dorsal/arxiv
View SchemaRecirculating BBU thresholds for polarized HOMs with optical coupling
| Authors | Georg H. Hoffstaetter, Ivan V. Bazarov, Changsheng Song |
|---|---|
| Categories | |
| ArXiv ID | physics/0508089 |
| URL | https://arxiv.org/abs/physics/0508089 |
Abstract
We will derive the general theory of the beam-breakup instability in recirculating linear accelerators with coupled beam optics and with polarized higher order dipole modes. The bunches do not have to be at the same RF phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where beam currents become very large and coupled optics are used on purpose to increase the threshold current. A remarkable agreement with tracking data is demonstrated. The general formulas are then analyzed for several analytically solvable cases, which show: (a) Why different higher order modes (HOM) in one cavity can couple and cannot be considered individually, even when their frequencies are separated by much more than the resonance widths of the HOMs. For the Cornell ERL as an example, it is noted that optimum advantage of coupled optics is taken when the cavities are designed with an $x$-$y$ HOM frequency splitting of above 50MHz. The threshold current is then far above the design current of this accelerator. (b) How the $x$-$y$ coupling in the particle optics determines when modes can be considered separately. (c) That the increase of the threshold current obtainable by coupled optics and polarized modes diminishes roughly with the square root of the HOMs' quality factors. Therefore the largest advantages are achieved with cavities that are not specifically designed to minimize these quality factors, e.g. by means of HOM absorbers. (d) How multiple-turn recirculation interferes with the threshold improvements obtained with a coupled optics.
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"date_created": "2026-03-02T18:01:00.767000Z",
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"abstract": "We will derive the general theory of the beam-breakup instability in\nrecirculating linear accelerators with coupled beam optics and with polarized\nhigher order dipole modes. The bunches do not have to be at the same RF phase\nduring each recirculation turn. This is important for the description of energy\nrecovery linacs (ERLs) where beam currents become very large and coupled optics\nare used on purpose to increase the threshold current. A remarkable agreement\nwith tracking data is demonstrated. The general formulas are then analyzed for\nseveral analytically solvable cases, which show: (a) Why different higher order\nmodes (HOM) in one cavity can couple and cannot be considered individually,\neven when their frequencies are separated by much more than the resonance\nwidths of the HOMs. For the Cornell ERL as an example, it is noted that optimum\nadvantage of coupled optics is taken when the cavities are designed with an\n$x$-$y$ HOM frequency splitting of above 50MHz. The threshold current is then\nfar above the design current of this accelerator. (b) How the $x$-$y$ coupling\nin the particle optics determines when modes can be considered separately. (c)\nThat the increase of the threshold current obtainable by coupled optics and\npolarized modes diminishes roughly with the square root of the HOMs\u0027 quality\nfactors. Therefore the largest advantages are achieved with cavities that are\nnot specifically designed to minimize these quality factors, e.g. by means of\nHOM absorbers. (d) How multiple-turn recirculation interferes with the\nthreshold improvements obtained with a coupled optics.",
"arxiv_id": "physics/0508089",
"authors": [
"Georg H. Hoffstaetter",
"Ivan V. Bazarov",
"Changsheng Song"
],
"categories": [
"physics.acc-ph"
],
"title": "Recirculating BBU thresholds for polarized HOMs with optical coupling",
"url": "https://arxiv.org/abs/physics/0508089"
},
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