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PARAXIAL SOLUTIONS FOR DECELERATED AXIALLY SYMMETRIC SPACE-CHARGE FLOW
STANFORD UNIV CALIF STANFORD ELECTRONICS LABS
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Solutions for space-charge-flow based on the well known axially symmetric paraxial approximation are presented. This permits, under a unified heading, some new solutions plus restatements and extensions of results previously appearing in separate contexts. In addition to the well known Universal Beam Spread Curve, solutions for linear, parabolic, and sinusoidal axial potential variations are obtained. The axial potential variation is solved for producing specified hyperbolic and parabolic beam trajectories. Following the trajectories and axial potentials obtained from the paraxial ray equation, representative approximate solutions are presented for the potentials within and outside the beam. These are obtained over limited regions by use of series expansions similar to those used in obtaining the paraxial approximation. The scale of the potential variations and trajectories were chosen primarily to show beam spreading in cases for which the space-charge forces are important and the beam potential is significantly depressed. This study had as a background the investigation of the axially symmetric depressed collector. Author
APPROVED FOR PUBLIC RELEASE