RESUMO
The envelope instability near the 90° phase advance in periodically focused space charge dominated beams is a well-known phenomenon in linear transport sections or linacs. The corresponding stop band is usually avoided because of the resulting strong mismatch oscillations and beam loss. We show that in circular accelerators or transport sections including bending magnets the instability is modified due to the effect of dispersion. Using the two-dimensional envelope equations extended by the dispersion equation we identify an additional stop band above 120°. For periodic focusing the stop band results from the confluence of an envelope mode with the newly identified coherent dispersion mode. Results from perturbation theory are compared with the full envelope model and particle-in-cell simulation, which all show good agreement. The newly identified mode has several implications and applications for the characterization of intense beams in circular machines.
RESUMO
Space charge can lead to emittance and/or energy exchange known as "equipartitioning issue" in linacs, or space-charge coupling in high-current synchrotrons. It is described here as an internal resonance driven by the self-consistent space-charge potential of coherent eigenmodes. By a detailed comparison of analytical theory with 2D particle-in-cell simulation for Kapchinskij-Vladimirskij (KV) and waterbag distributions, we discuss characteristic features of this resonance mechanism in the vicinity of the symmetric focusing resonance band--for practical purposes, the most important case--and discuss the applicability of the linearized KV theory.
RESUMO
The longitudinal space charge and resistive wall impedances have been investigated in a smooth cylindrical beam pipe. At any point from the beam axis, we obtained an expression for the total impedance, which at the beam surface r=a for infinite pipe wall conductivity gives the expression for the total impedance that was derived by Zotter and Kheifets in studying the impedance of uniform beams in concentric cylindrical wall chambers, when a single cylindrical chamber is considered [B. W. Zotter and S. A. Kheifets, Impedances and Wakes in High-Energy Particle Accelerators (World Scientific, Singapore, 1998), Chap. 6]. A fitting formula for the space-charge impedance at the beam surface (r=a), which is valid for arbitrary wavelengths, is given. Rather than calculating the impedance with the field on the axis [Joseph J. Bisognano, Fifth European Particle Accelerator Conference (EPAC96), edited by S. Myers, A. Pacheco, R. Pascual, Ch. Petit-Jean-Genaz, and J. Poole (Institute of Physics, Bristol, 1996), Vol. 1, p. 328], the fitting formula is obtained by averaging over the transverse beam distribution. We also give another approach for the calculation of the resistive wall impedance using the flux of the Poynting vector at the pipe wall and then compare it with the expression obtained from the volume integral over the beam distribution.
