One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866915059000672256 |
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| author | Davidson, Ronald C. Qin, Hong |
| author_facet | Davidson, Ronald C. Qin, Hong |
| contents | 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 $\langle E_{z}\rangle=-(\partial/\partial z)\langleϕ\rangle=-e_{b}g_{0}\partialλ_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}λ_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $λ_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ 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 (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 $F_{b}=const.$ in a bounded region of $p_{z}$-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 $\langle E_{z}\rangle$.
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| format | Preprint |
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arxiv_https___arxiv_org_abs_1504_04403 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams Davidson, Ronald C. Qin, Hong Accelerator Physics Pattern Formation and Solitons Plasma Physics 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 $\langle E_{z}\rangle=-(\partial/\partial z)\langleϕ\rangle=-e_{b}g_{0}\partialλ_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}λ_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $λ_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ 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 (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 $F_{b}=const.$ in a bounded region of $p_{z}$-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 $\langle E_{z}\rangle$. . |
| title | One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams |
| topic | Accelerator Physics Pattern Formation and Solitons Plasma Physics |
| url | https://arxiv.org/abs/1504.04403 |