<p> The conditions needed for the amplication of radiation by an ensemble of magnetized, relativistic electrons that are collisionally slowing down are investigated. The current study is aimed at extending the work of other researchers in developing solid-state sources of Terahertz radiation. The source type considered here is based on gyrotron-like dynamics of graphene electrons, or it can alternately be viewed as a solid state laser source that uses Landau levels as its band structure and is thus similar to a quantum cascade laser. Such sources are appealing because they offer the potential for a compact, tunable source of Terahertz radiation that could have commercial applications in scanning, communication, or energy transfer. An exploration is undertaken, using linear and nonlinear theories, of the conditions under which such sources might be viable, assuming realistic parameters. Classical physics is used, and the model involves electrons in monolayer graphene assumed to be pumped by a laser, follow classical laws of motion with the dissipation represented by a damping force term, and lose energy to the electromagnetic field as well. The graphene is assumed to be in a homogeneous magnetic field, and is sandwiched between two partially-transmissive mirrors so that the device acts as an oscillator. </p><p> This thesis incorporates the results of two approaches to the study of the problem. In the first approach, a linear model is derived semi-analytically, which is relevant to the conditions under which there is gain in the device and thus stable operation is possible, versus the regime in which there is no net gain. In the second approach, a numerical simulation is employed to explore the nonlinear regime and saturation behavior of the oscillator. The simulation and the linear model both assume the same original equations of motion for the field and particles that interact self-consistently. The model used here is very simplied, but the aim here is to elucidate the basic principles and scaling behavior of such devices, not necessarily to calculate what the exact dynamics, outputs, and parameters of a fully commercially realized device will be.</p><p>