Thermal-Neutron Space-Time Decay Constants in Various Order P_N Approximations

The thermal neutron space-time eigenvalue spectrum of the multigroup P_N approximation is investigated numerically for a modified form of the Radkowsky Kernel. Both discrete eigenvalues and eigenvalues that are assigned to a ‘continuum region,’ on the grounds that the corresponding eigenvectors exhibit singularities, are found. The continuum region so defined agrees well with that expected for the Boltzmann Equation. It is found that, when λ, the time decay constant, is plotted vs B², the square of the geometrical buckling, there is in the P_N approximation a critical value beyond which no real eigenvalues λ exist. The value of is sensitive to the order of the P_N approximation, increasing with increasing N. It is conjectured that corresponds, when the extrapolated endpoint is considered, to a slab of zero thickness through which a burst of neutrons would pass undisturbed as an ideal travelling wave.