Estimates of the beam energy required to compress a pellet to bum conditions can be obtained by starting with Eq.(11.17) in the form

Eth

Пс

and hence, from Eq.( 11.18)

Based on our previous considerations, the total thermal energy in the pellet of radius Rb at the beginning of the fusion bum is explicitly given by

E;h(0) = ^NeJTe(0) + lNuokTl(0))(^Ri)^4KNiJTLX (11.30)

where we have taken

Ne* = Nu, and Te(0)=Ti(0)=Tio. (11.31)

According to Eq. (11.28), the beam energy requirement is therefore

1

In order to avoid the explicit calculation of the reaction energy released during the fusion bum time, Tb, as suggested by Eq. (7.15), let us take here the

Inertial Confinement Fusion proportionality

Efu x NloVb^b

and combine this with Eqs. (11.29) and (11.30) to obtain Mp(4nNiokTio Rl) — rjcNl0-jitRlXb

Further, recalling the expression for the disassembly speed, Eq.( 11.11), and relating

(11.35)

we re-arrange Eq. (11.34) to isolate Rb as

Mr
(11.36)

The beam energy requirement now follows by substituting this expression for Rb in Eq. (11.32) to yield

M3P

Nlnt where Abe is a temperature dependent factor. The exponents here are significant since they indicate a beam energy sensitive to Nji0, t|c and Mp. For the case of a target at normal liquid density and with Mp = 100, and even for Г|с = 1, this energy is found to be of the order of 1012 J, which is inaccessibly large. (Note that relating this to the approximately 10’9 s during which this energy needs to be delivered would represent an input power greatly exceeding the total steady power capacity of all electric power plants in North America.) If, however, target compression increases the density by 103, then the energy requirement is reduced by 106. This illustrates the reason for the very strong interest in high compression of the target.