One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams

• Main Authors: Ronald C. Davidson, Hong Qin
• Format: Article
• Language: English
• Published: American Physical Society 2015-09-01
• Series: Physical Review Special Topics. Accelerators and Beams
• Online Access: http://doi.org/10.1103/PhysRevSTAB.18.094201

This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r_{w}. The average axial electric field is expressed as ⟨E_{z}⟩=-(∂/∂z)⟨ϕ⟩=-e_{b}g_{0}∂λ_{b}/∂z-e_{b}g_{2}r_{w}^{2}∂^{3}λ_{b}/∂z^{3}, where g_{0} and g_{2} are constant geometric factors, λ_{b}(z,t)=∫dp_{z}F_{b}(z,p_{z},t) is the line density of beam particles, and F_{b}(z,p_{z},t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where F_{b}=const in a bounded region of p_{z}-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field ⟨E_{z}⟩.