Matrix formalism of synchrobetatron coupling
In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams...
Ausführliche Beschreibung
Autor*in: |
Xiaobiao Huang [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2007 |
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In: Physical Review Special Topics. Accelerators and Beams - American Physical Society, 2003, 10(2007), 1, p 014002 |
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Übergeordnetes Werk: |
volume:10 ; year:2007 ; number:1, p 014002 |
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DOI / URN: |
10.1103/PhysRevSTAB.10.014002 |
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DOAJ045678324 |
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10.1103/PhysRevSTAB.10.014002 doi (DE-627)DOAJ045678324 (DE-599)DOAJ1ce9c553228f4805bd56ec1ba5de2c4b DE-627 ger DE-627 rakwb eng QC770-798 Xiaobiao Huang verfasserin aut Matrix formalism of synchrobetatron coupling 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. Nuclear and particle physics. Atomic energy. Radioactivity In Physical Review Special Topics. Accelerators and Beams American Physical Society, 2003 10(2007), 1, p 014002 (DE-627)306359588 (DE-600)1497130-6 10984402 nnns volume:10 year:2007 number:1, p 014002 https://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/article/1ce9c553228f4805bd56ec1ba5de2c4b kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/toc/1098-4402 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2021 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2007 1, p 014002 |
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10.1103/PhysRevSTAB.10.014002 doi (DE-627)DOAJ045678324 (DE-599)DOAJ1ce9c553228f4805bd56ec1ba5de2c4b DE-627 ger DE-627 rakwb eng QC770-798 Xiaobiao Huang verfasserin aut Matrix formalism of synchrobetatron coupling 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. Nuclear and particle physics. Atomic energy. Radioactivity In Physical Review Special Topics. Accelerators and Beams American Physical Society, 2003 10(2007), 1, p 014002 (DE-627)306359588 (DE-600)1497130-6 10984402 nnns volume:10 year:2007 number:1, p 014002 https://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/article/1ce9c553228f4805bd56ec1ba5de2c4b kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/toc/1098-4402 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2021 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2007 1, p 014002 |
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10.1103/PhysRevSTAB.10.014002 doi (DE-627)DOAJ045678324 (DE-599)DOAJ1ce9c553228f4805bd56ec1ba5de2c4b DE-627 ger DE-627 rakwb eng QC770-798 Xiaobiao Huang verfasserin aut Matrix formalism of synchrobetatron coupling 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. Nuclear and particle physics. Atomic energy. Radioactivity In Physical Review Special Topics. Accelerators and Beams American Physical Society, 2003 10(2007), 1, p 014002 (DE-627)306359588 (DE-600)1497130-6 10984402 nnns volume:10 year:2007 number:1, p 014002 https://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/article/1ce9c553228f4805bd56ec1ba5de2c4b kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/toc/1098-4402 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2021 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2007 1, p 014002 |
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10.1103/PhysRevSTAB.10.014002 doi (DE-627)DOAJ045678324 (DE-599)DOAJ1ce9c553228f4805bd56ec1ba5de2c4b DE-627 ger DE-627 rakwb eng QC770-798 Xiaobiao Huang verfasserin aut Matrix formalism of synchrobetatron coupling 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. Nuclear and particle physics. Atomic energy. Radioactivity In Physical Review Special Topics. Accelerators and Beams American Physical Society, 2003 10(2007), 1, p 014002 (DE-627)306359588 (DE-600)1497130-6 10984402 nnns volume:10 year:2007 number:1, p 014002 https://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/article/1ce9c553228f4805bd56ec1ba5de2c4b kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei http://doi.org/10.1103/PhysRevSTAB.10.014002 kostenfrei https://doaj.org/toc/1098-4402 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2021 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2007 1, p 014002 |
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In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. |
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In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. |
abstract_unstemmed |
In this paper we present a complete linear synchrobetatron coupling formalism by studying the transfer matrix which describes linear horizontal and longitudinal motions. With the technique established in the linear horizontal-vertical coupling study [D. Sagan and D. Rubin, Phys. Rev. ST Accel. Beams 2, 074001 (1999)PRABFM1098-440210.1103/PhysRevSTAB.2.074001], we found a transformation to block diagonalize the transfer matrix and decouple the betatron motion and the synchrotron motion. By separating the usual dispersion term from the horizontal coordinate first, we were able to obtain analytic expressions of the transformation under reasonable approximations. We also obtained the perturbations to the betatron tune and the Courant-Snyder functions. The closed-orbit changes due to finite energy gains at rf cavities and radiation energy losses were studied by the 5×5 extended transfer matrix with the fifth column describing kicks in the 4-dimension phase space. |
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