Charged Particle Beam Optimization with Use of a Second Order Method

The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies t...
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Autor*in:	D.A. Starikov [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch ; Russisch

Erschienen:	2018

Schlagwörter:	optimal control dynamical system ensemble second order variation second order method charged particle beam

Übergeordnetes Werk:	In: Известия Иркутского государственного университета: Серия "Математика" - Irkutsk State University, 2018, 24(2018), 1, Seite 68-81
Übergeordnetes Werk:	volume:24 ; year:2018 ; number:1 ; pages:68-81

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Katalog-ID:	DOAJ021961344

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520			\|a The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method.
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allfields	(DE-627)DOAJ021961344 (DE-599)DOAJ5c6f2909a6aa4eea8143d7ab326503bf DE-627 ger DE-627 rakwb eng rus QA1-939 D.A. Starikov verfasserin aut Charged Particle Beam Optimization with Use of a Second Order Method 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method. optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics In Известия Иркутского государственного университета: Серия "Математика" Irkutsk State University, 2018 24(2018), 1, Seite 68-81 (DE-627)721347320 (DE-600)2677883-X 25418785 nnns volume:24 year:2018 number:1 pages:68-81 https://doi.org/10.26516/1997-7670.2018.24.68 kostenfrei https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf kostenfrei http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus kostenfrei https://doaj.org/toc/1997-7670 Journal toc kostenfrei https://doaj.org/toc/2541-8785 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_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 68-81
spelling	(DE-627)DOAJ021961344 (DE-599)DOAJ5c6f2909a6aa4eea8143d7ab326503bf DE-627 ger DE-627 rakwb eng rus QA1-939 D.A. Starikov verfasserin aut Charged Particle Beam Optimization with Use of a Second Order Method 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method. optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics In Известия Иркутского государственного университета: Серия "Математика" Irkutsk State University, 2018 24(2018), 1, Seite 68-81 (DE-627)721347320 (DE-600)2677883-X 25418785 nnns volume:24 year:2018 number:1 pages:68-81 https://doi.org/10.26516/1997-7670.2018.24.68 kostenfrei https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf kostenfrei http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus kostenfrei https://doaj.org/toc/1997-7670 Journal toc kostenfrei https://doaj.org/toc/2541-8785 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_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 68-81
allfields_unstemmed	(DE-627)DOAJ021961344 (DE-599)DOAJ5c6f2909a6aa4eea8143d7ab326503bf DE-627 ger DE-627 rakwb eng rus QA1-939 D.A. Starikov verfasserin aut Charged Particle Beam Optimization with Use of a Second Order Method 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method. optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics In Известия Иркутского государственного университета: Серия "Математика" Irkutsk State University, 2018 24(2018), 1, Seite 68-81 (DE-627)721347320 (DE-600)2677883-X 25418785 nnns volume:24 year:2018 number:1 pages:68-81 https://doi.org/10.26516/1997-7670.2018.24.68 kostenfrei https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf kostenfrei http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus kostenfrei https://doaj.org/toc/1997-7670 Journal toc kostenfrei https://doaj.org/toc/2541-8785 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_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 68-81
allfieldsGer	(DE-627)DOAJ021961344 (DE-599)DOAJ5c6f2909a6aa4eea8143d7ab326503bf DE-627 ger DE-627 rakwb eng rus QA1-939 D.A. Starikov verfasserin aut Charged Particle Beam Optimization with Use of a Second Order Method 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method. optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics In Известия Иркутского государственного университета: Серия "Математика" Irkutsk State University, 2018 24(2018), 1, Seite 68-81 (DE-627)721347320 (DE-600)2677883-X 25418785 nnns volume:24 year:2018 number:1 pages:68-81 https://doi.org/10.26516/1997-7670.2018.24.68 kostenfrei https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf kostenfrei http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus kostenfrei https://doaj.org/toc/1997-7670 Journal toc kostenfrei https://doaj.org/toc/2541-8785 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_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 68-81
allfieldsSound	(DE-627)DOAJ021961344 (DE-599)DOAJ5c6f2909a6aa4eea8143d7ab326503bf DE-627 ger DE-627 rakwb eng rus QA1-939 D.A. Starikov verfasserin aut Charged Particle Beam Optimization with Use of a Second Order Method 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method. optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics In Известия Иркутского государственного университета: Серия "Математика" Irkutsk State University, 2018 24(2018), 1, Seite 68-81 (DE-627)721347320 (DE-600)2677883-X 25418785 nnns volume:24 year:2018 number:1 pages:68-81 https://doi.org/10.26516/1997-7670.2018.24.68 kostenfrei https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf kostenfrei http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus kostenfrei https://doaj.org/toc/1997-7670 Journal toc kostenfrei https://doaj.org/toc/2541-8785 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_2014 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 68-81
language	English Russian
source	In Известия Иркутского государственного университета: Серия "Математика" 24(2018), 1, Seite 68-81 volume:24 year:2018 number:1 pages:68-81
sourceStr	In Известия Иркутского государственного университета: Серия "Математика" 24(2018), 1, Seite 68-81 volume:24 year:2018 number:1 pages:68-81
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	optimal control dynamical system ensemble second order variation second order method charged particle beam Mathematics
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callnumber-first	Q - Science
author	D.A. Starikov
spellingShingle	D.A. Starikov misc QA1-939 misc optimal control misc dynamical system ensemble misc second order variation misc second order method misc charged particle beam misc Mathematics Charged Particle Beam Optimization with Use of a Second Order Method
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topic_title	QA1-939 Charged Particle Beam Optimization with Use of a Second Order Method optimal control dynamical system ensemble second order variation second order method charged particle beam
topic	misc QA1-939 misc optimal control misc dynamical system ensemble misc second order variation misc second order method misc charged particle beam misc Mathematics
topic_unstemmed	misc QA1-939 misc optimal control misc dynamical system ensemble misc second order variation misc second order method misc charged particle beam misc Mathematics
topic_browse	misc QA1-939 misc optimal control misc dynamical system ensemble misc second order variation misc second order method misc charged particle beam misc Mathematics
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title	Charged Particle Beam Optimization with Use of a Second Order Method
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title_full	Charged Particle Beam Optimization with Use of a Second Order Method
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journal	Известия Иркутского государственного университета: Серия "Математика"
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title_sort	charged particle beam optimization with use of a second order method
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title_auth	Charged Particle Beam Optimization with Use of a Second Order Method
abstract	The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method.
abstractGer	The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method.
abstract_unstemmed	The problem of optimization of charged particle beam dynamics is considered. The problem is formulated as the control problem for a dynamical system ensemble with a fixed endpoint. A state of the dynamical system ensemble is described by a density of the systems in the phase space, which satisfies to the Liouville equation or to the Vlasov equation. The problem is to minimize a functional depending on terminal state of the ensemble. It is proposed to use an algorithm based on calculation of the first and the second variations of trajectory of a dynamical system under the control function variation. If the control function is parametrized, expressions for the first and the second variations allow to find the first and the second derivatives of the functional being minimized over control parameters. Using of the second derivatives can make the optimization process sufficiently quicker, as compared with algorithm using only first derivatives. The proposed algoritm is realized for a beam in the Radio Frequency Quadrupole (RFQ) channel, which is often used as initial part of a charged particles accelerator. The simplest problem of of optimization of longitudinal dynamics of the beam in this channel is considered. The numerical solution is finding on the base of the method of macroparticles. The comparison between the first order and the second order methods is conducted. The second order method shows sufficient increase of the rate of convergence as compared with the first order method.
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title_short	Charged Particle Beam Optimization with Use of a Second Order Method
url	https://doi.org/10.26516/1997-7670.2018.24.68 https://doaj.org/article/5c6f2909a6aa4eea8143d7ab326503bf http://mathizv.isu.ru/journal/downloadArticle?article=_42f4c6181650466c8f2db14e0fd76219&lang=rus https://doaj.org/toc/1997-7670 https://doaj.org/toc/2541-8785
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