RINGBEARER is a particle simulation code for modelling an electron beam propagating in a gas characterized by a space and time varying conductivity generated by the beam. The code has two spatial dimensions, the beam is assumed to be axially symmetric. Equations for the beam driven pinch field, the plasma density, and the conductivity are given along with the appropriate initial conditions and boundary conditions. The equations governing particle energy loss, transverse motion, and scattering, in the beam generated pinch field are presented. The analytic models used in the code are presented with either references or derivations.