Abstract
A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image-charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet-beam model is then applied to analyze several problems of fundamental interest. A sheet-beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- and three-dimensional thermal equilibrium models in terms of the equilibrium structure and Debye screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability relative to beams with weak space-charge.
Highlights
Analysis of self-consistent space-charge effects in beams is notoriously difficult due to the nonlinear structure of the Vlasov-Poisson models for realistic, smooth distribution functions
Even the equilibrium structure is generally highly nonlinear which complicates the analysis of the stability and evolution of collective wave perturbations evolving on the equilibrium
Large-scale numerical simulations play a central role in the analysis of charged particle beams
Summary
Analysis of self-consistent space-charge effects in beams is notoriously difficult due to the nonlinear structure of the Vlasov-Poisson models for realistic, smooth distribution functions. Davidson et al analyzed a waterbag distribution in periodic focusing channels in terms of the evolution of the phase-space boundary [14] In spite of this success in sheet-beam modeling, an issue of concern stems from the Coulomb force being radically different in physical 3D (inverse distance squared), 2D transverse cylindrical (inverse radial distance), and 1D slab (constant; long range) geometries suggesting the possibility of nonphysical collective interactions in the lowerdimensional models. The simple structure of the equilibrium is exploited to explicitly calculate the distribution of particle oscillation frequencies within the sheet beam including linear applied focusing and nonlinear defocusing space-charge forces (Sec. III C).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical Review Special Topics - Accelerators and Beams
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
