Improved envelope and emittance description of particle beams using the Fokker-Planck approach
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911749712642048 |
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| author | Struckmeier, Jürgen |
| author_facet | Struckmeier, Jürgen |
| contents | Beam dynamics calculations that are based on the Vlasov equation do not permit the the treatment of stochastic phenomena such as intra-beam scattering. If the nature of the stochastic process can be regarded as a Markov process, we are allowed to use the Fokker-Planck equation to describe the change of the phase space volume the beam occupies. From the Fokker-Planck equation we derive equations of motion for the beam envelopes and for the rms-emittances. Compared to previous approaches based on Liouville's theorem, these equations contain additional terms that describe the temperature balancing within the beam. Our formalism is applied to the effect of intra-beam scattering relevant for beams circulating in storage rings near thermodynamical equilibrium. In this case, the Fokker-Planck coefficients can be treated as adiabatic constants of motion. Due to the simplified analysis based on `beam moments', we obtain fairly simple equations that allow us to estimate the growth rate of the beam emittance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12272 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved envelope and emittance description of particle beams using the Fokker-Planck approach Struckmeier, Jürgen Accelerator Physics Beam dynamics calculations that are based on the Vlasov equation do not permit the the treatment of stochastic phenomena such as intra-beam scattering. If the nature of the stochastic process can be regarded as a Markov process, we are allowed to use the Fokker-Planck equation to describe the change of the phase space volume the beam occupies. From the Fokker-Planck equation we derive equations of motion for the beam envelopes and for the rms-emittances. Compared to previous approaches based on Liouville's theorem, these equations contain additional terms that describe the temperature balancing within the beam. Our formalism is applied to the effect of intra-beam scattering relevant for beams circulating in storage rings near thermodynamical equilibrium. In this case, the Fokker-Planck coefficients can be treated as adiabatic constants of motion. Due to the simplified analysis based on `beam moments', we obtain fairly simple equations that allow us to estimate the growth rate of the beam emittance. |
| title | Improved envelope and emittance description of particle beams using the Fokker-Planck approach |
| topic | Accelerator Physics |
| url | https://arxiv.org/abs/2307.12272 |