A reaction statement for d-t fusion which incorporates both mass flow and energy flow may be written as

+ d + t —^ (t/r) —^ n + cc + Qdt (7.63)

where Ed, is the energy supplied to heat the deuterium and tritium to thermonuclear temperatures and to sustain their high kinetic energies against all energy loss mechanisms; (dt) is the short-lived intermediate nuclear state previously denoted by (5He)*. Energy viability evidently demands Edt < Qdt.

In establishing fusion reactor conditions it is the electrostatic repulsion between the fuel ions which demands intensive heating of the plasma to high temperatures in order that the Coulomb barrier between two fusing nuclei can be more easily penetrated or overcome providing for a substantial fusion reaction rate. One might therefore speculate about the appealing prospects of using some "agent x" which could neutralize the Coulomb repulsion and induce a fusion event by making it easier for the ions to enter the range of their strong nuclear forces of attraction. That is, this agent might serve the function of a "catalyst" similar to the common practice of using catalyzing compounds to enhance the rate of chemical reactions. In particular, this catalytic agent x must be released after the d-t fusion event and subsequently induce another fusion reaction. Taking the average energy cost of producing one agent x to be Ex and if each x catalyzes % fusion events, then we write for the entire sequence

(7.64)

With Qat a known constant, the fusion catalyst should possess an average energy cost of production Ex and catalyze % d-t events such that now Eq.(7.65) is satisfied.

Interestingly, a catalyzing agent with properties suggested above does exist. It is a subatomic particle commonly called the "muon" and represented by the symbol (X. This particle appears as a product in various types of high energy nuclear reactions and possesses the following properties:

charge: q^ = — І. бхІО’19 C (same charge as an electron)

mass: тц = 207 me (207 times as heavy as an electron)

lifetime:^ = 2.2xl0"6 s (it is unstable) .

The property that a muon has the charge of an electron but a much larger mass means that it can enter into an orbit of a hydrogen atom with a Bohr radius 207 times smaller than that for an electron; we suggest this comparison between a conventional hydrogen atom and a muonic hydrogen atom in Fig.7.7.

A consequence of a much tighter muon orbit around a hydrogen nucleus is that to another hydrogen ion or hydrogen atom, the muonic hydrogen atom appears like an oversized and overweight neutron. Hence, this "oversize" neutron might approach another hydrogen ion or atom more closely because of a reduction of the repulsive Coulomb forces. Then, when this conventional hydrogen and the muonic hydrogen are sufficiently close to "notice" the details of spatial charge variation, they are already close enough for nuclear forces of attraction to dominate and to bring about a fusion event.

Several additional points are important in this context of muon catalyzed d-t fusion. Reactions of the type depicted in Fig.7.8 have been experimentally confirmed in liquid hydrogen at temperatures in the 300 К to 900 К range; the implication therefore is that muon catalyzed fusion may be sustained in a temperature environment more like that of existing fission reactors. Then, an appropriate accelerator for muon production has to be associated close to the muon-fusion chamber suggesting a system configuration similar to that of an ion beam-sustained inertial confinement scheme. Finally, the muon mean life-time of

2.2 (Is is unaffected by whether it is bound to a nucleus or not and hence demands that the various muonic induced reactions generally proceed at a fast rate.

Problems

7.1 Use «7v>dt from Appendix C for 10 keY and 100 keY and calculate Rfu for a 50:50% and 25:75% mixture of deuterium and tritium for which Nd + N, = N = 1021 m’3.

7.2 With the branching of the d-d fusion reactions occurring with essentially equal probability, determine the deuterium destruction rate and the helium-3 production rate.

7.3

For d-d catalyzed fusion, what are the ratios of (a) Nh / Nd, (b) Nt / Nd, (c)R+n / R+a> (Ф R+P / R+a> and (e) R+a(d-t) / R+a(d-d-p)’

7.4 Formulate reaction rate expressions for d, t and h as suggested in Table 7.2.

7.5 Undertake an analysis similar to that leading to the results of Fig.7.3 for the case of F = 0.

7.6 Fission reactors possess power densities of about 107 Wm’3, For this power range, determine the required particle density for d-t fusion at 10 keV.

7.7 Consider a catalyzed deuterium reactor operating under the conditions Nj=Ne=1020 rn3, kT=10 keV. Calculate the equilibrium concentrations of all three species (d, t, and h).

7.8 Physics requirements for d-h fusion are clearly more demanding than for d-t. Some advantages often cited involve environmental, safety, and cost factors. Discuss how these factors are advantageous and whether or not the advantages outweigh the disadvantages. Do you foresee any advances in physics that might significantly affect any trade-offs? Discuss which confinement system might be best suited for burning d-h.

7.9 It has been suggested that running a “lean” deuterium mixture (e. g. 30 % d, 70 % h) could further reduce neutron production. However, this is a trade-off against power density. Suggest, using equations and sketches of graphs, how to determine an “optimum” mixture ratio. (You may assume that a 1000 MW — electric plant is desired and that this power level is fixed; describe how to find what mixture ratio would provide 1000 MWe for the least input power.)

Energetics, Concepts, Systems