Abstract
A study is made of the generation of intense hollow relativistic electron beams in a foil-less diode. A strong magnetic field is assumed so that the electron motion is one dimensional. Also, the electron motion is considered to be ultra-relativistic. The problem of the self-consistent space charge in the diode is reduced to a singular integral equation. This integral equation is solved and the nature of the solutions is discussed. The beam density increases at the beam edges and has a minimum in the beam interior. The diode impedance as a function of the beam thickness and geometry is discussed.
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