Magnetic quadrupole formation of elliptical sheet electron beams for high-power microwave devices

Sheet electron beams are attractive for high-power microwave sources due to their ability to transport high current, at reduced current density, through thin clearance apertures and in close proximity to walls or RF structures. This paper reports on the theoretical investigation of magnetic quadrupole formation of elliptical sheet electron beams for use in high-power microwave devices. The beam envelope equations for an initially round beam passing through a physical non-symmetric quadrupole pair in the presence of space-charge, finite beam emittance, and under the effects of third-order field components and longitudinal velocity variations are presented. The presence of space-charge compensates for over-focusing in the thin beam-dimension and allows for the formation of highly elliptic sheet electron beams. As an example, the results of our study were applied to an existing Pierce gun source with a beam radius of 0.6 cm, beam energy of 10 keV and current density of 2.0 A/cm². We find that an elliptical beam with major radius r_a=3.61 cm, minor radius r _b=0.16 cm and ellipticity (r_a/r_b) of 22.5 can be produced with only modest quadrupole gradients of 64 G/cm and 18 G/cm. Quadrupole formation of elliptical sheet-beams may be particularly suited for experimental research applications since existing round-beam electron guns may be used and changes in beam ellipticity may be made without breaking the vacuum system