Vacuum propagation of solid relativistic electron beams

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Abstract
An investigation of equilibrium, stability, and space‐charge‐ limiting current of a solid relativistic beam propagating along a finite external magnetic field has been carried out and compared with experiments. The concept of a rigid‐rotor equilibrium is only approximately valid when the beam current is much less than the Alfvèn critical current. Typically, low‐voltage beams rotate fastest at the beam edge whereas high‐voltage beams rotate fastest near the beam axis. A limited investigation of the rigid rotor stability condition indicates, at worst, a weak instability may be present if the rigid‐rotor equilibrium is artificially imposed, and no instability at all for a self‐consistent equilibrium. Numerical solutions for the space‐charge limiting current and relativistic factor on axis are presented and compared with two‐dimensional, cylindrical, space‐ and time‐dependent simulations. Analytical expressions for the limiting current are valid for ωc/ωb≳5, where ωc is the cyclotron frequency and ωb is the beam frequency. For external magnetic field strengths below this level, the limiting current increases monotonically with decreasing field strength until the beam collides with the drift tube. Expressions for foil scattering are also presented. The results are in good agreement with experiments.