In 2010, the Fermi Bubbles were discovered at the galactic center of the Milky Way. These giant gamma-ray structures, extending 50 degrees in galactic latitude and 20-30 degrees in galactic longitude, were not predicted. We wish to develop a model for the gamma-ray emission of the Fermi Bubbles. To do so, we assume that second order Fermi acceleration is responsible for the high-energy emission of the bubbles. Second order Fermi acceleration requires charged particles and irregular magnetic fields-both of which are present in the disk of the Milky Way galaxy. I use the assumption of second order Fermi acceleration in the transport equation, which describes the diffusion of particles. By solving the steady-state case of the transport equation, I compute the proton spectrum due to Fermi second order acceleration and compare this analytical solution to a numerical solution provided by Dr. P. Mertsch. Analytical solutions to the transport equation are taken from Becker, Le, & Dermer and are used to further test the numerical solution. I find that the numerical solution converges to the analytical solution in all cases. Thus, we know the numerical solution accurately calculates the proton spectrum. The gamma-ray spectrum follows the proton spectrum, and will be computed in the future. Show Partial Abstract