Separative power of an optimised concurrent gas centrifuge

TL;DR

This paper analytically derives the separative power of an optimized concurrent gas centrifuge, providing a formula that aligns with empirical data and exploring the conditions for optimal separation performance.

Contribution

It presents an analytical solution for the separative power of optimized concurrent gas centrifuges, including a formula and conditions for optimal operation.

Findings

Derived an analytical formula for separative power.

Confirmed the formula's agreement with empirical data.

Identified the optimal condition line for centrifuge parameters.

Abstract

The problem of separation of uranium isotopes in a concurrent gas centrifuge is solved analytically. Separative power of the optimized concurrent gas centrifuges equals to $\delta U=12.7(V/700~{\rm m/s})^2 (300 ~{\rm K}/T)L, ~{\rm kg ~SWU/yr}$, where $L$ and $V$ are the length and linear velocity of the rotor of the gas centrifuge, $T$ is the temperature. This formula well agrees with an empirical separative power of counter current gas centrifuges. The optimal value of the separative power is not unique on the plane $(p_w,v_z)$, where $p_w$ is pressure at the wall of the rotor and $v_z$ is axial velocity of the gas. This value is constant on a line defined by the equation $p_wv_z=constant$. Equations defining the mass flux and the electric power necessary to support the rotation of the gas centrifuge are obtained.