The differential equations of motion of an electron beam of high space charge moving through an axially symmetric magnetic field are readily solved by an analog computer. The solutions produced by the computer represent the beam radius and slope as a function of axial distance for any desired variation of axially symmetric magnetic field.nThe equations of motion are derived and normalized so as to be easily translated into the machine variables of the analog computer Three particular field variations are considered in order to illustrate the method of solution. The behavior of an electron beam in the fringing magnetic field region required by Brillouin flow conditions establishes the radius and slope of the beam as it enters the region of the fringing field,nRelationships between the magnitude of a periodic magnetic focusing field and its spatial period are developed for electron beams with “minimum –ripple” boundaries.
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