Sheet electron beams focused by periodically cusped magnetic (PCM) fie
lds are stable against low-frequency velocity-shear instabilities (suc
h as the diocotron mode). This is in contrast to the more familiar uns
table behavior in uniform solenoidal magnetic fields. A period-average
d analytic model shows that a PCM-focused beam is stabilized by ponder
omotive forces for short PCM periods. Numerical particle simulations f
or a semi-infinite sheet beam verify this prediction and also indicate
diocotron stability for long PCM periods is less constraining than pr
oviding for space-charge confinement and trajectory stability in the P
CM focusing system. In this article the issue of beam matching and sid
e focusing for sheet beams of finite width is also discussed. A review
of past and present theoretical and experimental investigations of sh
eet-beam transport is presented.