Simulation of the Proton Transport in Matter
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lation of the Proton Transport in Matter M. B. Markova and S. V. Podolyakoa, * a
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia *e-mail: [email protected] Received August 13, 2019; revised August 13, 2019; accepted October 21, 2019
Abstract—A mathematical model of proton transport in matter is considered. The interaction of protons with the electron subsystem of the medium’s atoms is modeled in the approximation of the average energy loss during ionization scattering. Nuclear interactions are considered in the model of individual collisions. An algorithm for modeling proton transfer in piecewise-homogeneous media is developed, combining the continuous deceleration approximation when interacting with electrons with the implicit direct modeling of elastic and inelastic scattering on the nuclei. The calculations that demonstrate the effect of nuclear scattering on the distribution of the energy released by protons during scattering are presented. Keywords: proton, ionization deceleration, tracing, Bragg curve, individual collisions DOI: 10.1134/S2070048220050142
1. INTRODUCTION The study of the interaction of high-energy charged particles, in particular, protons, with a substance is not only a fundamental task of the physics of penetrating radiation [1] but also an urgent technical problem in a number of high-technology industries, including those protecting spacecraft from radiation and creating effective methods of radiation therapy. Protons are one of the main components of all types of cosmic radiation: the Earth’s radiation belts, as well as solar and galactic rays. The effect of protons on spacecraft leads to the degradation of their functional properties during operation due to dose and single effects. Dose effects consist in the accumulation by individual elements of the equipment of the energy released by protons during scattering. Energy is spent on the formation of conduction electrons and holes of the valence band in semiconductor devices, which entails the degradation of their characteristics. The absorbed dose [1–5] is a quantitative measure of this class of radiation exposure. A single heavy charged particle pierces through the semiconductor device through the spacecraft’s body, creating a highly ionized heated track. A quantitative measure of such an effect is the power density of the energy released by the particle in the region of the track [6]. Also, protons electrify the spacecraft. The accumulation of charge leads to electrostatic discharges, which destroy protective coatings and solar panels. Here, the distribution of the charge density over the spacecraft’s design [7, 8] is the quantitative measure. Proton radiation therapy has established itself as a treatment for many tumors. The advantage of protons over gamma rays is that they increase the likelihood of controlling the tumor and reducing the radiation loads on healthy tissues. Sources of protons may be the only possible means of irradiating tumors close to critical structures, for example, in the he
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