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

Abstract

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.

Final Report for Sheet Beam Klystron Program

“…Figure 15a provides no focusing in the X plane; however, this is achieved with the configurations shown in Figures 15b and 15c. Basten found good propagation with c with very thin, elliptically shaped beams [5]. Unfortunately, as pointed out in Ref.…”

“…Studies by Booske et al [3] indicate that either PPM or wiggler focusing is feasible for the SBK. PPM was chosen because of the existence of calculations by Booske et al [4] and Basten et al [5] on configurations specifically for sheet beams. Those configurations include those shown in Figure 15.…”

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

“…h Step 3.-The derivative dðk 0 Þ=dH is numerically calculated as a function ofH using the discretized data in (2). h Step 4.-Equations (88) and (81) are applied to parametrically plot the frequency distribution Fðk =k 0 Þ versus k =k 0 using the discretized data points inH.…”

“…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.…”

W-band sheet beam klystron design

“…PCM is favored over wiggler focusing because the 1.2 em magnet period results in a fairly large wiggle motion that would require a wider beam tunnel. The PCM design follows the analysis ofBooske [2] and Basten [3] using offset magnets to provide focusing in the wide dimension of the beam. The magnetic field required varies from I kG at the input to 1.5 kG for the fully bunched beam in the output cavity.…”