Research and developmental activity towards the realization of fusion reactors has emphasized, first, magnetic confinement fusion and, second, inertial confinement fusion; low temperature fusion is a distant third. Concurrently, variations on these three as well as alternative concepts continue to appear and lead to some interest and research support. We consider two such approaches: one in the "mechanical" forcing of fusing reactions-impact fusion-and the other involving the complete transformation of the mass of the interacting particles into energy-annihilation energy.

Impact fusion is based on the notion that a macroparticle containing hydrogen atoms will-when accelerated to sufficiently high speed and made to impact upon a hydrogenous target-lead to a number of fusion reactions. An estimate of the required speed can be obtained as follows. Consider a macroparticle of mass M and speed v hitting a target. The kinetic energy of the atoms in the projectile must be of the order of the Coulomb barrier, U0= U(R0) of Ch. 2, in order for fusion reactions to occur. For the N* atoms in the projectile of mass M, we should

Then, using U0 ~ 400 keV and ma ~ 3.3 x 10’27 kg for deuterium, yields a speed of v ~ 6200 km/s.

A speed of 6200 km/s is, by terrestrial standards, exceedingly high; recall that the speed of a bullet is < 1 km/s and the escape speed from the earth is ~ 11 km/s. Hence, the use of chemical explosives to attain such high speeds seems unlikely. One might, however, consider electromechanical means as suggested by the following.

Consider extending the principle of nuclear particle accelerators to macroparticles. Suppose a charge of Q is established on a projectile of mass M in a space characterized by a constant potential difference Ee per unit length. The force relation is evidently

M — = QEe (16.35a)

dt

and its integration using ds = v dt leads to

Here, L is the total path length. Currently attainable electric field strengths Ee, a reasonable length L, and assuming a constant Q/M suggest that speeds in the range of — 100 km/s are achievable.

A working device for such electromechanical acceleration is known as a rail gun or electromagnetic launcher, Fig. 16.6. As suggested therein, a current flows through a circuit of conducting rails and movable armature to which the projectile is attached. An increasing current flow generates a time varying magnetic field which, by its Lorentz force on the conductor and for the case of rigid rails, accelerates the projectile towards a stationary target.

Numerous other concepts have been suggested to aid in high speed attainment. Among them are speed multiplication by momentum conservation, electromagnetic energy focusing and the use of losses to generate high speed ablation.

Finally, we consider "fusion" energy by annihilation.

It is interesting to note that for either fission or fusion, the mass transformed into energy represents a small fraction of that of the interacting particles; typically

(16.36)

and is thus very small.

There exists, however, one type of reaction which converts all of its mass into energy: annihilation. Annihilation occurs whenever a particle meets its antiparticle. For example, a proton p and its antiproton p combine-without any external force effects-to yield

p + p —> 1456 MeV

with all subnuclear particles decaying very quickly to high energy gammas.

While the conversion of matter into energy is here complete and hence the energy release per initial mass of particles is a maximum, energy must still be

supplied: antiprotons p do not "exist" naturally and have to be produced in high energy accelerators.

Thus, human ingenuity continues to be at a premium in the attainment of this ultimate source of energy.

[1]

x

Fig. 5.7: Positive ion and electron drift in a combined uniform magnetic and electric field.

We now consider a generalization of the drift velocity caused by an arbitrary force F on a charged particle moving in an uniform В-field. To begin, we decompose the particle velocity into the components

v = Vsc+Vs (5.30)

where vgc is the velocity of guiding centre motion and vg is the velocity of gyration relative to the guiding centre. The equation of motion is now written as

m-^+m~[f=F + q(vgcx’B)+q(vgx B). (5.31)

Evidently the terms describing the circular motion, i. e. the second term on the left and the third on the right cancel one another according to Eq.(5.6). Further, in a static field exhibiting straight В-field lines the charged particle motion will be such that, averaged over one gyroperiod X, the total acceleration perpendicular to В must vanish; that is, the guiding centre is not accelerated in any direction perpendicular to B. Therefore, we average the transverse part of Eq.(5.31) over

[2] Note that from here on, the subscript kin, which was used in Eq. (4.11) for instruction and distinction purposes, is dropped.