Review for Test #1
For the Chapter 1 material, you need to be able to:
Explain the significance of any of the seven physical approximations we
Derive the mean free path as the inverse of the macroscopic cross section
Expand the directional dimension of the scattering cross section in Legendre
polynomials, using the orthogonality condition to arrive at the coefficients
- Show that the total derivative flux with respect to distance traveled
(d(psi)/ds) is equivalent to the Omega dot Del psi.
I will expect you do expand the total derivative FULLY (in terms of
all of the dependent variables of flux and explain why some of the terms
disappear in Cartesian coordinates.
- List and discuss the explicit and implicit boundary condition types
we studied -- void, surface source, reflected, white, periodic. Be able to show that
the incoming angular flux for the white boundary condition is four times
the outgoing partial current.
Develop the streaming operator in spherical coordinates as done in the
example in the notes.
- Demonstrate the equivalence of a conservative and non-conservative
version of the streaming operator for any curvilinear coordinate system.
(No need to memorize the versions.)
Explain the use of spherical harmonic moments and spherical harmonic distributions
to represent the scattering source term.
Explain why source problems must be subcritical.
- Develop the k-effective (lambda), buckling (B2), or time-absorption
(alpha) eigenvalues, showing how the Boltzmann Equation is modified
for each of them and indicating the range of values corresponding to
subcriticality, criticality, and supercriticality.
Develop the adjoint of any of the forward Boltzmann sub-operators -- L1,
L2, L3, or L4 -- as was done in class.
Explain through use of the definition of the adjoint -- <a,Lb>=<b,L*a>
-- that either the forward or adjoint solution can be used to find a detector
response. Included in this is a description of how it is done (each
way) and examples of when one method would be preferred over the other.