Quantum Physics

982 Chapter 30 Nuclear Energy and Elementary ParticlesLawson’s criterion heating the fuel to extremely high temperatures (about 10 8 K, far greater than theinterior temperature of the Sun). As you might expect, such high temperaturesare not easy to obtain in a laboratory or a power plant. At these high temperatures,the atoms are ionized and the system consists of a collection of electrons andnuclei, commonly referred to as a plasma.In addition to the high temperature requirements, there are two other critical factorsthat determine whether or not a thermonuclear reactor will function: the plasmaion density n and the plasma confinement time — the time the interacting ions aremaintained at a temperature equal to or greater than that required for the reaction toproceed. The density and confinement time must both be large enough to ensurethat more fusion energy will be released than is required to heat the plasma.Lawson’s criterion states that a net power output in a fusion reactor is possibleunder the following conditions:n 10 14 s/cm 3 Deuterium–tritium interaction [30.5]n 10 16 s/cm 3 Deuterium–deuterium interactionThe problem of plasma confinement time has yet to be solved. How can a plasma beconfined at a temperature of 10 8 K for times on the order of 1 s? The basic plasmaconfinementtechnique under investigation is discussed following Example 30.3.EXAMPLE 30.3 Astrofuel on the MoonGoal Calculate the energy released in a fusion reaction.ProblemStrategyFind the energy released in the reaction of helium-3 with deuterium:32 He 2 1 D : 4 2 He 1 1 HThe energy released is the difference between the mass energy of the reactants and the products.SolutionAdd the masses on the left-hand side, and subtract themasses on the right, obtaining m in atomic mass units:Convert the mass difference to an equivalent amount ofenergy in MeV:m m He-3 m D m He-4 m H 3.016 029 u 2.014 102 u 4.002 602 u 1.007 825 u 0.019 704 uE (0.019 704 u) 931.5 MeV1u 18.35 MeVRemarks This is a large amount of energy per reaction. Helium-3 is rare on Earth, but plentiful on the Moon,where it has become trapped in the fine dust of the lunar regolith. Helium-3 has the advantage of producing moreprotons than neutrons (some neutrons are still produced by side reactions, such as D–D), but has the disadvantageof a higher ignition temperature. If fusion power plants using helium-3 became a reality, studies indicate that itwould be economically advantageous to mine helium-3 robotically and return it to Earth. The energy return per dollarwould be far greater than for mining coal or drilling for oil!Exercise 30.3Find the energy yield in the fusion of two helium-3 nuclei:32He 3 2He : 4 2He 2( 1 1H)Answer12.9 MeVMagnetic Field ConfinementMost fusion experiments use magnetic field confinement to contain a plasma. Onedevice, called a tokamak, has a doughnut-shaped geometry (a toroid), as shownin Figure 30.5a. This device, first developed in the former Soviet Union, uses a