The Lawson criterion and general energy flow analyses of Ch. 8 can be applied to inertial confinement as well as to magnetic confinement. However, the parameters of interest and the nomenclature is different for each. We now re­examine the energy balance specifically for an inertial confinement fusion system, where one pulse is still taken as the characteristic time interval for which an energy balance is established.

For present purposes, we define the following three energy components necessary in a parametric analysis of an inertial confinement fusion system, Fig. 11.2:

Ebe* = energy contained in the laser or ion beam which triggers compression;

E, h = thermal energy of the compressed target ions and electrons following impingement of the beam;

Efu = fusion energy released during the associated bum time xb.

Not all of the beam energy will appear as thermal energy of the ions and electrons in the target; a fraction may be reflected or scattered and some energy is carried off with the ablated outer layer. Hence, a coupling efficiency T]c can be defined which relates Ebe and Eth by

Е*н= ЛсЕІе > 0 <т)с<1. (П.17)

A characteristic pellet energy multiplication Mp relates Efu* to Ebe* by

E*ju = МрЕІе > (П.18)

and for an energetically viable system, Mp has to substantially exceed 1. Note that T]e and Mp are design parameters of the system.

The overall energy flow for an electricity producing inertial confinement fusion reactor system is suggested in Fig. 11.2 for which the station electrical energy output is given by

Ena = Vju Efu — El • (11-19)

Here рь, is the efficiency of converting the fusion energy into electrical form and Ej„ is the circulating electrical energy component required to sustain the lasers or ion accelerators. The conversion of this electrical energy into beam energy is taken to occur with an efficiency T)in defined by

^ = % 0<Пт<1. (11.20)

Em

The station electrical energy output can be compactly written by defining an electrical energy multiplication as

Л fuE’fu

El

The essential requirement for a viable inertial confinement fusion system is therefore

Me> 1.

This energy viability criteria can be related to the several conversion efficiencies and the pellet multiplication already defined. A substitution of Eqs.(11.18), (11.20) and (11.21) into Eq.(11.23) yields

ЛыЛ/иМР> 1, (11.24)

and thus specifies the necessary pellet energy multiplication required. As currently envisioned, lasers are relatively inefficient with r|in ~ 0.06, while qfu ~ 1/3 for conventional energy conversion; this yields a requirement of Mp > 50. This demanding result can be reduced if the driver is more efficient; for example

for ion accelerators, T|jn ~ 0.3 may be possible, giving Mp >10. Further, the beam coupling efficiency enters via

Note that (Eft, / Eth ) is the ratio of fusion energy produced to the energy deposited in the pellet and hence, in analogy to Eq. (8.6), can be identified as the according pellet plasma Q-value which, upon introduction in Eq. (11.26), has to satisfy the requirement

for energy viability. Evidently, a very high coupling efficiency ric is desired. For example, for a laser with ric = 0.05 and the previous tiin and r)tu values, we require Qpp > 1000. One way to meet this requirement is to have a high fusion gain pellet which in turn implies a very high compression.