Nuclear Science and Engineering / Volume 22 / Number 3 / July 1965 / Pages 321-327
Technical Paper / dx.doi.org/10.13182/NSE65-A20936
Articles are hosted by Taylor and Francis Online.
The time dependent P1 approximation to the neutron transport equation has been solved for the case of an oscillating source on one face of a finite parallelepiped. An oscillatory solution to the differential equations describes the propagation of neutron waves through the medium. Attenuation lengths of plane neutron waves were identical at low frequencies (ω < ½ νΣa) for the P1 and diffusion approximations but differ considerably at high frequencies (ω > 2ν Σtr). Wave lengths and wave speeds for the two approximations were slightly different at low frequencies, identical at immediate frequencies and considerably different at high frequencies. A new method, which considers the transient behavior of a spatially-integrated positive-definite function of flux and current, is used to show that the transient part of the solution decays to zero.