{"id":"https://openalex.org/W4200211819","doi":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","title":"\u041e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0432\u0438\u0440\u0438\u0430\u043b\u0430 \u0434\u043b\u044f \u043c\u0430\u0433\u043d\u0438\u0442\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0441 \u043a\u0432\u0430\u0437\u0438\u0431\u0435\u0441\u0441\u0438\u043b\u043e\u0432\u044b\u043c\u0438 \u043e\u0431\u043c\u043e\u0442\u043a\u0430\u043c\u0438","display_name":"\u041e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0432\u0438\u0440\u0438\u0430\u043b\u0430 \u0434\u043b\u044f \u043c\u0430\u0433\u043d\u0438\u0442\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0441 \u043a\u0432\u0430\u0437\u0438\u0431\u0435\u0441\u0441\u0438\u043b\u043e\u0432\u044b\u043c\u0438 \u043e\u0431\u043c\u043e\u0442\u043a\u0430\u043c\u0438","publication_year":2021,"publication_date":"2021-12-10","ids":{"openalex":"https://openalex.org/W4200211819","doi":"https://doi.org/10.21883/jtf.2022.02.52022.249-21"},"language":"ru","primary_location":{"id":"doi:10.21883/jtf.2022.02.52022.249-21","doi":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","is_oa":true,"landing_page_url":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","pdf_url":"https://journals.ioffe.ru/articles/viewPDF/52022","source":{"id":"https://openalex.org/S4210225974","display_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","issn_l":"0044-4642","issn":["0044-4642","1726-748X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310321811","host_organization_name":"Ioffe Institute","host_organization_lineage":["https://openalex.org/P4310321811","https://openalex.org/P4310321756"],"host_organization_lineage_names":["Ioffe Institute","Academy of Sciences of the USSR"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.ioffe.ru/articles/viewPDF/52022","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059424796","display_name":"German Abramovich Shneerson","orcid":"https://orcid.org/0000-0002-7087-098X","observed_orcids":["https://orcid.org/0000-0002-7087-098X"]},"institutions":[{"id":"https://openalex.org/I212220629","display_name":"Peter the Great St. Petersburg Polytechnic University","ror":"https://ror.org/02x91aj62","country_code":"RU","type":"education","lineage":["https://openalex.org/I212220629"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"\u0413.\u0410. \u0428\u043d\u0435\u0435\u0440\u0441\u043e\u043d","raw_affiliation_strings":["\u0421\u0430\u043d\u043a\u0442-\u041f\u0435\u0442\u0435\u0440\u0431\u0443\u0440\u0433\u0441\u043a\u0438\u0439 \u043f\u043e\u043b\u0438\u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u041f\u0435\u0442\u0440\u0430 \u0412\u0435\u043b\u0438\u043a\u043e\u0433\u043e, \u0421\u0430\u043d\u043a\u0442-\u041f\u0435\u0442\u0435\u0440\u0431\u0443\u0440\u0433, \u0420\u043e\u0441\u0441\u0438\u044f"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0421\u0430\u043d\u043a\u0442-\u041f\u0435\u0442\u0435\u0440\u0431\u0443\u0440\u0433\u0441\u043a\u0438\u0439 \u043f\u043e\u043b\u0438\u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u041f\u0435\u0442\u0440\u0430 \u0412\u0435\u043b\u0438\u043a\u043e\u0433\u043e, \u0421\u0430\u043d\u043a\u0442-\u041f\u0435\u0442\u0435\u0440\u0431\u0443\u0440\u0433, \u0420\u043e\u0441\u0441\u0438\u044f","institution_ids":["https://openalex.org/I212220629"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016708520","display_name":"\u0421. \u041b. \u0428\u0438\u0448\u0438\u0433\u0438\u043d","orcid":"https://orcid.org/0000-0002-9599-3900","observed_orcids":["https://orcid.org/0000-0002-9599-3900"]},"institutions":[{"id":"https://openalex.org/I137513774","display_name":"Vologda State University","ror":"https://ror.org/05hcp8p49","country_code":"RU","type":"education","lineage":["https://openalex.org/I137513774"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"\u0421.\u041b. \u0428\u0438\u0448\u0438\u0433\u0438\u043d","raw_affiliation_strings":["\u0412\u043e\u043b\u043e\u0433\u043e\u0434\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442, \u0412\u043e\u043b\u043e\u0433\u0434\u0430, \u0420\u043e\u0441\u0441\u0438\u044f"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u0412\u043e\u043b\u043e\u0433\u043e\u0434\u0441\u043a\u0438\u0439 \u0433\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442, \u0412\u043e\u043b\u043e\u0433\u0434\u0430, \u0420\u043e\u0441\u0441\u0438\u044f","institution_ids":["https://openalex.org/I137513774"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"92","issue":"2","first_page":"303","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11808","display_name":"Superconducting Materials and Applications","score":0.301800012588501,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11808","display_name":"Superconducting Materials and Applications","score":0.301800012588501,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10278","display_name":"Electric Motor Design and Analysis","score":0.17790000140666962,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11920","display_name":"Pulsed Power Technology Applications","score":0.0786999985575676,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/virial-theorem","display_name":"virial theorem","score":0.9940000176429749},{"id":"https://openalex.org/keywords/weight-minimization","display_name":"weight minimization","score":0.628000020980835},{"id":"https://openalex.org/keywords/electromagnetic-force","display_name":"electromagnetic force","score":0.6190000176429749},{"id":"https://openalex.org/keywords/local-equilibrium","display_name":"local equilibrium","score":0.5630000233650208},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.4740000069141388}],"concepts":[{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.5354537963867188},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.5039750933647156},{"id":"https://openalex.org/C30403606","wikidata":"https://www.wikidata.org/wiki/Q2981904","display_name":"Electromagnetic coil","level":2,"score":0.4907442331314087},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47696220874786377},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4724562466144562},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.443334698677063},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.43888288736343384},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.43262091279029846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.345718115568161},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3051472306251526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15250876545906067},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11704763770103455},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.21883/jtf.2022.02.52022.249-21","doi":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","is_oa":true,"landing_page_url":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","pdf_url":"https://journals.ioffe.ru/articles/viewPDF/52022","source":{"id":"https://openalex.org/S4210225974","display_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","issn_l":"0044-4642","issn":["0044-4642","1726-748X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310321811","host_organization_name":"Ioffe Institute","host_organization_lineage":["https://openalex.org/P4310321811","https://openalex.org/P4310321756"],"host_organization_lineage_names":["Ioffe Institute","Academy of Sciences of the USSR"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.21883/jtf.2022.02.52022.249-21","doi":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","is_oa":true,"landing_page_url":"https://doi.org/10.21883/jtf.2022.02.52022.249-21","pdf_url":"https://journals.ioffe.ru/articles/viewPDF/52022","source":{"id":"https://openalex.org/S4210225974","display_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","issn_l":"0044-4642","issn":["0044-4642","1726-748X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310321811","host_organization_name":"Ioffe Institute","host_organization_lineage":["https://openalex.org/P4310321811","https://openalex.org/P4310321756"],"host_organization_lineage_names":["Ioffe Institute","Academy of Sciences of the USSR"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u0416\u0443\u0440\u043d\u0430\u043b \u0442\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200211819.pdf","grobid_xml":"https://content.openalex.org/works/W4200211819.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2490297958","https://openalex.org/W6724797037"],"related_works":["https://openalex.org/W4392901094","https://openalex.org/W7214124709","https://openalex.org/W4253621646","https://openalex.org/W2079757336","https://openalex.org/W4210277237","https://openalex.org/W2059414442","https://openalex.org/W7128896981","https://openalex.org/W3090218721","https://openalex.org/W3115886684","https://openalex.org/W2887609679"],"abstract_inverted_index":{"The":[0,116,154],"article":[1],"shows":[2],"that":[3,209],"in":[4,21,82,174,210,224],"a":[5,9,15,18,53,66,71,83,90,160,164,168,185,235],"magnetic":[6,44,73],"system":[7,45,161,212],"with":[8,52,202,220],"thin-walled":[10,120],"balanced":[11,119,171,203],"winding":[12,80],"close":[13],"to":[14,32,47,99,141,256],"force-free":[16],"one,":[17],"significant":[19],"increase":[20,223],"the":[22,33,37,40,43,48,59,75,79,95,104,107,125,134,137,142,145,148,175,194,200,211,215,225,230,242],"parameter":[23,218],"\u03b8=WM":[24],"\u03b3/M":[25],"\u03c3\u041c":[26],",":[27],"is":[28,81,97,207],"possible,":[29],"which,":[30],"according":[31],"virial":[34],"theorem,":[35],"characterizes":[36],"ratio":[38],"of":[39,42,50,61,78,85,94,106,118,136,147,150,159,163,170,177,184,187,196,227,229,237,244],"energy":[41],"WM":[46],"weight":[49,105,112],"equipment":[51,96],"material":[54],"density":[55],"\u03b3,":[56],"where":[57],"under":[58,213],"action":[60],"electromagnetic":[62],"forces":[63],"there":[64],"appears":[65],"mechanical":[67],"stress":[68],"\u03c3\u041c.":[69],"In":[70],"quasi-force-free":[72],"system,":[74,109],"main":[76,165,231],"part":[77,93,102,166,232],"state":[84],"local":[86],"equilibrium,":[87],"and":[88,110,144,152,180,190,240],"only":[89],"relatively":[91],"small":[92],"subject":[98],"stress.":[100],"This":[101],"determines":[103],"entire":[108],"this":[111],"can":[113,233],"be":[114],"minimized.":[115],"configurations":[117],"windings":[121],"are":[122,130],"developed,":[123],"at":[124],"boundaries":[126],"two":[127],"boundary":[128,143],"conditions":[129],"fulfilled":[131],"simultaneously":[132],"-":[133,167,250],"absence":[135],"induction":[138,151],"component":[139],"normal":[140],"constancy":[146],"product":[149],"radius.":[153],"authors":[155],"consider":[156],"an":[157,221],"example":[158],"consisting":[162,183],"sequence":[169],"\"transverse\"":[172,188],"modules":[173,189],"form":[176,195],"flat":[178],"discs":[179],"end":[181,204],"parts,":[182],"combination":[186],"\"longitudinal\"":[191],"ones,":[192],"having":[193],"rings":[197],"elongated":[198],"along":[199],"axis":[201],"parts.":[205],"It":[206],"shown":[208],"consideration,":[214],"characteristic":[216],"dimensionless":[217],"\u03b8":[219],"unlimited":[222],"number":[226,243],"elements":[228,246],"reach":[234],"value":[236],"about":[238],"24,":[239],"when":[241],"these":[245],"changes":[247,253],"within":[248],"20":[249],"40,":[251],"it":[252],"from":[254],"6":[255],"9.":[257]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2021-12-31T00:00:00"}