New Approximate Solution of Space- and Energy-Dependent Reactor Kinetics

An expression different from the conventional modal expansion about space-dependent linear system kinetics is proposed. The solution is expressed in the form of a Laplace-transformed source transfer function. The Taylor expansion of the function in ‘s’ (the variable in the transformed domain) is obtained by solving the related stationary equations. The series is approximately continued to the simple form of the transfer function such as the first-order lag or the transport lag expression. In this method, it is not necessary to solve the eigenvalue problem directly. This solution contains the contribution from the higher modes and gives a practical approximation in a simple form, even if the response includes much higher modes. A numerical example is shown. This method is also applicable to general linear distributed constant systems. Some applications to coupled reactor theory and to thermalization kinetics are mentioned.