Two-plane focusing of high-space-charge sheet electron beams using periodically cusped magnetic fields

Numerical and theoretical analyses show that stable, two-plane focusing of finite width, elliptical cross section, sheet electron beams with high space charge (low voltage, high current density) can be accomplished using periodically cusped-magnetic (PCM) fields. Magnetic field strength requirements for focusing high-space-charge sheet beams are within technological capabilities of modern permanent magnet technology. Both an offset-pole PCM stack and a PCM stack combined with a periodic quadrupole magnet (PQM) edge array are shown to be effective for two-plane sheet beam confinement. The PCM-PQM hybrid configuration offers inherent advantages for independent adjustment of confinement fields to achieve beam matching (minimum ripple) in both transverse dimensions. The offset-pole configuration offers the advantage of open-side access for applications such as vacuum electronic microwave devices. It is also shown that PCM-focused sheet beam envelope stability obeys criteria equivalent to that previously identified for round-cross-section electron beams in periodic permanent magnet focusing.