Transport of elliptic intense charged -particle beams

Abstract

The transport theory of high-intensity elliptic charged-particle beams is presented. In particular, the halo formation and beam loss problem associated with the high space charge and small-aperture structure is addressed, and a novel transport theory of large-aspect-ratio elliptic beams has been developed. In a small-aperture system image-charge effects have been found to be a new mechanism for inducing chaotic particle motion, halo formation and beam loss. The rms envelope equations have been derived and analyzed for unbunched intense charged-particle beams in an alternating-gradient focusing field and a cylindrical metal pipe. Numerical results have shown that for vacuum phase advance ao < 90°, the higher-order image-charge effects on the matched and slightly mismatched beam envelopes are negligibly small for all beams with arbitrary beam density profiles (including hollow density profiles) as well as for arbitrary small apertures (including beams with large aspect ratios). However, the main unstable region for the envelope evolution with image-charge effects, which occurs for 90: < a, < 270', depending on the value of the normalized beam intensity SKI e, has been found to be narrower than its counterpart without image-charge effects.

(cont.) Using the test-particle model it has been shown that in a small-aperture alternating-gradient focusing channel, image-charge effects induce chaotic particle motions and halo formation in intense charge-particle beams. This mechanism occurs for well-matched beams with the ideal Kapchinskij-Vladimirskij (KV) distribution. The halo formation and beam loss are sensitive to system parameters: the quadruple focusing field filling factor, the vacuum phase advance, the perveance and the pipe radius. As shown in our parametric studies, the beam loss increases rapidly as the perveance of the beam increases and as the pipe radius decreases. In addition, a self-consistent PIC simulation code, Periodically Focused Beam (PFB2D), has been developed, and used to simulate intense charged-particle beams in small-aperture alternating-gradient systems. PIC simulation results on the beam envelope are consistent with the envelope equation'solutions. However, due to numerical noise in PIC simulations, the beam loss predicted by PIC simulation has been found to be an order of magnitude higher than that predicted by the test-particle model.

(cont.) To analyze the noise in PIC simulations, an error scaling law for the edge emittance growth and particle diffusion due to the discrete macro-particle effects has been derived for self-consistent intense beam simulations. The error scaling law has been tested in the self-consistent Green's function simulations and self-consistent PIC PFB2D simulations. The simulation results have shown good agreement with the scaling law. Novel exact paraxial cold-fluid and Vlasov equilibria have been found for a high-intensity, space-charge-dominated charged-particle beam with a periodically twisted elliptic cross section in a non-axisymmetric periodic magnetic field. Generalized envelope equations, which determine the beam envelopes, ellipse orientation, density, and internal flow velocity profiles, have been derived, and solved numerically for nonrelativistic and relativistic examples of such beams. The equilibrium and stability of such beams have been demonstrated by self-consistent particle-in-cell (PIC) simulations. For current applications, the temperature effects are found to be small on a periodically twisted large-aspect-ratio elliptic beam.

(cont.) We anticipate that the equilibrium theory will provide a valuable tool in the design of high-intensity elliptic beams in novel vacuum electron devices, especially for ribbon-beam klystrons (RBKs) and ribbon-beam traveling-wave amplifiers (RBA). The ellipse-shaped beam equilibria may provide some flexibility in the design and operation of high-intensity accelerators.