Sheet electron beams focused by periodically cusped magnetic (PCM ) fields are stable against low-frequency velocity-shear instabilities (such as the diocotron mode). This is in contrast to the more familiar unstable behavior in uniform solenoidal magnetic fields. A period-averaged analytic model shows that a PCM-focused beam is stabilized by ponderomotive forces for short PCM periods. Numerical particle simulations for a semi-infinite sheet beam verify this prediction and also indicate diocotron stability for long PCM periods is less constraining than providing for space-charge confinement and trajectory stability in the PCM focusing system. In this article the issue of beam matching and side focusing for sheet beams of finite width is also discussed. A review of past and present theoretical and experimental investigations of sheet-beam transport is presented. I. lNTROllUCTlONA strong motivation for the use of thin ribbon or sheet electron beams in coherent radiation sources or accelerators derives from the ability to transport large currents at reduced current density through thin clearance spaces or in close proximity to walls or structures. This feature is a result of the opportunity to add current to the beam at constant current density by increasing one wide transverse beam dimension, while keeping the other beam transverse dimension very small. A historically strong disincentive to using sheet electron beams in the above-mentioned applications is their known susceptibility to the disruptive diocotron instability occurring in the presence of a uniform solenoidal magnetic (focusing) field.Recent research appears to have identified a solution to this decades-old problem, paving the way for implementation of sheet beams in both relativistic and nonrelativistic applications. The essence of the solution is to use ponderomotive focusing achieved with one of several configurations of spatially periodic magnetic fields.In this paper we present an organized review of the physics and recent results of research of periodically focused sheet electron beams, and we describe new results of simulation studies of beam stability and emittance growth. II. HISTORICAL REVIEWThe advantage of using sheet electron beams for high current applications was first noted over three decades ago.' However, around the same time, experiments with both thin annular2"1 and planar4 sheet beams identified a filamentation instability when the beams were propagated parallel to a uniform solenoidal magnetic focusing field. The simplest theoretical model was derived for a very thin, monoenergetic, nonrelativistic, planar sheet beam, and *Paper 212, Bull. Am. Phys. Sot. 38, 1901Sot. 38, (1993. 'Invited speaker. considered only low-frequency, quasistatic perturbations transverse to the magnetic field axis.5 Since then, both the experimental and theoretical details have become considerably more sophisticated, including finite beam thickness, thermal velocity spread, relatistic beam energies, nearby conducting boundaries, ion-space-charge neutra...

A recent design concept for millimeter-wave free-electron lasers [J. Appl, Phys, 60, 521 (1986) Jwould require the stable propagation of a sheet electron beam through a narrow waveguide channel. Experimental results reported in this article support the feasibility of such a configuration by demonstrating the stable propagation of relativistic sheet electron beams through a narrow waveguide gap (3.2 mm) using focusing by a short-period electromagnet wiggler. 90% of the electron current in a loo-keV sheet electron beam was transmitted through a S-cm-Iong channel with peak wiggler fields of 800 G. Almost 80% of a 400-keV beam was similarly confined with a 16oo-G wiggler field. The data were consistent with single electron trajectory models, indicating that space-charge effects were minimal. No evidence of beam breakup or filamentation instabilities was observed.

In this paper, simple expressions for optimized dimensions of the electromagnet wiggler are derived and experimentally verified.

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