Lesson 1


*NE581 Nuclear Reactor Shielding* *Return to Course Outline*


	Review for Test #1 To adequately prepare for this test, you should be able to: 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 Use 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 the explicit and implicit boundary condition types we studied -- void, surface source, reflected, albedo, white, periodic. 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. 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) 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.

For the Chapter 2 material, you need to be able to:

Define any of the group cross sections in notes.
Find a group total cross section, given the flux shape and cross section as a function of energy.
Justify the use of Fission-1/E-Maxwellian spectrum approximations
Break the multigroup B.E. into the H⁰ and H¹ operators. Using the matrix for (H y = q), be able to describe the outer and inner iteration strategies utilizing the upper, lower, and diagonal matrix subdivisions of the H matrix (with appropriate iteration counts).
Describe the basis for various acceleration techniques: coarse mesh rebalance, synthetic acceleration, and extrapolation.
Be able to explain the extrapolation methods based on error mode analysis--how the error eigenvalues are manipulated using straight extrapolation, SOR, and Chebyshev acceleration


*Return to Course Outline*

Review for Test #1

For the Chapter 1 material, you need to be able to:

For the Chapter 2 material, you need to be able to: