蒙特卡罗方法介绍MC_1-2

Detectors in Nuclear Physics:

Monte Carlo Methods

Dr. Andrea Mairani

Lectures I-II

INTRODUCTION

Sampling from a probability distribution

X λ

Sampling from a probability distribution

The problem of radiation transport

Each particle is represented by a point in phase space P=(r, E,Ω, t) Transport calculations are attempts to solve the Boltzmann Equation, i.e., a balance equation accounting for all“produced” (e.g., sources,“in-scattering”) and“destroyed” (e.g., absorption,“out-scattering”) particles at each point of the phase space The MC method can be formulated as an integral form of the Boltzmann equation, e.g., the“emergent particle density equation”

Density of emerging (from source or collision) particles of given position, energy, direction at a given time Collision integral operator

Density of particles generated by external source

Transport integral operator

Analog versus condensed history MCAnalog (event-by-event) MC simulation1.

Select the distance to the next interaction (random sampling e.g. based on probability p(r)dr that photon interacts in aninterval dr at a distance r from initial position:

ln(1 ξ ) r= µ2.

Transport the particle to the interaction site taking into account geometry constraintssection)

3.

Select the interaction type (random sampling based on interaction cross

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