Abstract
It is shown that, when placed in uniform crossed fields, a relativistic charged particle with an initial thermal velocity describes a prolate cycloid. Analytical formulas for the parameters of the relativistic ribbon-shaped beam (velocity straggling, oscillation amplitude, and spatial and time periods) forming in crossed fields are derived without allowance for space charge fields. All the desired parameters can be determined by presetting three initial parameters (beam velocity, magnetic field, and emitting surface area).
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