Electron cyclotron resonance heating has been successfully used in a number of experiments, firstly to raise the plasma temperature and secondly to drive currents noninductively. Recently the microwaves in tokamak experiment (MTX) has been proposed at the Lawrence Livermore Laboratory, which will involve pulsed heating at powers much higher than have previously been possible, using a Free Electron Laser (PEL). The physics of such an experiment differs greatly from the physics of experiments using less powerful but continuous operation gyrotron sources. An analytical model of the interaction between a wave and an electron is presented on the assumption that the wave amplitude experienced along the electron guiding centre changes slowly with time as it passes through the beam. This model is tested numerically by integrating the equations of motion governing the electron's motion as it interacts with the wave. Finally this model is used to predict the possible growth of instabilities in a plasma heated by a FEL. The growth rates of these waves may be large enough to act on the plasma in time scales much shorter than typical electron collision times.