| Popis: |
A new method of obtaining analytic solutions of the space independent reactor kinetic equations for arbitrary time dependent reactivities is presented. The method is based upon transforming the kinetic equations with one group of delayed neutrons into a single Ricatti equation for the system. This single equation permits a variety of useful approximate solutions which are generally considerably more accurate than approximate solutions obtained for the standard kinetic equations. General perturbation solutions of the single equation for the system are found and are shown to be valid even for very large changes of the dependent variables. Specific solutions for step, impulse, ramp sinusoidal and generalized reactivities are found. The solution for sinusoidal reactivities confirms that unstable exponential flux growth occurs due to the presence of delayed neutrons, while without delayed neutrons the solution is oscillatory but bounded. Finally the exact solution is found for the system when the reactivity is an analytic function. |
