Previous work has shown the Orion Bar to be an interface between ionized and molecular gas, viewed roughly edge-on, which is excited by the light from the Trapezium cluster. Much of the emission from any star-forming region will originate from such interfaces, so the Bar serves as a foundation test of any emission model. Here we combine X-ray, optical, infrared (IR), and radio data sets to derive emission spectra along the transition from H+ to H-0 to H-2 regions. We then reproduce the spectra of these layers with a simulation that simultaneously accounts for the detailed microphysics of the gas, the grains, and molecules, especially H-2 and CO. The magnetic field, observed to be the dominant pressure in another region of the Orion Nebula, is treated as a free parameter, along with the density of cosmic rays. Our model successfully accounts for the optical, IR, and radio observations across the Bar by including a significant magnetic pressure and also heating by an excess density of cosmic rays, which we suggest is due to cosmic rays being trapped in the compressed magnetic field. In the Orion Bar, as we had previously found in M17, momentum carried by radiation and winds from the newly formed stars pushes back and compresses the surrounding gas. There is a rough balance between outward momentum in starlight and the total pressure in atomic and molecular gas surrounding the H+ region. If the gas starts out with a weak magnetic field, the starlight from a newly formed cluster will push back the gas and compress the gas, magnetic field, and cosmic rays until magnetic pressure becomes an important factor.