The non-linear analysis of an adiabatic magnicon has been developed. In the configuration presented herein both the buncher and catcher cavities employ fast radiation fields in cyclotron resonance with an electron beam with exclusively axial electron velocity initially. The drift space between the cavities has both an adiabatically varying magnetostatic field and an axial electrostatic field. The properties of the strong azimuthal bunching, generated in the buncher, have been calculated and the conditions of the drift space have been determined, to satisfy the cyclotron resonance in the catcher. The idealized system has been calculated to operate in principle at electronic efficiency eta(e) = 100% with 25% gain, while reduced values of eta(e) give higher gain, still keeping the system efficiency at the nominal value of 100%.