Comparison of computational results obtained with different programs for radiation transfer

Abstract

A large number of codes and program packages, for example, [1--4], have been developed to solve many radiationphysics probIems on charged-particle accelerators involving calculation of the transfer of high-energy radiation. However, no code or program is universal --each program is restricted with respect to energy, type of particles, size and geometry of the region computed, and so on. Outside their region of applicability the programs often lead to incorrect results. The possibilities of computational methods and their restrictions are not always clear to the user. For this reason, we feel that all codes must be verified. However, the programs cannot always be verified on experimental results: special experiments are expensive and the experimental data obtained are, as a rule, insufficient for comprehensive verification of the programs. The way out of this situation is to test the programs on computational results obtained with so-called exact codes, i.e., codes which are designed for definite conditions with a known and quite low methodological error. An example of such a code in a wide range of particle (n, p, x, K, 3') energies is the program-constants system ROZ-6N + Sadko [5--7], which is based on solving a kinetic equation by the method of discrete ordinates.Our objective in the present work is to make a comparative analysis of the computational results for radiation transfer with some known codes and program packages and with the use of the ROZ-6N+Sadko program system for a diverse range of primary-particle energies.Methods for calculating the transport of particles generated by high-energy hadrons. Almost all programs developed for calculating the transport of high-energy particles employ analog modeling of the particle trajectories by the Monte Carlo method. This method is chosen because of its advantages, such as the mathematical simplicity of the modeling algorithm, the possibility and simplicity of taking into account within the scope of the method any physical process, and the possibility of calculating radiation transfer in a complicated geometry. At the same time, the Monte Carlo method has a limitation that determines its region of application --the deep-penetration problem.The limit of applicability of the Monte Carlo analog method can be easily estimated on the basis of the following obvious considerations. The error in estimating the mathematical expectation of a functional N (for example, N can be the number of particles) behind a shield of thickness t by the method of random tests is determined by the formula ~ = 1/x/N. The functional N can be approximated by the well-known function N -N o exp (-fiX), where N o is the number of histories and X is the attenuation length. The computation time is related linearly to No: T = T0N o, where T O is the average time for analyzing one history. Combining the three expressions into one, we obtain an approximate exponential dependence of the computation time on the thickness of the shield T -T O exp(t/X)/e 2, whence it follows, for example, that 10 h of...