Evolution and thermonuclear yield of a high β plasma column

The evolution of a high β linear ϑ pinch plasma is investigated by assuming a square density profile. A new analytic solution for the self-similar area wave is found for the case β=1, γ=2 and an exact integral of the motion of the reflected area wave is derived in the general case. The evolution of the plasma variables in the region between the reflected area waves is calculated numerically. Except for cases in which (1−β)1/2 is approximately equal to a/b (plasma radius/solenoid radius), the density in this region is a slowing varying function of position. The relative fusion power production and total energy field is estimated, assuming constant temperature, for combinations of β and b/a relevant to two conceptual designs. It is found that in most cases significant power is produced after the area waves have reflected from the midplane of the solenoid. The model predicts that programming the applied magnetic field to simulate infinite b/a enhances the yield by approximately 85% for a 3-m neutron source but only by approximately 18% a 1-km fusion reactor.