Hamiltonian map description of electron dynamics in gyrotrons

Electron dynamics in gyrotron resonators are described in terms of a Hamiltonian map. This map incorporates the dependency of electron dynamics on the parameters of the interacting radio-frequency (RF) field and it can be used for trajectory calculations through successive iteration, resulting in a symplectic integration scheme. The direct relation of the map to the physics of the model, along with its canonical form (phase space volume preserving) and the significant reduction of the number of iteration steps required for acceptable accuracy, are the main advantages of this method in comparison with standard methods such as Runge-Kutta. The general form of the Hamiltonian map allows for wide applications as a part of several numerical algorithms which incorporate CPU-consuming electron trajectories calculations