[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-203826-105":59,"doc-detail-203826-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","effects-of-collisions-on-the-saturation-dynamics-of-taes-in-tokamaks-and-stellarators-preprint-paper","Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators - Preprint paper","","Non-linear saturation dynamics of toroidicity-induced Alfvén eigenmodes (TAEs) are studied numerically in tokamaks and stellarators. The investigation focuses on how pitch-angle collisions among fast ions modify behavior in the non-linear regime. A perturbative workflow is employed: the CKA three-dimensional ideal reduced MHD eigenvalue code provides mode frequency and structure, then EUTERPE calculates growth rate and temporal amplitude evolution. Tokamak results match analytic transition and scaling predictions inside the theory validity range, while outside it additional scaling laws emerge.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/effects-of-collisions-on-the-saturation-dynamics-of-taes-in-tokamaks-and-stellarators-preprint-paper/203826/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/effects-of-collisions-on-the-saturation-dynamics-of-taes-in-tokamaks-and-stellarators-preprint-paper/203826.png","ImageObject",300,407,{"name":92,"@type":93},"Kyle","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-11","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main topic of the preprint?","Question",{"text":112,"@type":113},"The preprint investigates how collisions affect the non-linear saturation dynamics of TAEs in tokamaks and stellarators.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which numerical tools are used to study the TAE saturation dynamics?",{"text":117,"@type":113},"It uses the CKA three-dimensional ideal reduced MHD eigenvalue code to obtain mode frequency and structure, and then the EUTERPE non-linear gyro-kinetic particle-in-cell code to compute growth rate and amplitude evolution.",{"name":119,"@type":110,"acceptedAnswer":120},"How do collisions influence the saturated behavior differently for tokamaks and stellarators?",{"text":121,"@type":113},"In tokamaks, analytical transition and saturated-amplitude scaling predictions are influenced by collisions and agree within the theory validity range; outside it, different scaling laws appear. In the Wendelstein 7-X stellarator, the saturated perturbed magnetic field becomes non-monotonic as a function of collision frequency ν.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},203826,1788564176,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},3985741905716,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","WP15ER-CPR(17) 18192  \nC. Slaby et al.  \nEffects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators  \nPreprint of Paper to be submitted for publication in Proceeding of 15th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems  \nThis work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053 . The views and opinions  \nexpressed herein do not necessarily reflect those of the European Commission.  \nThis document is intended for publication in the open literature. It is made available on the clear understanding that it may not be further circulated and extracts or references may not be published prior to publication of the original when applicable, or without the consent of the Publications Officer, EUROfusion Programme Management Unit, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK or e-mail Publications.Offi[cer@euro-fusion.org](cer@euro-fusion.org)  \nEnquiries about Copyright and reproduction should be addressed to the Publications Officer, EUROfusion Programme Management Unit, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK or e-mail Publications.Offi[cer@euro-fusion.org](cer@euro-fusion.org)  \nThe contents of this preprint and all other EUROfusion Preprints, Reports and Conference Papers are available to view online free at [http://www.euro-fusionscipub.org. This](http://www.euro-fusionscipub.org. This) site has full search facilities ande-mail alert options. In the JET specific papers the diagrams contained within the PDFs on this site are hyperlinked  \nEffects of collisions on the saturation dynamics of TAEs in tokamaks  \nand stellarators  \nChristoph Slaby∗ , Axel Könies, and Ralf Kleiber  \nMax-Planck-Institut für Plasmaphysik,  \nWendelsteinstraße 1, 17491 Greifswald, Germany  \nJosé Manuel García-Regaña  \nLaboratorio Nacional de Fusión Ciemat,  \nAv. Complutense 40, 28040 Madrid, Spain  \n(Dated: November 17, 2017)  \nAbstract  \nThe non-linear saturation dynamics of TAEs (toroidicity-induced Alfvén eigenmodes) is investigated numerically in tokamaks and stellarators. Special attention is given to the in􀀃uence that pitch-angle collisions among the fast ions have in the non-linear regime.  \nFor this investigation a perturbative model is used. We employ the three-dimensional ideal reduced MHD eigenvalue code CKA to obtain the mode frequency and mode structure. This information is given to the non-linear gyro-kinetic particle-in-cell code EUTERPE, which calculates the growth rate of the mode and the temporal evolution of the mode amplitude. The mode structure remains 􀀂xed for the entire calculation.  \nIn the tokamak, analytical predictions regarding the transition from periodic non-linear behaviour to a steady-state solution and the scaling of the saturated amplitude are available. Both are in􀀃uenced by collisions. The numerical results are in agreement with the theoretical predictions within the validity range of the theory [H. L. Berk et al., Phys. Rev. Lett. 68, 3563 (1992)] . Beyond the validity range of the theory different scaling laws are found numerically.  \nWe show that using a momentum-conserving collision operator does not change the scaling signi􀀂cantly for small ν, but is important for high collision frequencies.  \nThe stellarator case, a Wendelstein 7-X high-mirror con􀀂guration, shows some differences when compared with the tokamak. Most notably, the saturated perturbed magnetic 􀀂eld becomes a non-monotonic function of ν .  \n∗ E-mail address: [christoph.slaby@ipp.mpg.de](christoph.slaby@ipp.mpg.de)  \nI. INTRODUCTION  \nIn fusion devices, present-day experiments or future fusion reactors, there typically exists a supra-thermal population of fast ions. Today, these particles are created mainly by heating methods, such as neutral beam injection (NBI) or ion cyclotron resonance heating (ICRH) . In future fusion reactors also self-generat","cbCaikuLqIp6R8Hg","https://ap.wps.com/l/cbCaikuLqIp6R8Hg","pdf",1016504,31,"English","# Abstract\n## Numerical model workflow\n## Collisional influence and scaling results\n## Tokamak versus stellarator comparison","[{\"question\":\"What is the main topic of the preprint?\",\"answer\":\"The preprint investigates how collisions affect the non-linear saturation dynamics of TAEs in tokamaks and stellarators.\"},{\"question\":\"Which numerical tools are used to study the TAE saturation dynamics?\",\"answer\":\"It uses the CKA three-dimensional ideal reduced MHD eigenvalue code to obtain mode frequency and structure, and then the EUTERPE non-linear gyro-kinetic particle-in-cell code to compute growth rate and amplitude evolution.\"},{\"question\":\"How do collisions influence the saturated behavior differently for tokamaks and stellarators?\",\"answer\":\"In tokamaks, analytical transition and saturated-amplitude scaling predictions are influenced by collisions and agree within the theory validity range; outside it, different scaling laws appear. In the Wendelstein 7-X stellarator, the saturated perturbed magnetic field becomes non-monotonic as a function of collision frequency ν.\"}]","Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators - Preprint paper | PDF",78]