Summer Practice in JINR

Mathematical modeling of

high-energy particle beams in accelerators

Laboratory

List of participants: Marek Puchrowicz

Supervisor: dr Aleksander Polanski

Laboratory of Information Technologies

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.

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.

Equipment description

Computer and program MCNP (m4b.exe)

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 Jnucl[ψ] and Jelec[ψ] are collision integrals describing, respectively, nuclear and electronic interactions.

Target of SAD (Subcritical Assembly in Dubna)

Examples of geometry

Project descriptionYALINA-Booster assembly showing the different zones

Obtained resultsY-Z cross-sectional view of the YALINA-Booster assembly (at X=4)

Obtained results

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