1. Summer Practice in JINR Mathematical modeling of high-energy particle beams in accelerators

2. Laboratory List of participants: Marek Puchrowicz Supervisor: dr Aleksander Polanski Laboratory of Information Technologies

3. Monte Carlo Methods Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. Monte Carlo methods are very important in computational physics, physical chemistry, and related applied fields, and have diverse applications from complicated quantum chromodynamics calculations to designing heat shields and aerodynamic forms.

4. Application Areas Monte Carlo methods in finance Monte Carlo method in statistical physics In experimental particle physics, for designing detectors, understanding their behavior and comparing experimental data to theory Nuclear and particle physics codes using the Monte Carlo method: – GEANT - CERN's Monte Carlo for high-energy particles physics – MCNP(X) – A General Monte Carlo N-Particle Transport Code – FLUKA Particle Transport Code - a particle physics Monte Carlo simulation package The software is sponsored by INFN and CERN. FLUKA has many applications in high energy experimental physics and engineering, shielding, detector and telescope design, cosmic ray studies, dosimetry, medical physics and radiobiology.

5. Equipment description Computer and program MCNP (m4b.exe)

6. Transport equation Particles transport is described by the classical linear Boltzmann or transport equation Where ψ(r,E,Ω) is the ion angular flux, and J nucl [ψ] and J elec [ψ] are collision integrals describing, respectively, nuclear and electronic interactions.

8. Target of SAD ( Subcritical Assembly in Dubna)

9. Examples of geometry

10. Project description YALINA-Booster assembly showing the different zones

11. Obtained results Y-Z cross-sectional view of the YALINA-Booster assembly (at X=4)

12. Obtained results X-Y cross-sectional view of the YALINA-Booster assembly (at X=4)