JL *H3 __ __ IiB Nuclear Instruments and Methods in Physics Research B 100 ( 1995) 31-46 lYk!lllM B Beam Internotions with Materials & Atoms ELSEVIER PENELOPE: An algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter J. Barba, J. Sempau b, J.M. Ferntidez-Varea ‘, F. Salvat ‘,* a Senwis Cientt$ico-T&tics, llniversitat de Barcelona, Marti i FranquPs s/n, 08028 Barcelona. Spuin ’ fmtitut de TPcniques Ener@tiques, Universitot Politknica de Catalunya. Diagonal 647 his. 08028 Barcelona. Sparn Foultut de Fisica (ECMJ. Universitat de Barcelona, So&tat Catalana de Fkica (IECI. Diagonal 647. 08028 Barcehnu. Span Received 30 September 1994 Abstract A mixed algorithm for Monte Carlo simulation of relativistic electron and positron transport in matter is described. Cross sections for the different interaction mechanisms are approximated by expressions that permit the generation of random tracks by using purely analytical methods. Hard elastic collisions, with scattering angle greater than a preselected cutoff value, and hard inelastic collisions and radiative events, with energy loss larger than given cutoff values, are simulated in detail. Soft interactions, with scattering angle or energy loss less than the corresponding cutoffs, are simulated by means of mukiple scattering approaches. This algorithm handles lateral displacements correctly and completely avoids difficulties related with interface crossing. The simulation is shown to be stable under variations of the adopted cutoffs; these can be made quite large, thus speeding up the simulation considerably, without altering the results. The reliability of the algorithm is demonstrated through a comparison of simulation results with experimental data. Good agreement is found for electrons and positrons with kinetic energies down to a few keV. 1. Introduction The problem of the penetration and energy loss of fast electrons in matter has attracted great attention since the beginning of this century. Since most of our knowledge about nuclear, atomic, molecular and solid state structure has been, and is being, achieved by using electron beams to probe matter, this problem is of fundamental interest. A detailed description of electron, and positron, transport is required in a number of fields such as beta-ray spectrometry [ 1,2], electron microscopy [ 31 and electron and positron surface spectroscopy 1451. Accurate information on high energy electron and positron transport is also needed in radiation dosimetry and radiotherapy [ 61. Electron multiple scattering processes were first treated on the basis of the transport theory [ 7,8]. Since the beginning of the sixties, with the increasing availability of fast com- puters, Monte Carlo (MC) simulation methods have been developed and applied to many experimental situations (see e.g. Ref. [ 91) The characteristics of different MC simula- tion schemes depend mainly on the energy range of inter- est. “Detailed” MC simulation [ 10,111 where all scattering events experienced by an electron are described in chrono- * Corresponding author. Tel. +34 3 402 1186, fax +34 3 4021174,e-mail: [email protected] 0168-583X/95/$39.50 @ 1995 Elsevier Science B.V. All rights reserved SSDIOl68-583X(95)00349-5 logical succession, is feasible at low energies, Detailed sim- ulation is virtually exact, i.e. simulation results are identi- cal to those obtained from the exact solution of the trans- port equation with the same scattering model (except for statistical uncertainties). For progressively higher energies, however, the average number of scattering events per track increases graduaily and eventually detailed simulation be- comes unfeasible. For high energies, most of the MC codes currently avail- able (e.g. ETRAN [9], EGS4 [12], GEANT 1131) have recourse to multiple scattering theories which allow the sim- ulation of the global effect of a large number of events in a track segment of a given length (step). Following Berger [ 141, these simulation procedures will be referred to as “condensed” MC methods. The multiple scattering theo- ries implemented in condensed simulation algorithms are only approximate and lead to systematic errors, which arise mainly from the lack of knowledge about the spatial dis- tribution of the particle after travelling a given path length. These errors can be made evident by the dependence of the simulation results on the adopted step length [9]. To an- alyze their magnitude, one can perform simulations of the same experimental arrangement with different step lengths. Usually, it is found that the results stabilize when reducing the step length, but the computation time increases rapidly. roughly in proportion to the inverse of the step length. Thus,32 .I. Bar6 et al./Nucl. Instr. and Meth. in Phys. Res. B 100 (1995) 31-46 for each particular problem, one must reach a compromise between available computer time and attainable accuracy. It is also worth noting that, owing to the nature of certain mul- tiple scattering theories and/or to the particular way they are implemented in the simulation code, the use of very short step lengths may introduce artifacts in the simulation results. For instance, the multiple elastic scattering theory of Moliere [ 151, which is the one used in EGS4 based codes, is not ap- plicable to step lengths shorter than a few times the elastic mean free path [ 16,171 and multiple elastic scattering has to be switched off when the step length becomes smaller than this value [ 181. Evidently, stabilization for short step lengths does not necessarily imply that simulation results are correct. Condensed schemes also have difficulties to prop- erly handle particle tracks in the vicinity of an interface, i.e. a surface separating two media of
View Full Document
Unlocking...