Fission and Fusion Reactors

John Belz (for Carleton Detar)01 March 2010

www.physics.utah.edu/~belz/phys5110/reactors.pdf

Question: Which is more like a nuclear power plant?

Boiling a kettle of water Firing a piston engine

Fission● The act or process of splitting into parts● Spontaneous fission

– e.g. decay

– Quantum-mechanical “tunnelling”

Fission● Induced Fission

– By neutron capture

– “Pairing Term” in Bethe-Weizsäcker mass formula

– Even-even nuclei fragment, emit 2-3 neutrons

Chain Reactions● Neutrons produced in fission events induce a

next generation of fission events.● To be useful for energy production, the

fission →neutrons→fission →neutrons process must be self-sustaining

● “Reproduction factor” k: – k < 1 reaction dies out; subcritical

– k = 1 reaction just continues; critical

– k > 1 reaction accelerates; supercritical

Self-Sustaining Chain Reactions● Suppose we have a sphere of pure fissile material

– fissionable nuclei ~ volume ~ r3

– neutron leakage ~ surface area ~ r2

● As you increase r (at constant density)

– volume/surface ratio increases

– k increases● Sphere with k = 1 is called a “critical mass”

– 235U →r = 8.5 cm, mass = 52 kg

– 239Pu→r = 5 cm, mass = 10 kg● In practice, this much pure fissile material is hard to

obtain...

Natural Uranium

● 0.7% 235U, 99.3% 238U● Generally “enriched” for

reactor applications:– Power plants 3% 235U

– Research 20% 235U

– Nuclear Subs 90% 235U

Neutron interactions in Natural Uranium

Neutron interactions in Natural Uranium

f = fission reaction = radiative reaction

Neutron interactions in Natural Uranium

238U requires > 1 MeVneutrons to fission. Higher

than typical fission products

Neutron interactions in Natural Uranium

10 eV to 1 MeV, 238U radiative dominates

Neutron interactions in Natural Uranium

Below 1 eV, 235U fission dominates

Fusion in Natural Uranium

● Uranium used in reactors is typically only 3% (power plant) or 20% (research, e.g. TRIGA) 235U.

● There is no “critical mass” at these concentrations

● Still possible to achieve chain reaction if one can slow down neutrons via the use of a moderator

– Light elements, take away kinetic energy in collisions.

– Capture cross section << elastic cross section

– e.g. carbon, D20

● Typically also use high capture cross section materials (e.g. boron carbide) to control reaction

Reactors: Moderation and Control

Graphite Moderator

“Breeder” Reactors

● Graphite Moderator– e.g. Manhattan

Project, Chernobyl

– “Breed” Pu

– If core overheats, reaction speeds up

● Water Moderator– Typical American

power plant reactor

– No Pu breeding

– If core overheats, water boils away and reaction stops

Energy by Nuclear Fusion

● Lots of hydrogen... potential as energy source

● Source of Sun's power

● Problem: thermal energies won't work, can't overcome Coulomb repulsion.

Energy by Nuclear Fusion

● Lots of hydrogen... potential as energy source

● Source of Sun's power

● Problem: thermal energies won't work, can't overcome Coulomb repulsion.

Fusion Fission

Energy by Nuclear Fusion: The Sun

● kT @ 300 K (room) = 0.026 eV

● kT @ 5,000 K (surface of sun) = 0.43 eV

● kT @ 20,000,000 K (core of sun) = 1,700 eV

– Only particles in the tails of the Maxwell distribution will be able to fuse in the Sun

– i.e. The Sun is barely burning!

Solar Energy: Proton-Proton Cycle

Fusion Reactors

International Thermonuclear Experimental Reactor (ITER)

● 30 year project● Goal: 500 MW of power

for 1,000 seconds● (Current record 16 MW,

< 1 second)● Under construction in

Cadarache, France● Estimated turn-on 2018