Nuclear Science and Engineering / Volume 177 / Number 1 / May 2014 / Pages 19-34
Technical Paper / dx.doi.org/10.13182/NSE12-95
We investigate the degeneracy of the first-order PN equations and construct interface and boundary conditions that ensure a unique solution. Our technique is based on establishing an equivalence between the first- and second-order PN equations and showing that the (regular) second-order equations with opposite parity to N are nondegenerate. Assuming bounded angular flux moments and sources, we derive interface and boundary conditions for the regular second-order equations that, via the equivalence, are those to be used with the first-order PN equations. While providing independent derivations, our results reproduce those derived using solid harmonic expansions by Davison and Rumyantsev in the 1950s.