Analytical solutions of the molten salt reactor equations

Highlights: ► The solution of the diffusion theory MSR equations are given in a compact analytical form. ► The integral terms are given a physical interpretation. ► The approximation of no precursor recirculation is introduced. -- Abstract: The one-group diffusion theory of molten salt reactors in a homogeneous reactor model is revisited. First, the integral terms in the equation for the flux, obtained after the elimination of the delayed neutron precursors, are given a physical interpretation. This gives an understanding of the physical meaning of the concept of infinite fuel recirculation velocity, which eliminates one of the two integral terms, introduced in earlier work in order to find analytic solutions. In the light of the physical interpretation, another approximation, representing a different limiting case can be defined, corresponding to long recirculation times, i.e. no recirculation of the delayed neutron precursors to the core. This approximation incurs the neglecting of the other integral term, and it can also be solved analytically. Finally it is shown that the full equation, without neglecting any of the integral terms, has also a compact analytical solution and it is demonstrated how the case of the infinite velocity can be obtained as a limit case of the full solution. The analytical solutions open up the possibility to study a number of questions in analytical form, such as the calculation of the point kinetic response of the reactor, or the effect of the different boundary conditions. As an illustration, the solutions corresponding to the vanishing of the flux at the extrapolated boundary are compared to those obtained from the logarithmic boundary conditions.