Theoretical models for longitudinal coupled-bunch instabilities driven by harmonic cavities in electron storage rings
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908343525703680 |
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| author | Alves, Murilo B. |
| author_facet | Alves, Murilo B. |
| contents | We present a theoretical framework for analyzing longitudinal coupled-bunch instabilities in double-rf systems with even filling patterns, accounting for potential-well distortion and multiple azimuthal modes. The linearized Vlasov equation is solved in the frequency-domain for an arbitrary rf potential to derive the Lebedev equation. We unified different formulations, obtaining results from recent publications as particular cases. Applications to Robinson dipole-quadrupole mode coupling and the periodic transient beam loading (PTBL)/mode-1 instability are presented. Notably, for the first time, theoretical predictions of the mode-1 thresholds show excellent agreement with experimental data. The analysis reveals that the PTBL instability is a zero-frequency effect dependent on azimuthal mode interactions and resistant to Landau damping, providing new insights into its mechanism. The methods are implemented in the open-source package pycolleff, offering a useful semi-analytical tool for studying instabilities in electron storage rings with harmonic cavities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19308 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theoretical models for longitudinal coupled-bunch instabilities driven by harmonic cavities in electron storage rings Alves, Murilo B. Accelerator Physics We present a theoretical framework for analyzing longitudinal coupled-bunch instabilities in double-rf systems with even filling patterns, accounting for potential-well distortion and multiple azimuthal modes. The linearized Vlasov equation is solved in the frequency-domain for an arbitrary rf potential to derive the Lebedev equation. We unified different formulations, obtaining results from recent publications as particular cases. Applications to Robinson dipole-quadrupole mode coupling and the periodic transient beam loading (PTBL)/mode-1 instability are presented. Notably, for the first time, theoretical predictions of the mode-1 thresholds show excellent agreement with experimental data. The analysis reveals that the PTBL instability is a zero-frequency effect dependent on azimuthal mode interactions and resistant to Landau damping, providing new insights into its mechanism. The methods are implemented in the open-source package pycolleff, offering a useful semi-analytical tool for studying instabilities in electron storage rings with harmonic cavities. |
| title | Theoretical models for longitudinal coupled-bunch instabilities driven by harmonic cavities in electron storage rings |
| topic | Accelerator Physics |
| url | https://arxiv.org/abs/2412.19308 |