{"id":"https://openalex.org/W4294958991","doi":"https://doi.org/10.3390/sym14091875","title":"Liouville Theory for Fully Analytic Studies of Transverse Beam Dynamics in Laser-Plasma Ion Accelerators","display_name":"Liouville Theory for Fully Analytic Studies of Transverse Beam Dynamics in Laser-Plasma Ion Accelerators","publication_year":2022,"publication_date":"2022-09-08","ids":{"openalex":"https://openalex.org/W4294958991","doi":"https://doi.org/10.3390/sym14091875"},"language":"en","primary_location":{"id":"doi:10.3390/sym14091875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091875","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1875/pdf?version=1662621513","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/9/1875/pdf?version=1662621513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038657600","display_name":"Alessandro Curcio","orcid":"https://orcid.org/0000-0002-1777-5078"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Alessandro Curcio","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":"https://orcid.org/0000-0002-1777-5078","affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066800216","display_name":"Jon Imanol Api\u00f1aniz","orcid":"https://orcid.org/0000-0001-5053-8886"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jon Imanol Api\u00f1aniz Aginako","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073576041","display_name":"Teresa Cebriano Ram\u00edrez","orcid":null},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Teresa Cebriano Ram\u00edrez","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054695661","display_name":"M. Ehret","orcid":"https://orcid.org/0000-0002-7671-6246"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Michael Ehret","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7671-6246","affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081229364","display_name":"Berkahoum Kebladj","orcid":null},"institutions":[{"id":"https://openalex.org/I184999862","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51","country_code":"ES","type":"education","lineage":["https://openalex.org/I184999862"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Berkahoum Kebladj","raw_affiliation_strings":["Fundamental Physics Department, University of Salamanca, 37008 Salamanca, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fundamental Physics Department, University of Salamanca, 37008 Salamanca, Spain","institution_ids":["https://openalex.org/I184999862"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019734679","display_name":"Antonia Morabito","orcid":"https://orcid.org/0000-0002-0914-6087"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonia Morabito","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074545056","display_name":"Alberto P\u00e9rez\u2010Delgado","orcid":"https://orcid.org/0000-0001-6698-1065"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alberto P\u00e9rez Delgado","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020891844","display_name":"C. Salgado","orcid":"https://orcid.org/0000-0001-9653-993X"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Carlos Salgado L\u00f3pez","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9653-993X","affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086964157","display_name":"L. Volpe","orcid":"https://orcid.org/0000-0002-0385-498X"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Luca Volpe","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0385-498X","affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029666786","display_name":"G. Gatti","orcid":"https://orcid.org/0000-0001-7730-7893"},"institutions":[{"id":"https://openalex.org/I4210150328","display_name":"Spanish Center for Pulsed Lasers","ror":"https://ror.org/03pp6gj92","country_code":"ES","type":"other","lineage":["https://openalex.org/I4210150328"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Giancarlo Gatti","raw_affiliation_strings":["Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Laseres Pulsados (CLPU), Edificio M5. Parque Cient\u00edfico. C/Adaja, 8., 37185 Villamayor, Spain","institution_ids":["https://openalex.org/I4210150328"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038657600"],"corresponding_institution_ids":["https://openalex.org/I4210150328"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02799168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"14","issue":"9","first_page":"1875","last_page":"1875"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10384","display_name":"Laser-Plasma Interactions and Diagnostics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10384","display_name":"Laser-Plasma Interactions and Diagnostics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11854","display_name":"Laser-induced spectroscopy and plasma","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10413","display_name":"High-pressure geophysics and materials","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.751459538936615},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.6691359877586365},{"id":"https://openalex.org/keywords/beam","display_name":"Beam (structure)","score":0.624559223651886},{"id":"https://openalex.org/keywords/plasma","display_name":"Plasma","score":0.6179314851760864},{"id":"https://openalex.org/keywords/ion","display_name":"Ion","score":0.5601941347122192},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5501877665519714},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.5394163727760315},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5149355530738831},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.5007374286651611},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4982447624206543},{"id":"https://openalex.org/keywords/laser","display_name":"Laser","score":0.46948084235191345},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.41583240032196045},{"id":"https://openalex.org/keywords/atomic-physics","display_name":"Atomic physics","score":0.38005247712135315},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.36406761407852173},{"id":"https://openalex.org/keywords/computational-physics","display_name":"Computational physics","score":0.3448212742805481},{"id":"https://openalex.org/keywords/quantum-electrodynamics","display_name":"Quantum electrodynamics","score":0.33664193749427795},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20874997973442078},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.19182142615318298},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1499459147453308},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1037435233592987}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.751459538936615},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6691359877586365},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.624559223651886},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.6179314851760864},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.5601941347122192},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5501877665519714},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.5394163727760315},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5149355530738831},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.5007374286651611},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4982447624206543},{"id":"https://openalex.org/C520434653","wikidata":"https://www.wikidata.org/wiki/Q38867","display_name":"Laser","level":2,"score":0.46948084235191345},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.41583240032196045},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.38005247712135315},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36406761407852173},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.3448212742805481},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.33664193749427795},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20874997973442078},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.19182142615318298},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1499459147453308},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1037435233592987},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym14091875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091875","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1875/pdf?version=1662621513","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:24e295732e5641df975649811cb2df53","is_oa":true,"landing_page_url":"https://doaj.org/article/24e295732e5641df975649811cb2df53","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 9, p 1875 (2022)","raw_type":"article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1749016","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1749016","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/9/1875/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14091875","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14091875","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14091875","pdf_url":"https://www.mdpi.com/2073-8994/14/9/1875/pdf?version=1662621513","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4294958991.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1588822808","https://openalex.org/W1638744931","https://openalex.org/W1964467331","https://openalex.org/W1964697571","https://openalex.org/W1968642339","https://openalex.org/W1972199097","https://openalex.org/W2006277161","https://openalex.org/W2012352859","https://openalex.org/W2044043696","https://openalex.org/W2056690543","https://openalex.org/W2064229474","https://openalex.org/W2065969373","https://openalex.org/W2074050428","https://openalex.org/W2140695545","https://openalex.org/W2169248656","https://openalex.org/W2343929520","https://openalex.org/W2964242122","https://openalex.org/W2975517649","https://openalex.org/W2992870143","https://openalex.org/W3092812850","https://openalex.org/W3138967401","https://openalex.org/W3181633332","https://openalex.org/W4220867427","https://openalex.org/W4224312928"],"related_works":["https://openalex.org/W2980143039","https://openalex.org/W4390055535","https://openalex.org/W2303560784","https://openalex.org/W2349033857","https://openalex.org/W2002586420","https://openalex.org/W44758131","https://openalex.org/W2766565942","https://openalex.org/W1992104806","https://openalex.org/W2774201881","https://openalex.org/W2114959981"],"abstract_inverted_index":{"The":[0],"exact":[1],"solution":[2,31],"of":[3,10,19,32,39,60],"the":[4,15,30,33,37,53,58,76],"Liouville":[5],"equation":[6,35],"expressed":[7],"in":[8,22,52],"terms":[9],"exponential":[11],"operators":[12],"can":[13],"describe":[14],"phase":[16],"space":[17],"evolution":[18],"particle":[20,47],"beams":[21,48,65],"transport":[23],"lines.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28],"generalize":[29],"above":[34],"for":[36,46],"case":[38],"beam":[40],"losses":[41],"induced":[42],"by":[43,67],"apertures":[44],"and":[45,81],"with":[49,71],"large":[50],"spreads":[51],"momentum":[54],"space.":[55],"We":[56],"discuss":[57],"applicability":[59],"such":[61],"approach":[62],"to":[63],"ion":[64],"produced":[66],"high-intensity":[68],"lasers":[69],"interacting":[70],"critical":[72],"plasmas,":[73],"based":[74],"on":[75],"comparison":[77],"between":[78],"theoretical":[79],"findings":[80],"measurements.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}