Non-laminar electron beams in high magnetic fields

The nature of non-laminar electron flow in long electron beams, originating from magnetically-shielded electron guns and focused by a uniform magnetic field (shielded flow) is considered. Neglecting space-charge forces, the particle equations of motion in normalized form are used to obtain current- and charge-density variations across the beam and to account for the formation, by velocity dispersion, of current envelopes of high density. These are similar to those observed in experimental beams in high magnetic fields. From consideration of the forces at the start of the magnetic region, where space-charge forces may not be negligible, a qualitative exposition accounts for several features noted by workers on shielded-flow beams. In particular, reasons are given for expecting experimental non-uniform beams in shielded flow to show least variation in diameter at magnetic fields somewhat higher than the Brillouin value. The resulting beam will be non-laminar and doubly scalloped, owing to the non-uniform cross-section of most experimental beams at the entry to the magnetic region. Shielded flow appears to be laminar for the Brillouin condition, only approximately laminar for low magnetic fields, and completely non-laminar for high magnetic fields. The velocity dispersion effect will not account for the cumulative anomalous scalloping noted in work on u.h.f. noise waves. Many beams, in strong magnetic fields and obtainable vacua, may produceion densities considerably higher than their primary electron densities.