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Effects of azimuthal and radial spreads of canonical momentum on electron‐beam focusing characteristics in the presence of space‐charge forces

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2 Author(s)
Cohen, Moshe ; Department of Electrical Engineering–Physical Electronics, Faculty of Engineering, Tel‐Aviv University, Ramat‐Aviv 69978, Israel ; Gover, A.

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A theoretical and numerical investigation of the effects of azimuthal and radial spreads of canonical momentum on an electron beam focused by a magnetic lens in the presence of space‐charge forces is presented. The particles are inserted with an initial Gaussian distribution in the transverse space and in the momentum coordinates or with a uniform initial current distribution. The particle trajectory equation is derived for parameters of an arbitrary applied fields configuration with cylindrical symmetry, and a nonvanishing initial canonical momentum. In the absence of an initial momentum spread particles launched above a critical radial distance from the axis exhibit a phase‐space tearing effect in the electron distribution. The inclusion of initial canonical momentum spread in the model allows for skewed trajectories with strong centrifugal force which prevents the appearance and overshadows the effect of strong space‐charge forces near the axis, which are responsible for the phase‐space tearing effect. © 1995 American Institute of Physics.

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Journal of Applied Physics  (Volume:78 ,  Issue: 1 )