Periodic magnetic focusing of sheet electron beams*

Abstract

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...

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

“…Side focusing in the larger transverse dimension of the beam in this configuration should be provided by the fringe fields of this array. 18 Some support for this hypothesis can be based on experimental studies of offsetpole planar wiggler focusing of high-voltage sheet beams with very low space charge, 20,24 but investigations of offsetpole planar PCM confinement of low-voltage, high-spacecharge beams have never been reported. Analytic expressions for the fringe fields of offset-pole configurations can be obtained by replacing the offset-pole regions with semiinfinite sheets of ''surface magnetic charge'' as discussed in Ref.…”

“…Generalization to relativistic expressions is illustrated for infinitely wide sheet beams in Ref. 20.…”

“…Recent articles have shown that space-charge-dominated, infinitely wide sheet electron beams can be stabilized in periodically varying magnetic field configurations based on the PCM array. [18][19][20] This article describes the results of advanced theoretical and computational studies of the focusing and transport of sheet electron beams in planar PCM fields. The beam dynamics are examined using analytic methods, numerical solutions of the transverse beam envelope equations, and detailed particle simulations.…”

“…More importantly, this work addresses the issue of beam edge confinement for finitewidth sheet beams. For the latter issue, two complementary magnet configurations are investigated: ͑1͒ the offset-pole PCM configuration, 18,20 and ͑2͒ a hybrid periodic scheme combining a planar PCM array for bulk beam confinement with periodic-quadrupole-magnetic ͑PQM͒ fields for beam edge focusing. With either approach, robust side focusing is observed for remarkably high-space-charge beams.…”

Sheet beam model for intense space charge: Application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam

“…One-dimensional (1D) sheet-beam models have been applied in the analysis of microwave devices and free-electron lasers [1][2][3][4][5]. 1D sheet-beam models have also been exploited as a simplified framework to gain insight into higher-dimensional models of beams in particle accelerators-particularly on difficult spacecharge effects.…”