2. NUCLEAR FISSION
Chief 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 .
3.
4. NUCLEAR CHAIN
REACTION
When 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.
6. NUCLEAR CHAIN
REACTION
The 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.
8. NEUTRON LIFE CYCLE
In 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 moderator
When moderating “fast”
neutrons,gains and losses occur
9. 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
10. 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
11. Simplified neutron life cycle:
All neutrons are born as fast neutrons
Some fast neutrons are absorbed by fuel
and cause fast fission
Some fast neutrons leak out of reactor
core
Some fast neutrons undergo resonance
capture while slowing down
All remaining fast neutrons become
thermalized
12. 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
13. K Neutron production from fission in one generation
Neutron absorption in the preceding generation
pfK
14. 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
15. ◦ 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
16. 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
17. With leakage included,considers six
factors
fpLLK thfeff
18. FOUR-FACTOR FORMULA
Also 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
19. EFFECTIVE MULTIPLICATION
FACTOR (KEFF) & CRITICALITY
When 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
20. EFFECTIVE MULTIPLICATION
FACTOR (KEFF) & CRITICALITY
When neutron production is less than
losses due to absorption and leakage
◦ Reactor is subcritical
◦ Keff < 1
◦ Neutron flux is decreasing each
generation
When keff is not equal to exactly 1,
neutron flux and therefore reactor
power will be changing
21. 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
22. 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
23. 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)
24. 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
25. 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 fission
For PWRs, 1.02 is a good value for ε,
with a range of 1.02 to 1.05
26. 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
27. All nuclei within reactor core have
some probability of absorbing
neutrons
◦ Microscopic cross-section for absorption (σa) for each
material
σa is not a constant value, dependent
on energy level of incident neutron
Absorption cross-sections increase as
neutron energy level decreases
28. 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
29. 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
30. 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
