The preceding discussion stressed the energy multiplication potential of the fusion hybrid. Next, we consider the fissile fuel breeding capacity of such a reactor. Recall the schematic depiction of the d-t fusion-fission system as suggested in Fig. 15.4. The total fusion reaction rate is given by

Rd, = NdNt <<Jv>dt d (15.14)

with the integration carried out over the fusion core volume Vc. Similarly, we define the neutron-nucleus interaction of type і [і: a (absorption), c (capture), t
(tritium breeding)] involving nuclei j Ц: g, f, £ , x] of density Nj according to

/?;, = (15.15)

V,,v„

where ф is the neutron flux depending on vn and the integration is carried out over the entire neutron speed range and the blanket volume Vb.

A fissile fuel recycle fraction er, representing the fraction of bred fuel burning in situ in the blanket, is now introduced. Then, l-er is the fraction of bred fuel made available for external fission reactors. For every X units of fuel bred, only the fraction ЄгХ is retained and subsequently fissions in the blanket. For steady state operation, it will be seen below that the fissile breeding ratio is conveniently identified to equal l/er.

Our objective now is to find a suitable expression for the hybrid breeding ratio

dN* dt

in terms of lumped reactor physics parameters. To do this we must formulate reaction rate equations which describe the production and removal of the various nuclear species of interest in the hybrid reactor. The rate equations for the total populations of tritium Nt* in the system, and of fissile fuel Nf* and neutrons Nn* in the blanket are given by

dN*f dt

— Rn(,l ‘ Rdl

= c. — Г?….

= ЬК, + X К ‘ +(Rf ])Rnf, a -{J-VS )Kg, a -(J-Vl )Kta ‘ К

(15.17c)

Here b represents the blanket coverage factor introduced in Sec. 13.7 and ту denotes the average number of neutrons emitted per neutron absorbed in j — nuclides. Obviously r| > 1 for neutron-multiplying and fissile nuclei, while the fertile materials feature r|g < 1 and T), < 1, respectively.

= 0, dt dt dt leads therefore to the following conditions on the reaction rates: Rnt, a Rnt. t Rdt * * Rnfa ~ £r Rng, c }~x, ft m=f,2n,3n where in Eq. (15.19c) we have substituted

dN*n dt

The case of steady-state operation, defined by dN; _ dN) _ dNn

v R

n* = —

, r g, m ng, m

with Vg, m indicating the average number of neutrons released per neutron- multiplying reaction of type m [m: f, 2n, 3n] in fertile nuclei g. The set of Eqs. (15.19a) — (15.19c) can be manipulated to give the following explicit expression for the hybrid breeding ratio, Eq. (15.16):

R*

,(15.21)

x lynf, a m=f,2n,3n, a,a

where we have assumed a blanket design such that b ~ 1 — Tjt. The first term on the right hand side of Eq. (15.21) resembles the breeding ratio of an "infinite"
fast breeder, but here its numerical value may be much larger because the neutron spectrum in the hybrid blanket driven by 14.1 MeV d-t fusion neutrons can peak at a higher energy. Indeed, for neutron energies up to 14 MeV, the energy dependence of T|f is given by

rjf~a]+a1E (15.22)

where ai is in the range 1 to 1.5 and 0<a2<0.2-depending upon the isotopes involved-for E in units of MeV. Employing a neutron multiplier, which obviously features T|x > 1, will provide for an increased breeding ratio. Further neutron gain takes place by fast fissions of fertile nuclei and inelastic scattering from them associated with vgif = 3, vg>2„ = 2 and vg,3„ = 3, respectively. All these neutron production mechanisms together are capable of maintaining a high neutron availability-for-breeding against parasitic absorption and leakage out of the blanket. Hence, the breeding ratio for such a fusion-fission hybrid can substantially exceed the breeding ratios obtainable with fast breeder fission reactors.

Indeed, for recent hybrid concepts designed to stress fuel production, it is estimated that a single hybrid can support up to 10 fission reactors each having a thermal power level equal to that of the hybrid; in contrast, the typical fast breeder may typically support about one companion fission reactor of comparable power. Thus, the roles of such systems would be quite different: the hybrid focuses upon fuel breeding whereas the fast-fission breeder emphasizes energy production with some breeding.