## Evaluation of Magnetic Refocusing in Linear-beam Microwave Tubes |

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axial component axial distance Axisymmetric beam expansion beam microwave tubes beam radius Brillouin radius Cathode field classes is computed classes of electrons collector efficiency constant plateau field cyclotron frequency cylindrical coordinates dc velocity decay slope decaying magnetic field Electron Beam electron charge electron trajectories equation B6 equations of motion fast electrons field are parameters Gewartowski and Watson Hamiltonian initial axial velocities initial conditions initial injection angles integrated Klystron Lewis Research Center linear beam microwave linear decay magnetic configuration magnetic decay magnetic field decays Magnetic field plateau magnetic flux density NASA NASA TN Normalized axial coordinate output angles particles percent plasma frequency plateau design velocity plateau length plateau region plateau value Poisson's equation radial refocusing region rms deviation rms value slope and plateau space charge forces spent beam spent electrons trajectories are computed traveling wave tube Traveling-Wave Tube tuning capability units of tunnel vector potential Watson ref