Cherenkov free electron laser (CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.