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 density͒ can be accomplished using periodically cusped-magnetic ͑PCM͒ 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 ͑PQM͒ 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 ripple͒ 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.

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...

No abstract

Particle simulations compare the behavior of nonrelativistic sheet electron beams in uniform static and nonuniform time-harmonic magnetic fields. The time-harmonic fields are equivalent to periodically cusped magnetic (PCM) fields. While the sheet beam in a uniform field exhibits diocotron instability, the PCM-focused beam is stabilized by ponderomotive forces, in agreement with recent analytic predictions [J. Appl. Phys. 73, 4140 (1993)]. Mismatched PCM-focused beams exhibit envelope oscillation and initially rapid emittance growth followed by a region of slower increase, in agreement with a recent semianalytic Fokker-Planck model. PACS numbers: 41.85.Lc, 41.85.Ja, 52.30.Bt Sheet or ribbon electron beams are intrinsically well suited for use where high beam currents and small beam-channel clearances are required. Applications include high-average-power free electron lasers [1], conventional low-voltage microwave tubes [2], and quasioptical gyrotrons [3]. Other applications may include gas laser excitation and high-current electron accelerators. The principal advantage of sheet beams over round crosssection beams is that by spreading the current out in the wide transverse dimension, one can propagate high currents through small beam-channel clearances without excessive space charge repulsion. The principal disadvantage of sheet beams is their susceptibility to disruption and filamentation in uniform solenoidal focusing magnetic fields. This behavior arises from ExB drift velocity shear and is most commonly referred to as "diocotron" instability.Ponderomotive stabilization of instabilities is a familiar concept in plasma physics [4-6] and using ponderomotive forces to confine round cross-section electron beams is a familiar concept in accelerator physics [7,8]. As demonstrated in this Letter, periodically cusped magnetic (PCM) fields [2] provide both effective focusing and stabilization of the diocotron instability in nonrelativistic sheet electron beams.The ponderomotive force of interest to this work is illustrated by a time-harmonic magnetic field of the form B(y,t) -B 0^j -sin(co B t)y + B 0 cos(co B t)z .(1)These fields are applied to a sheet electron beam having a uniform charge density no, a thickness S in the y dimension, infinite width in the x dimension, and uniform velocity UQ along the z dimension. The equations of motion in the transverse Cx,j>) plane are x =-y~-E x + (D cz (t)y -Q) cy (t)uo, m y = -^-E y -co cz (t)x , (2b) m where co cy (t)=qB y (t)/m, CQ cz (t) = qB z (t)/m, and we as-sume that perturbations to the velocity along z are negligible, i.e., Z~UQ. We proceed to solve Eq.(2) using a multiple-time-scale approach, assuming that we can separate fluctuating quantities into linear sums of fast and slow time scale responses, e.g, JC(/) =Xf(t)+x s (t), y(t) -y/iri+ysit),etc. The magnetic field terms (oscillating with frequency Q>B) are assumed to be varying rapidly, while the electric field terms associated with beam space charge fluctuations are considered to be slowly varying. Assuming that...

No abstract