The static theory of the cylindrical magnetron

A set of equations is obtained for the state of the space charge in a magnetron when the electrons have zero initial velocity. Assuming low cathode current, an averaging method is used to obtain first and improved first approximations to the solution of the set of equations; approximate expressions are also obtained for the electron trajectories and velocities, and the space charge density and potential distributions. The range of application of the formulas is assessed by a comparison with the results of numerical integration.