30][31][32], and stars depict experimental data for tissue-equivalent gas [28].…”

Energy deposition around swift proton tracks in polymethylmethacrylate: How much and how far

“…These trends are of great relevance for the different applications, such as proton beam writing or ion beam cancer therapy: Lower proton energies produce both (i) larger amounts of energy deposited and (ii) larger concentration of these energies in shorter distances, thus increasing the efficiency and spatial resolution of the proton beam techniques. The radial dose dependence as a function of the distance r from the proton track only follows an approximate r −2 behavior for intermediate distances, with sizable deviations appearing at large distances r, analogously to the results obtained in similar studies performed for other targets and projectiles using different methodologies [58][59][60].…”

Monte Carlo Simulation of Electromagnetic Interactions of Radiation with Liquid Water in the Framework of the Geant4-DNA Project

“…The second approach [24]- [25] takes into account eight electronic excitation states of the water molecule and it can be applied in the energy range between 300 keV and 10 MeV; it is empirically based on electron impact data following the appropriate velocity scaling for protons. Pre-calculated tables provided by the authors [26] are used in the software implementation.…”