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《Topological Constraints on Magnetic Relaxation磁弛豫的拓?fù)浼s束》由會(huì)員上傳分享，免費(fèi)在線(xiàn)閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
1、TopologicalConstraintsonMagneticRelaxationA.R.Yeates,?G.Hornig,andA.L.Wilmot-SmithDivisionofMathematics,UniversityofDundee,Dundee,DD14HN,UK(Dated:August6,2018)AbstractThe?nalstateofturbulentmagneticrelaxationinareversed?eldpinchiswellexplainedbyTaylor’shypothesis.However
2、,recentresistive-magnetohydrodynamicsimulationsoftherelaxationofbraidedsolarcoronalloopshaveledtorelaxed?eldsfarfromtheTaylorstate,despitetheconservationofhelicity.Wepointouttheexistenceofanadditionaltopologicalinvariantinany?uxtubewithnon-zero?eld:thetopologicaldegreeof
3、the?eldlinemapping.Weconjecturethatthisconstrainstherelaxation,explainingwhyonlyoneofthreeexamplesimulationsreachestheTaylorstate.PACSnumbers:52.30.Cv,52.65.Kj,52.35.Vd,96.60.HvarXiv:1007.4925v1[astro-ph.SR]28Jul20101ThelandmarkpaperofJ.B.Taylor[1]showedhowthe?nal,relaxe
4、d,magnetic?eldinaturbulentplasmaexperimentcouldbepredictedtheoreticallybyassumingconservationRofthetotalmagnetichelicityH=A·Bd3x,whereB=?×A.TaylorhypothesizedVthat,inaturbulentplasmawithsmallbutnon-vanishingresistivity,Histheonlyrelevantconstraintontherelaxation.Theresul
5、tingminimumenergystateisthenalinearforce-free?eld[2],?×B=αB,whereαisaconstantdependingonthevalueofH.Thesuccessofthistheoryinpredictingthe?nalstateofrelaxationinareversed?eldpinchhasledtospeculationthatTaylor’shypothesismightapplymoregenerally,forexample,tomagneticstructu
6、resintheSun’satmosphere[3–6].Here,thenatureofthe?nalstateisofgreatinterestbecauseitlimitsthemagneticenergyavailableforconversiontoheatduringtherelaxation.Thisiskeytounderstandinghowmagnetic?eldsproducetheextremecoronaltemperaturesintheSunandotherstars.ToapplyTaylor’shypo
7、thesisinsuchmagneticallyopendomains,HisreplacedbytherelativehelicityHRwithrespecttoareference?eld[4,7],typicallyapotential?eld.Alocaldomain,suchasanisolatedloop,istaken(thecoronacannotbegloballyalinearforce-free?eld)andthehypothesishasmetwithsomenotablesuccess[6].However
8、,counter-examplesareknown[8,9]anditnowseemslikelythatconstraintsbeyondtheconservationofglobalmagnetiche
