Nuclear Power

Lecture April 20, 2011

Power from nuclear reactions

Energy from fusion in the sun (solar, fossil, water, bio)
Energy from nuclear decay inside the earth (geothermal)
Energy from fission of uranium (nuclear reactors)
Energy from hydrogen fusion

Matter = energy

Protons and neutrons consist of quarks, but the quark masses
account for only a few percent of the mass of matter.

The rest is energy (mainly kinetic energy of quarks).

Fortunately, the proton is stable.

Nuclear physics

Nucleons (protons and neutrons) attract each other with the
strong force, which has short range (10^

-15

meter)

Protons repel each other because of their electrical charge;
the Coulomb force has infinite range.
This results in an optimum size. Binding energy has a
maximum at iron, with 26 protons and 30 neutrons.
Very heavy nuclei like thorium, uranium and plutonium can
be made to split by high-energy neutrons.

Binding energy per nucleon in MeV as a function of mass
number
The curve peaks at Fe-56. Uranium-235 can gain energy
by splitting in two halves.

Fission of heavy nuclei according to the liquid drop model

The fragments repel each other because of their high electric
charge and separate with high kinetic energy (about 1 MeV
per nucleon, about 200 MeV per atom, over a million times
more than a chemical reaction). Two or three high-energy
neutrons are released, which can maintain a chain reaction.

Chain reaction

1. U-235 fissions in two

fragments and three
neutrons.

2. One neutron is absorbed

by U-238, one neutron
leaves the volume, one
neutron hits U-235 and
continues the chain
reaction.

3. Two neutrons are

released, producing 5
neutrons in the next
generation.

Conditions for chain reactions

Heavy nuclei like lead (Pb-208) or even thorium (Th-232) and
U-238 do not sustain chain reactions because:

energy thresholds are high
fission cross sections are small
capture cross sectins are large

Heavy odd-neutron-number nuclei U-235 and Pu-239:

have large cross sections for fission
can maintain chain reaction by fast neutrons
fast runaway multiplication
melon-sized solid sphere for a critical mass
for bombs, not for for power (however: fast reactors exist)

Slow-neutron chain reactions

U-235 and Pu-239 fission by capture of thermal neutrons
New fast neutrons are released and...
... slowed down (thermalized) in a moderator material,
captured and induce new fission events.

Process possible (just barely) with natural concentration of U-
235 (0.7 %) when using heavy water or graphite as a
moderator to slow down neutrons.

Controllable because of delayed neutrons emitted by
fragment nuclei (few seconds). Otherwise reaction would
proceed at velocities comparible to the speed of sound.

Controll rods with neutron-absorbing materials can fine-tune
the criticality factor k.

Uranium isotope enrichment

Natural uranium is 99.3 % U-238 and 0.7 % U-235.
Only U-235 kan fission by slow neutrons; U-238 is rather
inert
A higher percentage U-235 is necessary for maintaining a
chain reaction in light-water reactors
Isotopes cannot be separated by chemistry
Separation by ultracentrifuges, gaseous diffusion,
electromagnetic separation, etc (UF

6

-gas)

Enrichment to 2 or 3 % is sufficient för light-water reactors
More than 20 % is HEU (highly enriched uranium), used in
fast reactors, in principle useable for a bomb
More than 90 % enrichment is called weapons-grade
uranium
Enrichment costs a lot of energy

Unintended criticality

Aqueous solutions of fissionable isotopes can easily go
critical.
This happened 2 billion years ago in Oklo (Gabon), when
the natural U-235 content was still 3 %. A natural nuclear
reactor was running for several 100.000 years.
An accident in 1999 in Japan when operators at a fuel
reprocessing plant poured a few more liters 20 % enriched
uranium solution in a mixing tank. At 3 kg U-235 in 45 liters
of water a chain reaction started. Two operators died after
82 and 210 days.

Breeders

The amount of U-235 is limited (but currently the market i
glutted with downblended weapons-grade)
U-238 can also be made fissile.
Neutron capture gives rise to U-239.
After two beta decays this is Pu-239.
This can be chemically separated for use in bombs or in
MOX (mixed oxide fuel).
Fast breeders do not have a moderator; around the core,
depleted uranium is converted into plutonium (or thorium-
232 into fissile U-233). In this way, natural uranium can be
used to generate 70 times the energy compared to burning
U-235.

Fusion

Fusion of hydrogen nuclei also
gives nuclear binding energy
However, (fortunately), there is
a high Coulomb-force barrier

Methods:

Fusion in a hot, magnetically confined plasma in a
Tokomak
Z-pinch machine
Laser-induced implosions

Limitless source of energy when it works
No CO

2

emission

Still problems with radioactive waste