NEUTRON CYCLEAND

FOUR FACTOR FORMULAPRESENTED BY,

TEENA THANKACHENREG NO: 630-14126012

NUCLEAR FISSIONChief method of producing energy.Tremendous amount of energy is

released.When heavy nuclei are bombarded with

protons, deuterons, neutrons,α particles etc , then the nucleus is caused to breakdown into two roughily equal parts , known as fission fragments. This process is called NUCLEAR FISSION.

Frisch and Meitner in 1939 used the word FISSION .

NUCLEAR CHAIN REACTIONWhen a neutron produces fission

in uranium nucleus, besides the fission fragments a few fast neutrons are also emitted. If one or more of the emitted neutrons are used to fission of other nuclei, further neutrons are produced and the process is repeated.

The reaction thus becomes self-sustained and is known as CHAIN REACTION.

NUCLEAR CHAIN REACTION

NUCLEAR CHAIN REACTIONThe reaction is controlled in such

a way that only one of the neutrons emitted in a fission causes another fission, then the fission rate remains constant and the energy released steadily.

Such a reaction is called CONTROLLED CHAIN REACTION.

It is used in Nuclear Reactors.

NEUTRON LIFE CYCLE

NEUTRON LIFE CYCLEIn thermal reactors,neutrons that

cause fission are born at a much higher energy level than required

To make fission more probable,these neutrons must be “slowed” to thermal energy

PWRs use water as a moderatorWhen moderating “fast”

neutrons,gains and losses occur

This process is referred to as NEUTRON LIFE CYCLE .

Explains factors involved in controlling nuclear fission rate

Proper management of the neutron life cycle makes control of a nuclear reactor possible

Some of the fast neutrons born by fission in one generation will cause fission in the next generation

But…Fission neutrons “travel” through

a series of events as they slow to thermal energies, leak, or are absorbed in the reactor

Referred to as the neutron life cycle

Simplified neutron life cycle: All neutrons are born as fast neutronsSome fast neutrons are absorbed by

fuel and cause fast fissionSome fast neutrons leak out of reactor

coreSome fast neutrons undergo

resonance capture while slowing downAll remaining fast neutrons become

thermalized

Some thermal neutrons leak out of core

Some thermal neutrons absorbed by non-fuel material

Some thermal neutrons absorbed by fuel and not cause fission

Remaining thermal neutrons absorbed by fuel and cause thermal fission

K Neutron production from fission in one generationNeutron absorption in the preceding generation

pfK

EFFECTIVE MULTIPLICATION FACTOR Keff

Describes neutron life cycle in a real, finite reactor

A reactor of finite size will have neutrons leak out of it

Defined as ratio of neutrons produced by fission in one generation to number of neutrons lost through absorption and leakage in preceding generation

◦Like K∞, by its value, tells whether a new generation of neutrons is larger, smaller, or same size as preceding generation

◦ Also known as six-factor formula

 

fpLLK thfeff

INFINITE VS. EFFECTIVE MULTIPLICATION FACTOR

If leakage is small enough to be neglected, multiplication factor depends only on balance between production and absorption called Infinite multiplication factor

Also called four-factor formula , considers factors shown below:

pfK

With leakage included,considers six factors

fpLLK thfeff

FOUR-FACTOR FORMULAAlso known as Infinite

Multiplication Factor Used to consider a reactor of

infinitely large size where no neutron leakage can occur

Defined at ratio of neutrons produced by fission in one generation to number of neutrons lost through absorption in preceding generation

K

EFFECTIVE MULTIPLICATION FACTOR (KEFF) & CRITICALITYWhen value of keff is 1, a self-sustaining

chain reaction of fissions is occurring◦Neutron population is neither increasing nor

decreasing◦Called “critical” or critical reactor keff = 1

When neutron production is greater than the losses due to absorption and leakage◦Reactor is supercritical◦keff > 1◦Neutron flux is increasing each generation

EFFECTIVE MULTIPLICATION FACTOR (KEFF) & CRITICALITYWhen neutron production is less

than losses due to absorption and leakage◦Reactor is subcritical◦Keff < 1◦Neutron flux is decreasing each

generationWhen keff is not equal to exactly

1, neutron flux and therefore reactor power will be changing

INFINITE MULTIPLICATION FACTOR

Four factors independent of size and shape of reactor and do not consider any neutron leakage from the reactor.

Where : pfK

= fast fission factor

p = resonance escape probability

= reproduction factor

f = thermal utilization factor

FAST FISSION FACTOR (ε) = No of fast neutrons produced by all

fissions No of fast neutrons produced by thermal fissions•First event neutrons

incur after birth•Caused by neutrons that are in fast energy range•Results in a net increase in fast neutron population

Neutrons must pass close to a fuel nucleus while still fast

Value affected by fuel concentration and physical arrangement proximity to moderator

Essentially 1.00 for a homogenous reactor, fuel atoms surrounded by moderator atoms (rapid moderation)

Cross-section for fast fission in uranium-235 or uranium-238 is small

Still an appreciable number of fast neutrons cause fission in uranium-235, uranium-238, and plutomium-239

A large fraction of fast fissions occur with uranium-235 because of its wider fission energy spectrum

In a heterogeneous reactor (PWR/BWR), fuel atoms packed closely together in fuel pellets within fuel rods and assemblies ◦Neutrons emitted from fission of one fuel atom have a good chance of passing near another fuel atom before slowing down

◦Results in some fast fissionFor PWRs, 1.02 is a good value for ε,

with a range of 1.02 to 1.05

RESONANCE ESCAPE PROBABILITY (ρ)

ρ = No: of neutrons that reach thermal energy

No: of fast neutrons that starts to slow down

After fast fissions occur, neutrons continue to diffuse throughout reactor

Collide with nuclei of fuel, non-fuel material, and moderator◦ Lose energy in each collision and slow down

All nuclei within reactor core have some probability of absorbing neutrons ◦ Microscopic cross-section for absorption (σa) for

each materialσa is not a constant value,

dependent on energy level of incident neutron

Absorption cross-sections increase as neutron energy level decreases

THERMAL UTILIZATION FACTOR (f)

f=No:of thermal neutrons absorbed in the fuel

No: of thermal neutrons absorbed in all reactor materials

After thermal non-leakage, thermalized neutrons still dispersed throughout the core where they are subject to absorption by either fuel or non-fuel material

Thermal utilization factor describes how effectively thermal neutrons are being absorbed by fuel or underutilized by non-fuel materials

Thermal utilization factor is always less than one◦Not all thermal neutrons are absorbed in fuel◦These neutrons are lost to the fission process

A value range for thermal utilization factor is 0.70-0.80

REPRODUCTION FACTOR (η) η= No: of fast neutrons neutrons produced by

thermal fission

No: of thermal neutrons absorbed in the fuel

Most neutrons absorbed in fuel cause fission, but some do not

Reproduction factor represents net gain in neutron population

Value range of 1.65-2.0