Binding Energy: Fission Versus Nuclear Fusion

Ever since Einstein first penned his famous equation, E = mc2, showing the world that there is energy stored in matter waiting to be harvested, mankind has been searching for new ways to free it. Initial work towards this goal led to the development of nuclear fission, the pinnacle of which was the successful Trinity Test in 1945. As time went on the technology was improved upon, resulting in nuclear power plants and more powerful weapons. Still, there was a desire for a more efficient, less dangerous, and more powerful means of extracting energy from matter. This desire was met with nuclear fusion. Fusion and fission power differ in a number of significant ways, despite both being based on the concept of nuclear binding energy. Binding energy

This is simply a chart plotting the binding energy of an atom as a function of its atomic number (“Nuclear Binding”). The maximum in the graph around the atomic number of iron illustrates the transition from fission to fusion. Atoms with atomic numbers less than that of iron will require energy to be split apart as the binding energies of their constituent atoms are smaller, whereas atoms with atomic numbers greater than that of iron will produce energy when they split apart as the binding energies of their constituent atoms are larger (“Nuclear

Furthermore, the confinement time, which is a measure of how quickly power is lost to the environment is given by τ_E=W/P_loss where W is the energy density and Ploss is the energy loss rate per unit volume (Lawson, J. “Some”). Finally, by taking the volume rate, which is a function of the number of reactions per volume per time, and multiplying by the charge of the particles, we get a quantity that we know must be greater than the power loss, per the initial criterion (Lawson, J. “Some Criteria for a Useful”). Doing some algebra, we can then reduce to the expression

〖nτ〗_E≥L T/σv where L is a constant, T is the temperature of the system, σ is the nuclear cross section, or chance that two particles have to collide, and v is the relative velocity of the two particles. Multiplying both sides by T then gives the triple product as a function of temperature. This is useful because it provides a minimum value for the product of 〖nTτ〗_E for a fusion reaction to occur (Lawson, J. “Some”). The exact value of this minimum will change depending on the type of fuel used in the reaction. For a fusor, this fuel will almost always be a deuterium-deuterium combo or a deuterium-tritium combo (Unterweger et al.; Wanjek). Both deuterium and tritium are isotopes of hydrogen, with deuterium being H2 and tritium being H3. Out of the two, deuterium is