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Numerical Study of the Hamiltonian Gyrotron Map

The recently derived Hamiltonian map for description of electron dynamics replaces the original continuous gyrotron differential equation by a discrete iterative map which runs much faster on computers than the small-step standard numerical integration methods, such as Runge-Kutta. It allows a significant reduction of the number of iteration steps required for acceptable accuracy. The gyrotron map is studied numerically for different combinations of gyrotron operating parameters.