Add more documentation and references for the Milne BC

doc/content/bib/references.bib

@@ -0,0 +1,36 @@
+
+@article{placzek_milnes_1947,
+	title = {Milne's {Problem} in {Transport} {Theory}},
+	volume = {72},
+	url = {https://link.aps.org/doi/10.1103/PhysRev.72.550},
+	doi = {10.1103/PhysRev.72.550},
+	abstract = {A modified derivation of the Wiener-Hopf solution of Milne's problem is given in a form suitable for application to problems in the theory of neutron diffusion.},
+	number = {7},
+	urldate = {2024-05-31},
+	journal = {Physical Review},
+	author = {Placzek, G. and Seidel, W.},
+	month = oct,
+	year = {1947},
+	note = {Publisher: American Physical Society},
+	pages = {550--555},
+	file = {APS Snapshot:C\:\\Users\\Sun Myung\\Zotero\\storage\\IJVWPMDS\\PhysRev.72.html:text/html;Full Text PDF:C\:\\Users\\Sun Myung\\Zotero\\storage\\TVUWZQ6J\\Placzek and Seidel - 1947 - Milne's Problem in Transport Theory.pdf:application/pdf},
+}
+
+@article{rulko_variational_1995,
+	title = {Variational {P1} {Approximations} of {General}-{Geometry} {Multigroup} {Transport} {Problems}},
+	volume = {121},
+	issn = {0029-5639},
+	url = {https://doi.org/10.13182/NSE121-393},
+	doi = {10.13182/NSE121-393},
+	abstract = {A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional “optimally”determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for mono-energetic problems. Other boundary conditions are obtained by choosing different values of α. We discuss this indeterminancy of a in conjunction with numerical experiments.},
+	number = {3},
+	urldate = {2024-05-31},
+	journal = {Nuclear Science and Engineering},
+	author = {Rulko, Robert P. and Tomašević, Djordje and Larsen, Edward W.},
+	month = dec,
+	year = {1995},
+	note = {Publisher: Taylor \& Francis
+\_eprint: https://doi.org/10.13182/NSE121-393},
+	pages = {393--404},
+	file = {Full Text PDF:C\:\\Users\\Sun Myung\\Zotero\\storage\\8NHDX7DM\\Rulko et al. - 1995 - Variational P1 Approximations of General-Geometry .pdf:application/pdf},
+}

doc/content/source/bcs/VacuumConcBC.md

@@ -12,12 +12,18 @@ by parts to the neutron diffusion term ([GroupDiffusion](/GroupDiffusion.md)) is
 -\int_{\partial V}\psi D_g\nabla\phi_g\cdot\hat{n}\ dS =
 \int_{\partial V}\psi\frac{\phi_g}{\alpha}\ dS
 
-The value of $\alpha$ varies depending on the formulation selected using the `vacuum_bc_type`
-parameter.
+The value of $\alpha$ varies depending on the BC type selected using the `vacuum_bc_type`
+parameter. The available options are:
+
 1. Marshak: $\alpha=2$
 2. Mark: $\alpha=\sqrt{3}$
 3. Milne: $\alpha=3\times 0.710446$
 
+The Marshak and Mark BCs are derived from vacuum boundary condition approximations using
+$P_1$ and $S_2$ transport methods, respectively. The Milne BC is derived from the exact analytical
+solution of the Milne problem [!citep](placzek_milnes_1947) and has been proven to be accurate for
+a wide range of diffusive problems [!citep](rulko_variational_1995).
+
 ## Example Input File Syntax
 
 !! Describe and include an example of how to use the VacuumConcBC object.

src/bcs/VacuumConcBC.C

@@ -25,6 +25,8 @@ VacuumConcBC::VacuumConcBC(const InputParameters & parameters)
       _alpha = std::sqrt(3.);
       break;
     case MILNE:
+      // Derived from the exact analytical solution to the Milne problem. See MooseDocs-based
+      // documentation for more information.
       _alpha = 3 * 0.710446;
       break;
   }