MCNP/MCNPX Intermediate Workshop

NEA,NEA Paris France

October 22 - 26, 2012

Carlo Cazzaniga

Outline

● Introduction

● MCNP tools: geometry, sources, materials, tallies

● Variance reduction techniques

● Criticality

● My application

Introduction

History of MCNP

● Monte Carlo N-Particle Transport Code (MCNP) is a software package for simulating nuclear processes. It is developed by Los Alamos National Laboratory.

● More than 70 years of history.

● MCNPX (Monte Carlo N-Particle eXtended) was also developed at Los Alamos National Laboratory, and is capable of simulating particle interactions of 34 different types of particles (nucleons and ions) and 2000+ heavy ions

Enrico Fermi

The ENIAC computer

Applications (2012)

MC simulation of transport in the matter

Per la simulazione di un dato esperimento generiamo casualmente la storia di N particelle. Per questo ci serve un modello di interazione (Cross sections).

Cross sections per generare:

1) Libero cammino tra un'interazione e la successiva

2) Tipo di interazione che avviene

3) Angolo di scattering e perdita di energia in un particolare evento (e

stato iniziale delle nuove particelle formate, se presenti)

Se il numero di storie generate è sufficiente si possono ricavare informazioni

quantitative sui processi di trasporto.

Example

Neutral and charged particles

Interazione di particelle neutre

● Cammini semplici tra un'interazione e l'altra

● Rare

● Approccio alla simulazione: singola collisione

Interazione di particelle cariche

● Interazioni frequenti

● Interazioni a lungo raggio (forza di Coulomb)

● Approccio alla simulazione: rompere la traiettoria in brevi segmenti, lunghi abbastanza perchè sia valida una statistica, corti abbastanza perchè ∆E=0

MCNP input file

10 0 10

11 0 -10 20 50

20 0 -20

50 4 -1.0 -50

10 S 0 0 0 1000

20 RCC -16.9 0 -16.9 -0.00707 0 -0.00707 1.27

50 RCC 0 0 0 -0.140 0 -0.14 4

MODE N H

IMP:N 0 1 1 1

IMP:H 0 1 1 1

M4 6012 1 1001 2 $polietilene

MT4 poly.60t

PHYS:N 100 0 0 -1 -1 0 1

SDEF ERG=80 PAR=N POS=0 0 2 RAD=D4 AXS=0 0 1 EXT=0.0 VEC=0 0 1 DIR=-1

SI4 H 0.0 2 $flat beam of radius 2 cm

SP4 -21 1

F11:H 20.3

F21:N 20.3

E11 0 1 48I 80

CTME 20

CELL CARDS

SURFACE CARDS

DATA CARDS● Source● Materials● Physics ● Tally

MCNP tools (examples): geometry, sources, materials, tallies

Exercise: Geometry and materials

Advanced geometry

Exercise: Make a lattice with some changes in the materials

Exercise: Make an hexagonal lattice of rods in a moderator material

Source (MCNPX) and Tally

Tally example: neutron moderation

● Isotropic source of monoenergetic 14 MeV neutrons in the center

● Simulation of the energy spectrum at the surface for different radii

● R=1 cm → fast spectrum; R=100 cm → thermal spectrum

R

Polyethylene Sphere

Mesh example:Energy deposition in hadron therapy

1 MeV Photons

166 MeV/u Carbon Nuclei150 MeV Protons

Ions have a peaked profile which allows greater tumour dose at lower dose to the normal tissue around. Changing the ion energy shifts in depth the position of energy deposition.

Comparison of dose distributions between IMPT (right) and IMRT (left)

Variance Reduction Techniques

A million years problem(Variance Reduction techniques)

● Exercise: Calculate the dose at the detector position. Use variance reduction techniques to compute the problem in a finite time

Detector

Gamma source

Lead shielding (10 cm)

Total absorber (a lot of Lead)

Water phantom

Motivation for Variance Reduction

● Exchange user efficiency for computational efficiency.

● Few hours of user time often reduces computational time by 10-1000.

● Some problems can't be solved without.

● Most techniques decrease R2 more than T is increased.

Cautions:

● Don't get too elaborate too quickly

● Study the manual before using VRT

● Balance user time with computation time

● Study the output for peculiarities (eg. Weight balance table, FOM table...)

FOM=1

R2T

Weight WindowsSplitting Russian Rulette

Forced CollisionDxtran sphere

Criticality

Criticality

The k parameter is the multiplication factor defined as the ratio of « useful » neutrons produced in average per fission of one generation to the number of « useful » neutrons of the previous generation.

How to simulate k using Monte Carlo? If you follow every particle the simulation can't find a solution

“K” according to BoltzmannThe most general neutron transport equation (Boltzmann equation) is a balance statement that conserves neutrons. Each term represents a gain or a loss of a neutron, and the balance, in essence, claims that neutrons gained equals neutrons lost. It is formulated as follows:

Escape+Absorbtion=Fission−dNdt

Escape+Absorbtion=1kFission

An advantage of k eigenvalue formulation lies in the physical interpretations of theeigenvalue and the iterative technique derived from it. The technique is a powerful method forcarrying out criticality calculations.

A system containing fissionable material is said to be critical if there is a self-sustaining time-independent solution. But if we try to find a solution to and find that none exists? Criticality calculations are normally cast into the form of Eigenvalue problems, where the Eigenvalue provides a measure of whether the system is critical or subcritical and by how much.

What does MCNP do?

1) Start from your guess:

➔ Initial guess for k (usually 1 is ok)

➔ Initial guess for source distribution (put one source in every fissionable material)

➔ Watt fission spectrum (default)

2) Cycle (M times)

➔ Iteration of N neutrons per cycle

➔ Eigenvalue estimation

3) Did k converge?

Example of reactor core

My applications

Response of the LaBr3 gamma ray spectrometer

Response to gamma rays

Response to background induced by 2.5 and 14 MeV neutrons mostly via inelastic scattering and (n,2n) reactions.

Geometry of the detector

Study for a proton recoil neutron spectrometer

Ep'

= En cos2(θ)

Simulazione dei diversi contributi alla risoluzione con neutroni da 50 MeV

THE END