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 made
• 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.