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

Authors:  Ronald C. Davidson and Hong Qin

Abstract:  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 rw. The average axial electric field is expressed as (Ez) = −(∂/∂_z)(∅) = −e_bg₀∂λ_b/∂z − e_bg₂r²_w∂³ λ_b /∂z³, where g₀ and g₂ are constant geometric factors, λ_b (z, t) = ∫dpzFb(z, pz, t) is the line density of beam particles, and Fb(z, pz, t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) 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: (a) the nonlinear waterbag distribution, where Fb = const. in a bounded region of pz-space; and (b) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field (Ez).  PACS numbers: 29.27.Bd, 52.25.Dg
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Submitted to: Physical Review - Special Topic on Accelerators and Beams
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Download PPPL-5136 (pdf 2.4 MB 45pp)
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