Fission and Fusion

In $\text{induced fission}$, a heavy nucleus such as uranium-235 absorbs a slow neutron, becomes unstable, and splits into two medium-mass daughter nuclei plus two or three fast neutrons.

A typical reaction is ${}_{92}^{235}\mathrm{U}+{}_0^1\mathrm{n}\to {}_{56}^{141}\mathrm{Ba}+{}_{36}^{92}\mathrm{Kr}+3{}_0^1\mathrm{n}$. The daughters vary from one event to the next, but nucleon and proton numbers always balance.

Each fission releases about 200 MeV, mostly as kinetic energy of the fragments, which becomes thermal energy in the fuel.

The neutrons released can trigger further fissions — a $\text{chain reaction}$. For a steady output, exactly one neutron from each fission must go on to cause another. More than one and the reaction grows out of control; fewer and it dies away.

The $\text{moderator}$, often water or graphite, slows fast neutrons through collisions so they are much more likely to be absorbed by U-235. The best moderators have nuclei of similar mass to a neutron, so each collision transfers a large fraction of its kinetic energy.

$\text{Control rods}$, made of boron or cadmium, absorb neutrons. Lowering them reduces the number of neutrons available and slows the reaction. The $\text{coolant}$ carries thermal energy away to generate steam.

A minimum $\text{critical mass}$ of fuel is needed; with less, too many neutrons escape through the surface for the chain to sustain itself.

In $\text{fusion}$, two light nuclei join to form a heavier one. A reaction proposed for reactors is deuterium–tritium fusion: ${}_1^2\mathrm{H}+{}_1^3\mathrm{H}\to {}_2^4\mathrm{He}+{}_0^1\mathrm{n}$.

Both nuclei are positive, so they repel. To get close enough for the strong force to act — about $10^{-15}$ m — they need enough kinetic energy to overcome that electrostatic barrier.

That requires temperatures of the order of $10^7$ to $10^8$ K, at which matter is a $\text{plasma}$ of bare nuclei and electrons. A high density is also needed so collisions are frequent enough to produce useful power.

Fission is established technology, providing about a tenth of the world’s electricity with no carbon dioxide emissions from generation. Its drawbacks are long-lived radioactive waste and the need to contain the risk of accidents.

Fusion fuel — deuterium from seawater, and tritium bred from lithium — is plentiful, and fusion produces no long-lived fission products. But confining a plasma at over $10^8$ K with magnetic fields, and producing more energy than is put in, remains extremely difficult.

Stars solve the confinement problem with gravity: their immense mass holds the plasma together at the necessary density and temperature for billions of years.