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1、1.TemperatureandFrequencyDependentSurfaceImpedanceOnlyfractionsofourworldbe-havelinearly,butitisamazinghowfarlinearmodelinghaspro-ceeded.1.1PhysicalFrameworkThissectionintroducestheelectrodynamicsneededtounderstandthebasicconceptofsurfaceimpedanceofsuperconductors.Startingwith
2、Maxwell'sequationsandthekineticsofthechargeswhichcarrythemicrowavecur-rents,thetreatmentiskeptonaphenomenologicallevel.Threecharacteris-ticlengthsareidentifiedtodistinguishbetweendifferentlimitingregimesoftheelectrodynamicsofsuperconductors.Thephysicalconceptofthesurfaceresist
3、anceandthesurfacereactance(or,equivalently,thepenetrationdepth)aresubsequentlyillustratedintermsoftheenergydissipatedandstored,re-spectively,inthesuperconductor.Finally,theeffectoffinitefihnthicknessontheconceptofthesurfaceimpedanceisdiscussed.1.1.1FieldEquationsandCharacteris
4、ticLengthsPenetrationofMicrowaveFieldsintoSuperconductorsTheinteractionbetweenaplaneelectromagneticwaveatcircularfrequency=27randametalofconductivityaisdescribedbyMaxwell'sequations.ThesepresentexpressionsforthemicroscopicelectricfieldvectorEandthemagneticinductionB,andthemacr
5、oscopicdisplacementDandthemagneticfieldH.AdetailedtreatmentoftherelationsbetweenEandDandbetweenBandHcanbefound,e.g.,in[1].Takingintoaccounttheabsenceofmagneticmonopoles(i.e.,divB=0),andtheabsenceoffreeorpolarizedchargesinmetals(i.e.,divD=0),theremainingMaxwell'sequationsareOBc
6、urlE-Ot(1.1a)andODcurlH=J+0~-"(lAb)ThemagneticinductionBcanbeexpressedastherotationofthemagneticvectorpotentialA:B=curlA.Intheabsenceofmagnetizingeffectsandin21.TemperatureandFrequencyDependentSurfacehnpedancenonmagneticmaterials,BisproportionaltothemagneticfieldH,B=#0"Hwith#0
7、=47rx10-7Vs/Ambeingthemagneticpermeabilityofvacuum.InordertofindsolutionsforEandB,(1.1)needstobesupplementedbyacurrentfieldrelationlike,forinstance,J=a.E.(1.2)Withareal,(1.2)describesOhm'slawforisotropicmetals.However,aswillbeshownbelow,italsoremainsvalidforsuperconductors,the
8、conductivityofwhichiscomplex:(7:0"1--i(r2=al(1-itan0).(1.3)Le
