Abstract The self-consistent differential equations, which describe a laminar-flow equilibrium state in a magnetically focused intense relativistic electron beam propagating inside a conducting waveguide, are presented. The canonical angular momentum, $p_{\theta }$, defined under the conditions at the source, uniquely determines the possible solutions of these equations. By numerically solving these equations, the space-charge limited current and the externally applied magnetic field are obtained in a solid beam and a hollow beam in two cases of $p_{\theta }=0$ (magnetically shielded source) and $p_{\theta }=$ const. (immersed source) separately. It is shown that the hollow beam is more beneficial to the propagation of the intense relativistic beam through a drift tube than the solid beam.
Received: 16 July 2006
Revised: 03 February 2007
Accepted manuscript online:
Fund: Project supported by
the National Natural Science Foundation of China (Grant No~10476004).
Cite this article:
Li Jian-Qing(李建清) and Mo Yuan-Long(莫元龙) Space-charge limiting currents for magnetically focused intense relativistic electron beams 2007 Chinese Physics 16 2716
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