In this paper we study the validity of the model of one-dimensional motion of relativistic electrons taking into account the transverse gradients of their magnetic field in Maxwell’s equations and neglecting the effects of pinch and relativistic anti-pinch. When considering the problem of electron current amplification in planar unipolar and bipolar diodes with an ionic fountain, this model leads to a threefold increase in power at the same accelerating voltage in the case when the magnetic field of the beam is accounted for.
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