Abstract
A new method is presented to eliminate the undesirable end-effect appearing in the formation of a strip beam of charged particles according to the Pierce theory, without any additional device. By this method, a beam with finite length can be formed, regarding the cross section of the beam reasonably as a thin ellipse.An analytical solution is given for a rectilinear elliptic beam formation. It is troublesome, however, to perform the complete evaluation of the solution, but an approximation is also presented with sufficient accuracy.
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