Nonlinear rf Behavior of Electron Beams with Velocity Distribution. II. Application to Rectangular Velocity Distribution

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Abstract
The nonlinear disk electron analysis in Part I is applied to a practical example. Two changes are imposed on the analysis to decrease the computer running time. Electron trajectories and the first three components of current are calculated for a beam with a rectangular velocity distribution that is simulated by eight dc velocity classes. Excellent agreement is obtained with a linear theory for small values of initial density modulation. Periodic variation of the space‐charge parameter leads to the equivalent of scalloped beam amplification in a multivelocity beam. A linear force‐taper correction is derived and its stabilizing effect is shown. Its use is suggested for improving the accuracy of monovelocity disk electron calculations. The interpretation of space‐charge wave decay in multivelocity electron beams as spatial Landau damping of the fast wave is questioned. It is suggested that damping is due to multidimensional effects not taken into account by present linear and nonlinear one‐dimensional theories.

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