Critical Mass

1
Critical Mass
2
Critical Mass

• The critical mass of fissile material is the
  minimum amount needed for a sustained nuclear
  chain reaction.
• (a fissile material is one that is capable of
  sustaining a chain reaction of nuclear fission).

3
Critical

• Critical" implies an equilibrium (steady-state)
  fission reaction there is no increase in
  power/temperature/neutron population.

4
Subcritical

• "Subcritical" implies an inability to sustain a
  fission reaction a population of neutrons
  introduced to a subcritical assembly will
  decrease in number over time.

5
Supercritical

• "Supercritical" implies an increasing rate of
  fission until natural feedback mechanisms cause
  the reactor to settle into equilibrium (i. e. be
  critical) at an elevated temperature/power level
  or destroy itself (disassembly is an equilibrium
  state).

6
A nuclear fission chain reaction.

• 1. A uranium-235 atom absorbs a neutron, and
  splits into two new smaller atoms (fission
  fragments), releasing three new neutrons and some
  binding energy.

7
A nuclear fission chain reaction.

• 2. One of those neutrons is absorbed by an atom
  of uranium-238, and does not continue the
  reaction. Another neutron is simply lost and does
  not collide with anything, also not continuing
  the reaction. However one neutron does collide
  with an atom of uranium-235, which then splits
  and releases two neutrons and some binding energy.

8
A nuclear fission chain reaction.

• 3. Both of those neutrons collide with
  uranium-235 atoms, each of which fission and
  release between one and three neutrons, which can
  then continue the reaction.

9
What does it depend on?

• The critical mass of a fissionable material
  depends upon
• its nuclear properties (e.g. the nuclear fission
  cross-section a high one means that nuclear
  fission is highly likely)
• physical properties (in particular the density),
• its shape, and its
• enrichment.

10
Critical Mass

• The mass that allows the equilibrium of fissions
  to remain constant.
• This means that the number of fissions produced
  remains steady.
• One neutron from each fission goes on to produce
  another fission the other neutrons are lost

11
Critical Mass

• The number of fissions depends on the mass
  present.
• The number lost depends on the surface area (from
  which neutrons can escape).
• You therefore have to consider the mass/surface
  area ratio. The figure with the largest ratio is
  the sphere.

12
Best shape

• The shape with minimum critical mass is a sphere.
  This can be further reduced by surrounding the
  sphere with a neutron reflector.
• In the case of a bare sphere the critical mass is
  about 50 kg for uranium-235 and 10 kg for
  plutonium 239.

13
Self sustaining reaction

• Top A sphere of fissile material is too small to
  allow the chain reaction to become
  self-sustaining as neutrons generated by fissions
  can too easily escape.
• Middle By increasing the mass of the sphere to a
  critical mass, the reaction can become
  self-sustaining.
• Bottom By surrounding the original sphere with a
  neutron reflector, it can increase the efficiency
  of the reactions and also allow the material to
  become self-sustaining.

14
Enrichment

• Enriched uranium is a sample of uranium in which
  the percent composition of uranium-235 has been
  increased through the process of isotope
  separation.
• Natural uranium is 99.284 238U isotope, with
  235U only constituting about 0.72 of its
  weight.
• 235U is the only isotope existing in nature (in
  any appreciable amount) that is fissionable by
  thermal neutrons.

15
Enrichment

• The 238U remaining after enrichment is known as
  depleted uranium (DU), and is considerably less
  radioactive than even natural uranium, though
  still extremely dense.

16
Why?

• The 238U remaining after enrichment is known as
  depleted uranium (DU), and is considerably less
  radioactive than even natural uranium, though
  still extremely dense.
• U-235 half life 7.038x108 years
• U-238 half life 4.468x109 years

17
Enrichment

• It is useful for armour penetrating weapons, and
  other applications requiring very dense metals
  can you think of problems with this?

18
Problems?
19
How can you reduce the required mass?

• Surrounding fissionable material by a neutron
  reflector reduces the needed mass for
  criticality.
• (Beryllium is good at this)

A (simulated) sphere of plutonium surrounded by
neutron-reflecting blocks of tungsten carbide, as
part of a re-creation of a 1945 criticality
accident to measure the radiation produced when
an extra block was added, making the mass
supercritical.
20
Plutonium-239 critical mass 10kg

• Plutonium-239 is one of the three fissile
  isotopes used for the production of nuclear
  weapons and in nuclear reactors as a source of
  energy. Other fissile isotopes used are
  uranium-235 and uranium-233.
• Plutonium-239 has a half-life of 24,110 years.
• The nuclear properties of plutonium-239, as well
  as the ability to produce large amounts of nearly
  pure plutonium-239, led to its use in nuclear
  weapons and nuclear power.

21
Plutonium-239 critical mass 10kg

• The splitting of an atom of uranium-235 in the
  reactor of a nuclear power plant produces two to
  three neutrons, and these neutrons can be
  absorbed by uranium-238 to produce plutonium-239
  and other isotopes.
• Plutonium-239 can also absorb neutrons and
  fission along with the uranium-235. Plutonium
  fissions provide about one-third of the total
  energy produced in a typical commercial nuclear
  power plant.
• The use of plutonium-239 in power plants occurs
  without it ever being removed from the nuclear
  reactor fuel, i.e., it is fissioned in the same
  fuel rods in which it is produced.

22
Nuclear bombs

• Both types require subcritical fissile material
  and a method of making it supercritical.

23
The End