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

Davidson, Ronald C.; Qin, Hong

doi:10.1103/PhysRevSTAB.18.094201

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

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Abstract

This study 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_bg₀∂λ_b/∂z-e_bg₂r²_w∂³λ_b/∂z³, where g₀ and g₂ are constant geometric factors, λ_b(z,t)=∫dp_zF_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 >.

Authors:: Davidson, Ronald C.; Qin, Hong

Publication Date:: Mon Sep 21 00:00:00 EDT 2015

Research Org.:: Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1233865

Alternate Identifier(s):: OSTI ID: 1221815; OSTI ID: 1254755

Report Number(s):: PPPL-5136
Journal ID: ISSN 1098-4402; PRABFM; 094201

Grant/Contract Number:: AC02-09CH11466

Resource Type:: Published Article

Journal Name:: Physical Review Special Topics - Accelerators and Beams

Additional Journal Information:: Journal Volume: 18; Journal Issue: 9; Journal ID: ISSN 1098-4402

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 43 PARTICLE ACCELERATORS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; beams; electron; heavy ion; light ion; REB; nonlinear effects; nonlinear theories; nonneutral plasmas

Citation Formats


                    Davidson, Ronald C., and Qin, Hong. One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevSTAB.18.094201.

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                    Davidson, Ronald C., & Qin, Hong. One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams.  United States.  https://doi.org/10.1103/PhysRevSTAB.18.094201

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                    Davidson, Ronald C., and Qin, Hong. Mon .  
"One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams".  United States.  https://doi.org/10.1103/PhysRevSTAB.18.094201.

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@article{osti_1233865,

  title        = {One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams},

  author       = {Davidson, Ronald C. and Qin, Hong},

  abstractNote = {This study 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)<Φ>=-ebg0∂λb/∂z-ebg2r2w∂3λb/∂z3, where g0 and g2 are constant geometric factors, λb(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 (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 Fb=const in a bounded region of pz-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 < Ez >.},

  doi          = {10.1103/PhysRevSTAB.18.094201},

  journal      = {Physical Review Special Topics - Accelerators and Beams},

  number       = 9,

  volume       = 18,

  place        = {United States},

  year         = {Mon Sep 21 00:00:00 EDT 2015},

  month        = {Mon Sep 21 00:00:00 EDT 2015}

}

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