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A moving wavelength computer code developed for crossed-field amplifier simulations has been used to simulate the operation of a smooth-bore magnetron. Simulations using thermionic emission and a mixture of thermionic and secondary emission have been conducted. The simulations were run for about 24 000 cyclotron periods and were stationary for at least the last 18 000 of these periods. The results show the space charge does not settle to an approximation of a Brillouin state, but instead a charge distribution of lower density extends well beyond the edge of a theoretical Brillouin sheath. A small current reaches the anode. Trajectories extracted from the simulation show a mixture of shapes-some with substantial cycloiding, others with little cycloiding.