;,~ is the lth flux moment for group g
at~~,~1 and # ; are lth, kth associated cosine, sine flux moments for group g
P(pu) and Plk (pU) are the Legendre and Associated Legendre polynomials.
ql (x ,y z, p, cp)is independent source for group g
The SN methodology is a widely accepted deterministic scheme in yielding numerical
solution to neutral particle radiation transport problems, and can be applied to medical physics
problems, provided that discretization and truncation errors can be reduced to an acceptable level
over the problem space. Depending on the amount of data needed per floating point operation,
the SN method is more efficient than the Monte Carlo method for many problems, and with
proper discretization produces an accurate solution". The SN method is widely used in nuclear
engineering to obtain a numerical solution of the Boltzmann transport equation. The method
solves the BTE for a discrete number of ordinates (directions) with associated weightsl6. The
combination of discrete directions and weights is referred to as quadrature set l. A drawback of
the SN method is that with the limited number of directions involved, in certain situations, this
may lead to so called r~ay-e~ff~cts, which appear as unphysical flux oscillations. In general, this
behavior occurs for problems with highly angular dependent/localized sources and/or fluxes, or
when the source is localized in a small region of space, in low density or highly absorbent media.
This can make medical physics applications, which often require small mesh sizes, relatively
large models, and low density materials, suffer severe ray-effects.
The ray-effects can be alleviated naturally by the presence of a distributed isotropic source,
which tends to flatten the flux in the angular domain. However, in medical physics, the photon
transport problems may exhibit significant ray effects. This effect becomes worsen in a low