• C. Chen, R. Bhatt, A. Radovinsky, J.Z. Zhou
  MIT/PSFC, Cambridge, Massachusetts

A three-dimensional (3D) design is presented of a non-axisymmetric periodic permanent magnet focusing system which will be used to focus a large-aspect-ratio, ellipse-shaped, space-charge-dominated electron beam. In this design, an analytic theory is used to specify the magnetic profile for beam transport. The OPERA3D code is used to compute and optimize a realizable magnet system. Results of the magnetic design are verified by two-dimensional particle-in-cell and three-dimensional trajectory simulations of beam propagation using PFB2D and OMNITRAK, respectively. Results of fabrication tolerance studies are discussed.

• R. Bhatt, C. Chen, J.Z. Zhou
  MIT/PSFC, Cambridge, Massachusetts

The three-dimensional trajectory code, OMNITRAK, is used to simulate a space-charge-dominated beam of large-aspect-ratio elliptic cross-section propagating in a non-axisymmetric periodic permanent magnet focusing field. The simulation results confirm theoretical predictions in the paraxial limit. A realistic magnetic field profile is applied, and the beam sensitivity to magnet nonlinearities and misalignments is studied. The image-charge effect of conductor walls is examined for a variety of beam tunnel sizes and geometries.

• J.Z. Zhou, R. Bhatt, C. Chen
  MIT/PSFC, Cambridge, Massachusetts

A new class of equilibrium is discovered for a large-aspect-ratio ellipse-shaped charged-particle beam in a non-axisymmetric periodic permanent magnet focusing field. A paraxial cold-fluid model is employed to derive the equilibrium flow properties and generalized envelope equations with negligibly small emittance. A periodic beam equilibrium solution is obtained numerically from the generalized envelope equations. It is shown that the beam edges are well confined in both transverse directions, and that the equilibrium beam exhibits a small-angle periodic wobble as it propagates. A two-dimensional particle-in-cell (PIC) code, PFB2D, is used to verify the theoretical predictions in the paraxial limit, and to establish validity under non-paraxial situations and the influence of the conductor walls of the beam tunnel.

• R. Bhatt, T. Bemis, C. Chen
  MIT/PSFC, Cambridge, Massachusetts

A three-dimensional (3D) theory of non-relativistic, laminar, space-charge-limited, ellipse-shaped, charged-particle beam formation has been developed recently (Bhatt and Chen, PR:ST-AB, submitted Dec. 2004), whereby charged particles (electrons or ions) are accelerated across a diode by a static voltage differential and focused transversely by Pierce-type external electrodes placed along analytically specified surfaces. The treatment is extended to consider the perturbative effects of anode hole lensing, thermal isolation of the emitter, finiteness and nonuniformities of beam-forming electrodes, and an initial thermal spread. Analytic and semi-analytic results are presented along with 3D simulations utilizing the 3D trajectory code, OMNITRAK. Considerations with regard to beam matching into a periodic magnetic focusing lattice are discussed.