A confinement method with apparently more merit than the aforementioned is inertial confinement fusion, involving compression of a small fusion fuel pellet to high density and temperature by external laser or ion beams, Fig.4.1. The density — temperature conditions so achieved are expected to provide for a pulse of fusion energy before pellet disassembly. The incident laser or ion beam induces an
inward directed momentum of the outer layers of the pellet, thereby yielding a high density of material, the inertia of which confines the fuel against the fusion reaction explosive effect of disassembly for a sufficient time to allow enough fusion reactions to occur.

Laser or

Some critical characteristic features of inertially confined fusion can be described by the following. Consider, for this purpose, a d-t pellet at an advanced stage of compression with a plasma formed therefrom and fusion bum occurring. The tritium ion density Nt will, in the absence of leakage, decrease according to its bum rate

with the symbols here used as previously defined. In this context, we may further identify a triton mean-life, X,, by

with Nd = Nd,0 taken to be some suitable initial average deuterium population density and <Gv>dt is taken at some appropriate average temperature. Expecting the pellet disassembly to be rapid suggests that Ttu should also be small. Two possibilities of reducing Tfi, become evident from Eq.(4.3). One can enhance <Ov> by increasing the relative speed of the reactants which, however, is limited by the techniques of heat deposition in the fuel as well as by the more rapid disintegration at higher temperatures. The other option is to increase the fuel
density by several orders of magnitude. The reaction rate parameter <Ov>(lt is a maximum at an ion temperature of ~60 keV, and the density is a maximum at the onset of fusion bum which is also occurring at the time pellet disassembly begins.

A pellet, once compressed and with fusion reactions taking place, will evidently heat up further and hence tend toward disintegration. The speed of outward motion of the pellet atoms is, to a first approximation, given by the sonic speed vs which, in a d-t plasma, is given by

Here, у is the ratio of specific heats (7 = 5/3), Nj is the ion density, and m, the average ion mass.

As a characteristic expansion, we take the pellet’s spherical inflation from its initial radius Rb when the fusion bum began, to a size of radius 2Rb. During this process, the fuel density will have decreased by a factor of 23 and the rate of fusion energy release will have accordingly decreased by the factor (2 ) = 64; hence, most of the fusion reactions will have taken place during this initial stage of disassembly. Thus, the time for doubling of the pellet radius is taken as being representative of the inertial confinement time, Tlc, given by

Evidently, Tfu of Eq.(4.3) should be shorter than-or perhaps of the order of-Tic for sufficient fusion bum to take place so that, as a required initial condition, we must have

T fu ^ Tic

that is,

For the case of Nd,0 = Ntj0= Nii0/2, that is half of the compressed fuel density at the beginning of the fusion bum, we may therefore write the requirement as

ґ 1/2

‘ 4Ш,

Taking an average fusion fuel temperature of about Eth = 20 keV, we obtain by substitution,

Ni,0 Rb > 1024 cm2 • (4.8)

Some essential technical features of inertial confinement fusion may now be

qualitatively and quantitatively established. First, as will be shown in Ch. 11, the beam energy required to compress a pellet corresponds to the resultant heat content of the compressed pellet, and hence varies as RI. Existing laser beam powers are such that Rb needs to be kept in the range of millimetres or less. Second, the fuel density will evidently need to become very large, typically exceeding 103 times that of its equivalent solid density. Finally, the quantity of the initial fuel which bums up needs to be carefully specified since it relates to the overall energy viability of each fusion pulse as well as to the capacity of the surrounding medium to absorb the blast energy.

Thus, as an initial conclusion, we may assert that very high power drivers and very high compression is required for fusion energy achievement by inertial confinement. Further analysis of inertial confinement fusion is the subject of Ch. 11.