Characteristics of a Tapered Cascade for Isotope Separation by Gaseous Diffusion

Usually a number of separating stages have to be connected in series to attain the desired degree of isotope separation by gaseous diffusion. Such a series-connected group of stages is called a cascade. In this paper the differential equation describing the time-dependence of a tapered cascade in which the interstage flow changes stage by stage is derived and solved under some reasonable assumptions. On the basis of these analytical results, the static and dynamic characteristics of a tapered cascade are discussed. For the same total number of stages, the cascade requiring the largest equilibrium time to reach steady-state condition is described. Also shown is that the so-called ideal cascade is not recommended from the standpoint of dynamic characteristics, although its superiority in static characteristics is familiar. It is pointed out that by a slight reduction of the cut θ from that of the ideal cascade θ_ideal the dynamic characteristics are improved to some extent, but the selection of θ greater than θ_ideal results in both static and dynamic characteristics being unfavorable. It is also shown that the equilibrium time of a tapered cascade tends to increase with the total number of stages N in proportion to N² as in a square cascade. The top stage is not always the last to reach the steady-state condition. A simple method is proposed to predict how the equilibrium time differs in each stage of the cascade.