MONTE CARLO SIMULATION OFNEUTRON RADIATION

SHIELDING USING MATLAB

By: Mr. ROHIT YADAV (01240809712)

M. Tech (Engineering Physics)

Under the Supervision of

Prof. Vinod Kumar

USBAS

GGSIPU, New Delhi

Contents

• Monte Carlo Simulation• Random Numbers• Random Numbers Generators• Tests for Generators• Neutron Radiation• Shielding with various materials• Conclusions • References

Monte Carlo Simulation

• A broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

• Often used in physical and mathematical problems.• Most suited to be applied when it is infeasible to apply a

deterministic algorithm. • Mainly used in three distinct problems: optimization,

numerical integration and generation of samples from a probability distribution.

• Provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer.

History • Called after the city in the Monaco principality, because of

roulette, a simple random number generator, in 1944.• A. HALL 1873. " On an experimental determination of PI"• 1899 Lord Rayleigh - A one-dimensional random walk .• 1931 Kolmogorov - Relationship between Markov stochastic

processes and certain Integro-Differential equations. • Real use - As a research tool on the atomic bomb during the

Second World War.

A direct simulation of the probabilistic problems concerned with random neutron diffusion in fissile material

• About 1948 Fermi, Metropolis, and Ulam obtained Monte Carlo estimates for the Eigen values of Schrodinger equation.

Random Numbers

• Pseudo-Random Number • True Random Number

Random Numbers Generators

Pseudo Random Number Generators

• Linear congruential generator

and c are relatively prime.

(a-1)is divisible by all prime factors of m.

• Mid Square Generator

To generate a sequence of pseudorandom numbers, a 4-digit seed is created and squared, producing an 8-digit number . The middle 4 digits of the result would be the next number in the sequence, and returned as the result.

Tests for Generators

• Chi- Square Test:

To determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.

• Kolmogorov –Smirnov Test:

To determine if two datasets differ significantly.

Compare CDF Fo(x) (observed) and CDF Fe(x) (expected)

—difference between CDF Fo(x) and CDF Fe(x) should be small.

• Serial Correlation Test:

If the error terms are independent from one another – they are uncorrelated.

ρ=0 (no serial correlation)

ρ>0 (positive serial correlation)

If d < DL reject Ho, while if d > DU do not reject Ho.

DL and DU provided in “Course Documents/Statistical Tables folder”

Comparison between Generators

• The best method for generation of random numbers is through the default command given by MATLAB i.e. RAND and is used later for the simulation of Neutron Radiation Shielding through different materials.

Neutron Radiation

• Neutron radiation is a kind of ionizing radiation which consists of free neutrons.

• Large neutron sources are rare, and are usually limited to large-sized devices like nuclear reactors or particle accelerators (such as the Spallation Neutron Source).

• Is not as readily absorbed as charged particle radiation, which makes this type highly penetrating.

• Neutrons are absorbed by nuclei of atoms in a nuclear reaction. This most-often creates a secondary radiation hazard, as the absorbing nuclei transmute to the next-heavier isotope, many of which are unstable.

Neutron Shielding• Due to the high kinetic energy of neutrons, this radiation is

considered to be the most severe and dangerous radiation to the whole body when exposed to external radiation sources.

• In comparison to conventional ionizing radiation based on photons or charged particles, neutrons are repeatedly bounced and slowed (absorbed) by light nuclei, so hydrogen-rich material is more effective than iron nuclei.

• The light atoms serve to slow down the neutrons by elastic scattering, so they can then be absorbed by nuclear reactions. However, gamma radiation is often produced in such reactions, so additional shielding has to be provided to absorb it.

• Care must be taken to avoid using nuclei which undergo fission or neutron capture that results in radioactive decay of nuclei that produce gamma rays.

• In living tissue, neutrons have a relatively high relative biological effectiveness, and are roughly ten times more effective at causing biological damage compared to gamma or beta radiation of equivalent radiation exposure.

• Neutrons are particularly damaging to soft tissues like the cornea of the eye.

• The most effective shielding materials are hydrocarbons, e.g. polyethylene, paraffin wax or water.

• Concrete (where a considerable amount of water molecules are chemically bound to the cement) and gravel are used as cheap and effective biological shields due to their combined shielding of both gamma rays and neutrons.

Algorithm for MATLAB Simulation

• Give the neutron radiation energy• Draw shield of elements or compounds in geometrical shape e.g.

cube.• Mark the source of radiation at a distance x.• Calculate the linear attenuation coefficient of

elements/compounds from NIST webpage at particular wavelength and packed density.

• Calculate neutron total cross-section with the help of Ramsauer model.

• Determine the path of neutrons after every collision with help of direction cosines.

• Observe the count of neutrons that successfully penetrate the shield.

Figure showing how simulation looks like

Result with combination of different Elements

Conclusion And Result • Neutrons readily pass through most material, but interact

enough to cause biological damage. • The most effective shielding materials are hydrocarbons, e.g.

polyethylene, paraffin wax or water. • Concrete (where a considerable amount of water molecules

are chemically bound to the cement) and gravel are used as cheap and effective biological shields due to their combined shielding of both gamma rays and neutrons.

• Boron is an excellent neutron absorber (and also undergoes some neutron scattering) which decays into carbon or helium and produces virtually no gamma radiation, with Boron carbide a commonly used shield where concrete would be cost prohibitive.

• Commercially, tanks of water or fuel oil, concrete, gravel, and B4C are common shields that surround areas of large amounts of neutron flux, e.g. nuclear reactors.

• Boron-impregnated silica glass, high-boron steel, paraffin, and Plexiglas have niche uses.

References • http://www.ncnr.nist.gov/cgi-bin/neutcalc

National Institute Of Standards and Technology,

Center for Neutron Research • Ramsauer Model for Total Cross sections of Neutron-Nucleus scattering.

R. S. Gowda +, S. S. V. Suryanarayana† and S. Ganesan+†∗ Nuclear Physics Division,+ Reactor Physics Design Division,

Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India

(Dated: February 9, 2008)•  Wikipedia and Google• Computational Physics Text book by R C Verma• Cross section Library

http://wwwndc.jaea.go.jp , Nuclear Data Center

Japan Atomic Energy Agency

Thank you

"Nothing in nature is random... A thing appears random only through the incompleteness of our knowledge."

- Spinoza