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Superconducting materials in oscillating and rotating magnetic fields
Superconducting materials in oscillating and rotating magnetic fields V.A. Altov, V.V. Kurguzov and V.V. Sytchev* All-Union Research Institute ol Metrologtcal Service, M o s c o w 1 1 7 3 3 4 , USSR * M o s c o w Power Engineering Inst=lule, M o s c o w 1 0 5 8 3 5 , USSR
Received 26 Aprd 1984 The melhods ol measuremenl ol the oscdlaling held Ihreshold amplitude, AB v, are rev0ewed As Ih=s quanl=ly increases, an ellecl~ve resmlance occurs. The dependence ol AB v upon currenl and hequency for monohlamenl and mullddamenl conductors ~s sludied. A IheoreImal approach ~s suggested and similar effects are also shown to exmt m rolaling magnelm helds.
Keywords: s u p e r c o n d u c t o r s ; rotating m a g n e t i c fields
m a g n e t i c fields; a.c. losses; m u l t i f i l a m e n t a r y
'The behawour ol hard superc~mduch~rs under allernultng magnelte rtelds ts ac~.'ompan,ed by dissipal,ve pr~ce.sse.s The dependence orthe Ios.sescm Ihe allernatmg magnel,¢ held ampltlude changes sharply when Ihe amplilude exceeds Ihe penelralton held ~)r Ihe .st~-¢alled magneHc held threshold. Beh~re Ihe Ihre.shold umpl,lude Ihe hy.slere.sin h~s,se.s arc pr~q.~M~mal to B ~ al Ihe .superc(mdueh~r surface, and as Ihls quanlll3' increases above Ihe Ihre,d~old level the losses increase Itnearly w'Hh the held We have shown prev,ously t Ihal as Ihe rteld increase,~ beyund Ihe Ihre,~hold .'tmplllude, an ellecllve resistance h) Ihe Iransporl currenl arises in the superc~mduetint2 device whk'h can be c(m.sldered as a eoncen traled elemenl ()1 Ihe eleclrtcal t. irt.'utl placed in an ~scillal~ng magnel~v field ]-'his Paper deals with Ihe elle¢ls ol i)s~.'~llal~ng magnel~c held,, ~n Ihe eurrenl II(~w~ng a h m g the sample slud~ed.
currenl will appear AI an mcrea,se in the Iield ~.st:illallon Ihre.sh~ld amplilude Ab' v, due Io non.s'vmmelrlc I]eld penetraH~m inlo Ihe .supereonduLlor, Ihe Ilux mduved v~dlage changes d,scontmu~m.sly and Ihe inlegral llux value during a held change cycle is n~) hmger zero) A change in Ihe Ilux value h)r an external held chant.,e cycle wHh a .superc~mductinL2 dewee m an allernaling magnellc held Fed hy a con.slunl uurrenl source can he delermmed by InleL2ral~ng I' arising al Ihe ler'rn~nal~ ~1 the .'qJper ¢~mducl~ng device under .,,ludy T
'b :
--
(3)
and Ihe eurrenl .s~urt.'e will perh~rm Ihe Iollow,ng work per I'leld change period 'T'
P =
t
•
7'
1" I dl : /
F'r~m which I ro m
t"
I' d/ = Rel-I 17''T'
(,4)
(J
Ihe elk'dive re,~lslam.'e value in Iound
't' R~II = I T
(i)
=
when an area, ~r al lea.,,I a line, ~hev,, t`.7= I ~. v-/ = t) ~n Ihe .superc~mdm.'l~r during Ihe field change c'vcle By ch()o,~ln~, a L'lrCUll oJ IhlN area Jilr illlC~,rallon onecan ,~how thai durln~ Ihe cyclic chan~e ol induction ~wer Ihe periled o1' held r()lall~m Ihe v~fllage In Ihe ,~uperc~mductor becomes zero ":'V" . = - -.
. . (~(r+'r)
Blr)) d~
(1
where i IN Ihe c~m,stanl Iran.~pc~rl currc'nl value S(~. Ihe amplilude Ihre.shold value (an ,nerea.'.,e (~1 which cau,~e.~ an ell'ecllve re.~i.~lam.'e In an (~.~villullng magnellc Iield) can be delerrnlned experlrnenlally hy Ihe h)lh~wlng Ihree melhL)ds I
, S
O011 - 2275/B5,/OBO26154J5 $L)3 O0 tO '1985 Bull~rw~rlh 8 Co (Pubh~hwu) Lid
Cryogenics 1 9 8 5 Vol 25 M a y
measuring. Ihe currenl devuy in a .~hl)rl ~.lrculled devicej mea.~urm.~ Ihe amplilude al which a v~fllage jump ari,,e.~ in a supere~mduvllng .,,ample in a varying exlerrlal I'leld~. L
.. ('1
II th,.~canm~t he avhleved, lhen h~r a general ca,,e lhe llux wdl change and an elleclwe re~stance h~ the Iran~port
266
I'/d/
II
al .
T
/ /
Theory II has been shown ~ Ihal Ihe Ilux Ihrough a super conducting dewee in an allernaling ma~.,netic field ~,,,g~ven by
conductors;
t
measurm.p the Ilux Inle.p,ral vahJe.¢, per field vhange ~.'y~.'le
Superconducting T'he ah~,ve methods are vahd I'(~r h~,lh ~,scillal.ng and r~lalin[~, n]agnel=c I'teld`,. The c~md=l,on ~1 Ihe elleclive resLslance appearance in a rolal~ng ma[~nelic field wdl have Ihe h~rm 2Bo " 2Be, = B,,. - Bt
( .~)
where B,j s Ihe r4dal,ng Iield amphlude B, and B, are Ihe m a x i m a l inducts,ms on Ihe superc~nduclm~. Idamenl
,,urlace due I~ Ihc Crlll~.al Iran:.,p~rl L'UrlL'[II a,,d Ihe Iransp~)rl cLirrenl ~n Ihe IllameriL respec'l,vely F'~r a m~m~d'~lamenl ,~uperconduclor ~ t , ,s deler rn~ned by Ihe superc~mduch)r ~.'rll~cal pr~perlie`, and iIs ge~melr,~.'alsize and exhlh,ls hysleresl`, In c~mlrasl h~a m(m~d,lamenl c~mduel~r where ~ f f , doe.,, n~)l depend ~)n Ihe I'teld (~scdlal,~m Irequem.'V, Ihe ma~,nel~¢ pr~perlie`, (d a mullirflamenlar~ clm,p~s~le ~n an ~`,cdlal,n[:, I]eld become much m(~re c~mplicaled due Io Ihe C~)tipll,~g currenl`, in a mi, lr~x. F~r a c(m~p~s,le Ihe field Ihresh~ld amplilude ,,, delermined hv the exlernal Iield ~)scillatt~m amplilude al wh,ch. ,n an ~tiler laver ~1 Ihe o,npo:,,le ,.,uperc,mdud~n!, Ilh~menl,.,. ;~n ~'lh'~:l~e res,,.,lance h~, Ihe Iransp~rl current lion, in.p, in lhe,~e I'damenls appear,, 'TI~ lind Ihe Ihresh~fld ampl,lude ~1 Ihe ~'~n,p~),~,le ~n an ,~,~u'dlal~ng ma.gnel=c I'leld. 4me `,h,~uld lake mh~ ,.ICeOLIt,I Ihe c~)upl~ng currenls m Ihe malr,x In allernaHn L, magneli~, i'~eld,, and als~ Ihe sereerHnL.~ ellecl`, ~n _Z~I, Slrik'~' In ;llh'rll;,llnl? maL.,m'llc l'lehJs ~,. = H,~~I11 ~I -I- ~ Ihe cuupl~ng currents are clo:,ed m Ihe `,uperc~mdt, cl,ng filaments 'The maL.,.nellc Iield al Ihe rilamenl surla~e. H,. i, in c~mh,ned Ir(m~ Ihe exlernal I'~eld. Ihal ol Ihe o~upl~ng currenl and lhal ~1 Ihc c.~lernal lield screen,n[: The exper~menl`, described heh~w were u'arr,ed ~)ul ~m exper~menlal ~.'~mp~)`,lle`, wHh ~ne layer ~1 super CoN,dueling. I'llamenl`, F'~r these samples Ihe o~uplin[~. currenl;~ cah:ulal.m wan perh~rmed hy u`,~n[~, Ihe two. l',lamenl model i)l lhe ~.'I)ITIp(I`,II~. lak~ng mh) al.'l.'()IJlll the eleclr,e lield ~n lhe ,,Liperc~mducl,r,~ l'~lamenl`,./~ II In ,~ur s~)lLil,~!,ri Ihe c',,iJphlu.., ctirTenl ~aluc. I.,. can he wnllen an Ihe ,,urn ~fl' Ihe I~flal u'urrenL In-,. ohlained w,lhoul ~.' and w,lh Z~J add,l,~m which ,`, ohla,ned Irom Ihe equullon
Z 'J"~'
( '/i' ')
materials in m a g n e t t c helds • V . A . Altov el al.
where /~ lake,, ~nh~ a~.c¢~unl Ihe IiehJ ellecl ol ~)lher Iilamenls lur Ihe tt,wen compos=le 'The `,olul~on of Ihis equali~m wdh regard I,~ H,. allows u`, I~ delermine Ihe field Ihresh~dd ampl=lude, z~E./~,,the ,ncrease,d whk'h re`,ult,~ in an el'led~ve res~slance I,~ the Iran`,purl currenl We used a s=mflar melh~d when cuns=der,n.e, lhe m%,nehc behav,~ur ,~1 the compcmde superconduch~r In r~dalinL., nia~,~lelu.' fields We h ~ k mh~ a¢¢ounl lhe elle~.'l ,)I C~ml-flln ~, currenls [n lhe matrix and lhe Stil~erconducl,ng I'~lamenls and a `,creenin~, value (~1 Ihe exlernal Iield ~ndticed hy Ihe currenl'~ in Ihe ouler layer ¢~1Ihe slahd=z~nl~, maler=al. We ohlamed Ihe expres,~¢m h~r Ihe Ihreshold ampl=lude ul'a r(daling I'~ehJ liar a c=~mpo`,,le, an increa.`,e ~1 wh,ch led I~ Ihe appearance ~1 an efl'ecl,ve res,qance I~r Ihe Iran`,p~)rl eurrenl Ihal can he pre`,enled a`,
-I ~11,1.1 = ( B I ¢ - B ~ ) i l
+
[ ') 11 .1-o.~r] ) ~/'' ,
I + 4o2"r'~ t ~/z
I * ,.,'~ ~
.
where r~ is Ihe ¢Lirrenl quem.'hlnL.., clmslanl in Ihe i~uler la~er ,d `,lal'~dlztng n|;.ilertal, r~ I', II|e ~.¢~LipllnJ/, current cem'.;lanl helween Ihe malrL'~ and Ihe .`,uperc~.mduclm~, Idamcnls I + I/(I t- ( d r y ) " takes inh~c,m`,iderali*m a I'dumenl screenlngellecl Ihrough Iheu'urrenl clo,~ed =n Ihe ouler layer ~1 the.,,;lah=l=zm~ maler=al The Ih,rd mulHplier ol ItHs expres`,~on take.',; inlo acc(~unl Ihe c~uplm~, currenl elled ¢~n Ihe Ihre`,huld value As at, example, Ihe dependence ~1 Ihe relaltve Ihresh(~ld ampl,lude, Z~l~Bd.,(/)/~kBih(/ = I)), on the rotal,ng I'leh] Irequency h~r a one compunenl (r, = r~) and u rwoo)mp, menl matrLx wHh a hlt~h,~hm,c Ic~ luwc)hm,c nlalrlx rall¢~ equal h~ '~. ,n illuslraled ,n Fl~ I The calculal=on`, are perlormed lur r~ = ~ , IO ~ s(curves I), r~ = 2 . I() ~ ',(tu~'es2) and r= = '~ . I()z .`,(cu~'e,s ~). A`, Ls :,h~wn ~n It,~; I lhe relallve lhreshold amphlude depen denee on Irequem.'y greatly depends on lhe m a l n x ~.'~n ducliv,~, h=gh ~hmle to low.ohmic malrtx compunenl c~mduel,vil~ r a l , , , a n d l~isl length Wilh lhe ~ncrea.se,)l
") /~'~H I U
where/, ~,~ Ihe I~t`,l length and p,, ,',; Ihe re`,i,~lanee ol the mairLx
When
the p e n e i r a l i o n
I]eld v a l u e is s m a l l e r
Ihan
the threshuhl, and Ihe eleetr,c I'~eld al Ihe I]lamenl ,',;urlace can he wrHlen as Ell = /J.J~/rl h (where h ,s Ihe field penelrali~m deplh ,nh~ Ihe I]lamenl and H,. I the ma[~,nel,c field im Ihe I'damenl `,tirlaee) Ihe equalion can he `,olved
as z3J = -
,-= B~I ~'(.,,~ (11"/2/-,)
`,m (cur ~' 'r/)° ' '
('7)
',~ o.~
(n/21,)'Zlj~.l~,pe(oJ~r ~ ÷ I) ~ f~T
The correction h~r lhe couphng currenL I~. ,s imp(~rlanl ~)nlyalsmalllrequene,e`,(~//l m~i)4aloJ' I/r) Allarg, e Irequem.'~es oJ ~'. I/r) ~J/Irr , IS equal Io1) I The c'ondlllOn i~)r elfeellVe res,slanc'e ,n one of Ihe eomp~)`,tle filamenl`, ,n an ose,llalmng rna~.;neltc I]eld ~.'an he presented as
,1
~
(IdH~n'~/4-1.dl
÷A)I = +i,.(I--kl)l~') I/'~
L)
:2
rl
rz
• 5r
I
[ 5 f, I-Iz
L)
~- ([d H~n~/4 + I~(I - k ) i ~' ,I- ~,.,( I -k,)'z) '/~ I = ~ (~' - ~)
=
IO
Fig. 1 Dependence ol Ihe ;elalwu Ihreshold amphludes on Ihe frequency of Ihe samples wdh 'r t = 5 x 10 3 s (curves 1), r I = 2 X 10 " S (curves 2), r I = 5 x 1 0 " s (eurvRs 3)
Cryogenics
1985
Vol 25
May
267
Superconducting materials in magnetic fields: V.A. Altov el al. 03
frequency lhe Ihresht,ld value, ~l~lh , decreases and under the large frequencies ol field rolalion =1 approaches a conslanl value independenl of frequency.
~
Methods of measurement of the oscillating field threshold amplitude Three melhuds ol measuremenl ol fhe osc,llating field Ihresh~dd ampl,lude AS~,, are presented m this Paper I
"
The I'trsl melhud ~,1 measuremenl was as h.,llows 'The specimen slud,ed was included ,n Ihe clused supercnnducltng c,rcull wtlh 'lhe measuring' supercondueling s,.)leno,d ufa km,wn inductance as the sec,,nd elemenL 'T'h~s s,.J,len,L,td served as a 'currenl source' and allowed measuremenls I,L,he laken Irom a ma~leh.~ res~sl,ve hismulh transducer placed tn the solent,~d cenlre. 'The current was exciled in Ihe usual manner by means o1' a Ihermal swtlch. In an osctllaltng exlernal magnel~c Iield al higher Ihreshold o s c d l a l , m ampltlude h)r a gnven currenl and an exlernal magnel,c I]eld, Ihe appearance ol Ihe el'lecltve resislance resulls tn a current decay The Ihresh,,Id a m p h l u d e value was determined I'.,m the Iield amplilude when an increase or resislance P{~ll ~'" I0~" m appeared tn Ihe ctrcutl. 'The second method is hosed on Ihe lad Ihal in a variable magneltc Iield wilh c,.,nstanl b'. Ihe charucler ol Ihe vollage change vaned sharply whet] the I~eld Ihreshold value was exceeded In our opintun [he vollage on Ihe sample m a vat,able field can he divided tnlo Y. Ihe one reduced by Ihe exlernal Ilux change ~., and Ihat due I(, an It|dLt~.'lt,,l'l redts Irihuli,,n./.I, ins=de Ihe superc,,nduclor In lacL Y d,,es nt,I depend on a field dtslrihul,)n ,n Ihe super cc, nduclor Wilhin I h e e x p e r i m e n l by c,,mpensal~ng Ihe w~llage value induced hy Ihe exlernal Ilux change (I)0' ~,ne can delerrrime AB. I[om Ihe expermlenlal dependence U = U ( B J ,~ 'The exper,nlenlal sludy ol ~r./. li',r Ihe case when Ihe sample was dffeclly ji.ned Ii, a d c source was pul inl,) ellecl ,n the h,lh,wmg way 'The sample was placed m Ihe superconducltng s,.,len(,Id cenlre h) create an oscillaling magnetic I~eld wilh a given frequency and oscillalton amphrude A direcl Iransporl current ul a given value was passed Ihrough Ihe supercunducling sample. 1'he vollage I rom the sample tn the (,sollaltng magnelic Iield was led hi Ihe mlegrah,r tnpt, t. A S . was delermtned experimenlally rrom Ihe ¢naxJmurn field amphlude, Bma,~-Bmm, under which Ihe Ilux value, ~ = § I' el/, remained equal It, zen, I',.,r several field change cycles•
02 '
l-
J
i.~
(')~ (,,
• ,~
".~.
"~,~
I 05
(')()
113
//io Fig. 2 Dependen(.:e ol lhe o~c,illalmg held ll"ireshold amphlude lur ~amples ol dtamele,,r 0 . 0 8 turn (,'ui-ve I, B -- 0.3 T; curv~ 2, B = 0 55 1") arid dlameler 0.22 mm ((:urve 3, B = 5.0 1")
'The model ct.,mpuslte samples had a layer (,I superconducltng I]lamenls 6()p.rrL nn dnarneler nn a copper malrLX with an exlernal dtameler o1'11 '~t mm 'The I~rsl compustle sample had a Iwtsl lenglh ,,I 2t) mm, Ihe see,rod a rwml lenglh ~H'6() mm The Irequency dependence ABe,. h,r bulh sludted samples ts shown in Fl~. '~',Ihis shows thai Ihe field Ihresh,.dd ampl,tude decreases will, increasing frequency H(,wever. l h e c o u p h n g c u r r e n l s , n l h e s e c t , n d sample which had a large rw=sl length are larger Ihan Ihose tn Ihe Iirsl sample, and Ihey are closed tn Ihe supercunducltng filamenls which resulls in Ihe tnduclt,.,n redmtrtbul,,n m Ihe filaments and tn a reduclion ,d'lhe field Ihrest, dd value. A8~ With an ,ncrease ul Ihe Iield osctllaliun Irequency Ihe filament screening ellecl gr,,ws due Io Ihe currenls in Ihe t,uler slabiltz.=ng malrtx layer causing Ihreshold value t,., mcrease AI ,~, '.. I/r. ABe, ts constant and =ndependenl ,,f Ihe held (,scillalion frequency 02
• 25
T
I
]-
Oscillating field threshold amplitude and losses FIR 2 tllustrales Ihe exper,mer, lal dependences ,)1 Ihe osctllaltng I~eld threshold amplilude measured m Ihe exlernal field B e = B0 s,n oJ/ + B at an ,)sc,llal,t.,n Irequency / = ()l Hz Ior two m,,n,)lilament samples wllhoul a slah,hz,ng ci.,pper c,.,al,ng 'The expertmenlal results. AB,., were ()brained by the Ihree ahtwemenli(,ned meth,,ds h,r Ihe Nb-.-'T'l alloy samples, w,lh a d,ameter(,l'l)llX m m ( c u r v e s l ar,J2, t'L~ 2) and,'ltameler ,,I 022 mm (curve 3, Fig. 2) 'The exper,rnenlal dula uhla,ned using the lirsl mell],~id are marked by circles, Ihuse by Ihe sec,,nd melh,,d by cr,.,sses and Ih~,se hy the lhtrd (,he by Ir,angles
268
Cryogenics 1 9 8 5 Vol 2 5 May
¢j~ ot ,:1
" ~ c ~ c ~ " " ~).--cJ
o
(.)
I
I0 ~.~0 f ,Hi Fig. 3 FruquHncy depHnde, ncP ,)1 Ihe oscdlalmg Imld Ihreshold amphlude lot Ihe ,..;ample'= wtlh a IWlSl lenglh ol 2(') rnrn (curvH I) and 60 m m (¢:urve 2)
Superconducting 0 C~
materials
#n m a g n e t i c
fields ." V . A . A l t o v el al.
h (see /'/g
'~) T'he =nve.,.,Imgall,m wa,, carrted lILll in a I'lehl w,lll Ihc tl)riMillll tJ.lrllplmC'l|l L~ ]"ilL' vechlr iII Ihi!, c ( i m p l m e r l l ~a:, dtrecled parallel hi the aXl~ cd' Ihe e ~ p e r i m e n l a l spectmen a~ a n l l n - l n d u c l s v e wife coll. The I'ffsl e x p e r t m e n l a l .~pecilnen was Ihe lille u~ed previl~u'qy h~r Ihe .~lLtd~ i~1 Ihe erlecltve re.~i.~lance in i).~cdlalln~. ina~,nelic rleld,s,' 'The ,'..ample wa,~ a layered b t h l a r cud ~)1 an Nh-'T't-ha,.,ed alhly rncmld'flamenl c u n d u e h l r w l l h a d i a m e t e r 111'() I '~'~ m m 'T'he sludles p e r h l r n l e d have sh,lwn Ihal hlr hlqtl the riilaLin/,:.,, rteld and the o s c i l l a l l n ~ I]eld Ihere ext.sls a Illre,,,hlfld aitIpltlLidL' OI IIi(' rl)l;llllll~ riehJ an iiicrease iiI w h i t h cause.,., arl ellecltve reSl.'.,lance Ii) lilt" Iran,,,pl~rl cLirrerll rh)wmL.., ah_mg lilt' .``,'.,ample T h e ellecltve re~t.~lance resull.,., in Ihe l a d Ihal parl ol Ihe enerE'y dt~.',,Ipulln~, in Ihe .``,'.,ample i['~ Ihe rlllaltr'~L.~ ma,t.'neltc I]ehJ =~ hetn~, p r l w l d e d by Ihe eurrenl .'.,Lmrce (in Ihi.s ca~e due hi Ihe a c c u r n u l a l e d r'nert.,~ In Ihe sldemlld), and Ihe current trl Ihe etrCLitl specirnen ,sldem~td he~.,trls hi decay In our expertmerllS I he I h re,'.;hl dd a m p l l l u d e ul I he rol all n.~, held t~ l a ken as I he held value al w h i c h ,o{,tl = I() ~ ~ m appear,'.,. t'q, t h(u) tllu",lrale'., Ihe e~,pel [ m e n i a l dependerlce ~ll Ihe rlqalln/:.,, I~eld Ihre,,llldd valLle, ,~i~'ll ,, llri the cLtrrerll//I. m Ihe sample lur Ihe value t)1' tile mean rieht B = ()¢-~ T T'he a p p e a r a n c e i~1 st'reentrlL... , currents tn Ihe malrlX Cl)lnphc.'He,'., even m(~re Ihe hehavi(:.ur i~1 a m u l l d ~ l a m e n l c l m i p o s i l e tn a rl~laltn~, magnel=c I]eld We have exam=rled Ihe w o u n d Nh-'T'I- ha,,,r'd n~LilllrilarnerH c~mduehlr w i l h a cc~pper and a m i x e d (.'Lt-L'uNt i n a l r i x A N , i r n a x 'T'C' 13'pe c~mduchlr(Irl~m I M I I_JK) was laken as Ihe,',.;ample w l l h a m i x e d malrtx exlerrlal d t a n l e l e r i~1 ()~ rllnl and ~Ltper c l m d l l t l t n ~ . I'tlamerlls iiI I(I p rn dtarrleler I~lsled eve~' I f =nrrl Ill Ihe ;.,ilml'~h' wtlh ~.i rlq'q'~er m a l r l x w l l h art e~.lertl;.ll dl;irllelCr ~ll l) '~ rlllll ~lll~i .'.,ul~crciH1dlJclln~., ltlamcnl,., ~I d i a n i e h ' r 2", /.irn Iv,,i'.,led ever3, 2", man. lhe c()ppcr hi ,,uperc'imdLichlr rallo wa,., I I [ h e re,.,Ltlls h~r lhe lllresll~dd a m p l t l u d e ill lhe r u l a l i n ~ liehJ Irlmi lhe Iran.'..,pim CLirrenl ~,alue are l~re'.,enled irl ft~_~ hh T h e rlleasiJrell-letll~ ~ere carrted lILtl at a r~qalnn[., held Irequem.'V ill () I Hz II1 a CIHISIalll l'whJ B = i)h T These e x p e r i m e n l ~ have .'.,tll~wn Ihal tl Ihe Iran~porl t Lirrerll increases, Ihe t h r e s h u l d arni:,hlude iiI Ihe rlflalin~, I]eld decreases Llnder ~rnall Irequencte,,..id'p, l l u l , m Ihe sc'reenln[.., currenl ellecl,,,, in a rnalrtx are small, In lht,',, ca',ie ~ne can c~mslder ,~eparale I ] l a n l e n l s tn a cl~rnp,o~lle as isldaled llrle,~ ~lnce Ihe clmducllm~ Lttlder study have Ihe '.,arne crtflcal current derl,stty. Ihen Ihe r u l a l t n ~ rteld lhreshuhJ a m p l t l u d e Is dtreclly prlip~)rli(mal l~,~, lhe I'tlamenl diarneler a.',, vvtll he dern~m.,.,Iraled beh~w At all increase ~I file l,'hJ rolali~m Ireclueilt~' ,,~i.Bd,. the '.,creentn~., cLtrrenl.'., chased in Ihe m a t r i x he~lri Io [',rew.lll r(lll.lllllg
()()4 It
/'
[l')
;
I'l#'l I'~'I'l
j l . )
(.)
IJ
/
/I.) ,
i
O()
05 IO ,", I-~ Fig. 4 FrHquer,:y dependenl:e lil the .'.;pe,"ihc h.is.,.~e~=,Ir~,r the {,l.lmpLl',,lll-' ',,dm[Elh-H; wtlh a Iwl!=,l lerlglh 13160 turn
I t,lf ,4 ,.,hliv,'s e x p e r t l n v n l a l dependem.'e.',, i)1 Ihe hHal h~ssvs up~)n I l e q u e n c y ineasured by Itle cah~rtrrlelrl~,.' m e l h o d hlr Ihe seclmd curnpl~.'.,tle Wtlh all tncreased Irequencv. U sharTd',' I'alls, and ~..'cm.sequenllv tly.,.,lere~ls his.ses l..~rlll,v alli/ a Ilit'al ma~.llnum lit'curs
Rotating field threshold amplitude I h e e.~l~erlmenl w.i:., c;irrled (~=tl Irt Ille hdh~w=rG;, wa~ 'The h i l ] l a r .%lmple. 2, i r i t l u d e d in itle ctrcull ~ll the '.,uper t'lmiJili.'llll I" ",l_llClllild. I (',el" tl~t ~) wa,, l~l;.il.t'll tn Ihe i-lille (il iJ ~,uperi.'lml/UCllli~. hlur pl~le Uilll windlli~. II had ,,iril.I;,llidal vvlndlrlQs hi l.'reale a r~ilalinl7 iTi.iQnellC Ileld [ v v l l pair,, iiI ;~,l.lllerl.'lirldUcllnl.~ ~liidlnl~.~i were led I'lv I~,,,/ll c l l n l l ~ i l l e d ,.,iiLl Ice.% ill' allerrialinl., currenl. ,-I, Ihe .~i nu.sllldal Cl.lrrerll IreqLlerit'V arid iI.s anllL'llllude wl're l l h l a m e d hy Itltqalld,Jrd ',;l[.',nal tJelierahir, ~ T h e a m p l t l u d e ~alue ill Ihe a l l e l l l a l l l l [ 3 l'lJrrelll in Ihe Wllldln~2,~ was iTll'asured hy I~t,,li aln ml~lel ~. A Ill lhe s a m p l e sl)lemqd a t'llrrenl i~I given value was shlirled lJSln~, a lherrrial swtlch T h e curTenl rhlwln{., in the t'llCUll was mea,.,urecl hv lhe maL.meh~re.sislt,,.e Iransrlu,.'er.
02 )
~.l
I-
I~S ()1 ,J
() (.)
, Ftg. 5
I
1
D,aqram I)l Ih~ Pxpurirr=~,r=l.4 trlfslallaltorl
~
O6 T
f
(J I Hz
\%,., ,
C)6 I"
1.-.
~a'~()(' ,I
,
Z I (J
05
IW~
OI Hz
()1
b
L)
//1¢
t
i
5( )
K)( )
I,A
Fig 6 Threshuld value ol Ihe rulalmg compurlHnl amphlude, i~1 Ih~ exlerrlal h~.ld as a hJn¢:l,)n rd currenL a, Fr)r a munuhlamerll (',t)nduclur, Ih~,I',orlsldnl value qJI Ihe exlmnal he,ld t,~B = 0 6 T, b, lur Ih~ ,.,drnplm., wtlh a q:llpper c:l)rll]ul'.lflr (Z~) arid a mt~ed Cu-CuNI mdlrtx N,)max TC lype c:orlducllff (('))
Cryogenics
1985
Vol 25
May
289
Superconducting
materials
in m a g n e t i c
C)U(:~
f i e l d s ." V . A .
A l t o v el al. I i l a m e n l '~vr*.'enlnE, beE,ins h~ prevail due h.) Ihe +,'l~upling currenls tn Ihe ouler 'dahdnzt nj..; copper layer ol Ihe m a l r t x T h e ca h.'ulaled dependences ~ll Ihe r¢)lallng Ileld I hresh,dd a m p b l u d e h)r two comp¢i.sile samples under sludy arc presenh.'d by sillid lln4:.s ,n t'),t: 7 II Ls evtdenl Irl)m Ihls F'tglJr¢ Ihal Ihe cah.'ululed ~.'urve,,; agree q u a l l l a h v e l y w l l h e x p e r i m e n t a l resulls in Ihe i r e q u e n c y range i n w d v e d
/~ " Ob T ~ 50A
('104 I-
L .,1
Conclusions 'T'he resulls (pblalned can he (d praclieal tnleresl h.)r s u p e r c o n d u c l m g eleclrtcal m a c h i n e s wtlh a super c, m d u c t l n g =nduclor u p e r a l i n g tn a I'r,)zen Ilux regime, and l'~r the c a l c u l a t i o n ol h y s l e r e s l s and m a l r t x h ) s s e s in
UU~? I )
(i)
I.)
l.l
f,.'()m p< ~,st I~+."m a t e r i a l s .
I
C)(,
I
5
IO
I
t ,Hi
Fig. 7 Threshold value ol Ihe rolalmg compcmenl amphlude ill Ihe exlemal held as a luncllon I")1 Ihe h'equency lot Ihe sample wHh a copper conduclor (Ix) and a mixed Cu.-CuNi malrlx N.'imax TC rye.' i:onduclor (<:)). The solid hnes represenl calculated values ~k~'~ll- I
dependences
ol
rolalion
c
in
veluclty
Ior
Cryogenics
1985
Vol 25 May
Andnanov, V.V., Zenkemch, V.B., Kurguzov, V.V., Syl¢'hev, V.V. and 'T'ernovsluv, F'.F. F'.llecltv¢' reSlSlunee ol nun ideal supez
~.'Imduc.h)[ ~)1 the II I~'pe [n Lt,,i;lllallrl l, ITl,.ll,nc.Jtlt IlehJ Zh t/~ ',p Te, e t1." ( Iq71)) ~8 1',2~, .5'or Phl'~ .lt TP I IqTI)) 31, NI'~
2
Zenkevilch, V.B., Andrianov, V.V., Kurgazov, V.V., Svlehev, V.V. and 'Ternovskiv, F.F. Apparenl resl,~lanc'e ol nun-udeal ITp¢ II
nuperconduch~rs ('rv,g+'m¢'.','(Iq72) 12 42,4
(.)gasawala, T., Yasukochi, K., Nose, S. and Sekizawa, FL
[~()
t"/g 7 W H h l n Ihe
s m a l l Irequem.'y ranges Ihe svreenlng currents closed m s u p e r c o n d u v t i n g I'daments c o n s i d e r a b l y i n l l u e n c e Z~/~h, however, w i l h an increase in the r o l a l i o n I'requency
270
References
4
E.II,:cl we [e,,P;lance ol cunenl car rymg .'.,uper+.'ondu~.'llngwin.+ m osL'dlaling magnet.: I'wld,~ I, Cn,ugemc'.~'(Iq'7h) 16 1t Mm'gan., G.H. T'heoreltcal behawour ol rwi.,,led mullic¢,e supcrcl)nducllng, wile in a lime varying unllorm magnell,.' I'tehJ .I ,4ppl Pht,~ (Iq70) 41 th7t
Received 26 Aprd 1984 The melhods ol measuremenl ol the oscdlaling held Ihreshold amplitude, AB v, are rev0ewed As Ih=s quanl=ly increases, an ellecl~ve resmlance occurs. The dependence ol AB v upon currenl and hequency for monohlamenl and mullddamenl conductors ~s sludied. A IheoreImal approach ~s suggested and similar effects are also shown to exmt m rolaling magnelm helds.
Keywords: s u p e r c o n d u c t o r s ; rotating m a g n e t i c fields
m a g n e t i c fields; a.c. losses; m u l t i f i l a m e n t a r y
'The behawour ol hard superc~mduch~rs under allernultng magnelte rtelds ts ac~.'ompan,ed by dissipal,ve pr~ce.sse.s The dependence orthe Ios.sescm Ihe allernatmg magnel,¢ held ampltlude changes sharply when Ihe amplilude exceeds Ihe penelralton held ~)r Ihe .st~-¢alled magneHc held threshold. Beh~re Ihe Ihre.shold umpl,lude Ihe hy.slere.sin h~s,se.s arc pr~q.~M~mal to B ~ al Ihe .superc(mdueh~r surface, and as Ihls quanlll3' increases above Ihe Ihre,d~old level the losses increase Itnearly w'Hh the held We have shown prev,ously t Ihal as Ihe rteld increase,~ beyund Ihe Ihre,~hold .'tmplllude, an ellecllve resistance h) Ihe Iransporl currenl arises in the superc~mduetint2 device whk'h can be c(m.sldered as a eoncen traled elemenl ()1 Ihe eleclrtcal t. irt.'utl placed in an ~scillal~ng magnel~v field ]-'his Paper deals with Ihe elle¢ls ol i)s~.'~llal~ng magnel~c held,, ~n Ihe eurrenl II(~w~ng a h m g the sample slud~ed.
currenl will appear AI an mcrea,se in the Iield ~.st:illallon Ihre.sh~ld amplilude Ab' v, due Io non.s'vmmelrlc I]eld penetraH~m inlo Ihe .supereonduLlor, Ihe Ilux mduved v~dlage changes d,scontmu~m.sly and Ihe inlegral llux value during a held change cycle is n~) hmger zero) A change in Ihe Ilux value h)r an external held chant.,e cycle wHh a .superc~mductinL2 dewee m an allernaling magnellc held Fed hy a con.slunl uurrenl source can he delermmed by InleL2ral~ng I' arising al Ihe ler'rn~nal~ ~1 the .'qJper ¢~mducl~ng device under .,,ludy T
'b :
--
(3)
and Ihe eurrenl .s~urt.'e will perh~rm Ihe Iollow,ng work per I'leld change period 'T'
P =
t
•
7'
1" I dl : /
F'r~m which I ro m
t"
I' d/ = Rel-I 17''T'
(,4)
(J
Ihe elk'dive re,~lslam.'e value in Iound
't' R~II = I T
(i)
=
when an area, ~r al lea.,,I a line, ~hev,, t`.7= I ~. v-/ = t) ~n Ihe .superc~mdm.'l~r during Ihe field change c'vcle By ch()o,~ln~, a L'lrCUll oJ IhlN area Jilr illlC~,rallon onecan ,~how thai durln~ Ihe cyclic chan~e ol induction ~wer Ihe periled o1' held r()lall~m Ihe v~fllage In Ihe ,~uperc~mductor becomes zero ":'V" . = - -.
. . (~(r+'r)
Blr)) d~
(1
where i IN Ihe c~m,stanl Iran.~pc~rl currc'nl value S(~. Ihe amplilude Ihre.shold value (an ,nerea.'.,e (~1 which cau,~e.~ an ell'ecllve re.~i.~lam.'e In an (~.~villullng magnellc Iield) can be delerrnlned experlrnenlally hy Ihe h)lh~wlng Ihree melhL)ds I
, S
O011 - 2275/B5,/OBO26154J5 $L)3 O0 tO '1985 Bull~rw~rlh 8 Co (Pubh~hwu) Lid
Cryogenics 1 9 8 5 Vol 25 M a y
measuring. Ihe currenl devuy in a .~hl)rl ~.lrculled devicej mea.~urm.~ Ihe amplilude al which a v~fllage jump ari,,e.~ in a supere~mduvllng .,,ample in a varying exlerrlal I'leld~. L
.. ('1
II th,.~canm~t he avhleved, lhen h~r a general ca,,e lhe llux wdl change and an elleclwe re~stance h~ the Iran~port
266
I'/d/
II
al .
T
/ /
Theory II has been shown ~ Ihal Ihe Ilux Ihrough a super conducting dewee in an allernaling ma~.,netic field ~,,,g~ven by
conductors;
t
measurm.p the Ilux Inle.p,ral vahJe.¢, per field vhange ~.'y~.'le
Superconducting T'he ah~,ve methods are vahd I'(~r h~,lh ~,scillal.ng and r~lalin[~, n]agnel=c I'teld`,. The c~md=l,on ~1 Ihe elleclive resLslance appearance in a rolal~ng ma[~nelic field wdl have Ihe h~rm 2Bo " 2Be, = B,,. - Bt
( .~)
where B,j s Ihe r4dal,ng Iield amphlude B, and B, are Ihe m a x i m a l inducts,ms on Ihe superc~nduclm~. Idamenl
,,urlace due I~ Ihc Crlll~.al Iran:.,p~rl L'UrlL'[II a,,d Ihe Iransp~)rl cLirrenl ~n Ihe IllameriL respec'l,vely F'~r a m~m~d'~lamenl ,~uperconduclor ~ t , ,s deler rn~ned by Ihe superc~mduch)r ~.'rll~cal pr~perlie`, and iIs ge~melr,~.'alsize and exhlh,ls hysleresl`, In c~mlrasl h~a m(m~d,lamenl c~mduel~r where ~ f f , doe.,, n~)l depend ~)n Ihe I'teld (~scdlal,~m Irequem.'V, Ihe ma~,nel~¢ pr~perlie`, (d a mullirflamenlar~ clm,p~s~le ~n an ~`,cdlal,n[:, I]eld become much m(~re c~mplicaled due Io Ihe C~)tipll,~g currenl`, in a mi, lr~x. F~r a c(m~p~s,le Ihe field Ihresh~ld amplilude ,,, delermined hv the exlernal Iield ~)scillatt~m amplilude al wh,ch. ,n an ~tiler laver ~1 Ihe o,npo:,,le ,.,uperc,mdud~n!, Ilh~menl,.,. ;~n ~'lh'~:l~e res,,.,lance h~, Ihe Iransp~rl current lion, in.p, in lhe,~e I'damenls appear,, 'TI~ lind Ihe Ihresh~fld ampl,lude ~1 Ihe ~'~n,p~),~,le ~n an ,~,~u'dlal~ng ma.gnel=c I'leld. 4me `,h,~uld lake mh~ ,.ICeOLIt,I Ihe c~)upl~ng currenls m Ihe malr,x In allernaHn L, magneli~, i'~eld,, and als~ Ihe sereerHnL.~ ellecl`, ~n _Z~I, Slrik'~' In ;llh'rll;,llnl? maL.,m'llc l'lehJs ~,. = H,~~I11 ~I -I- ~ Ihe cuupl~ng currents are clo:,ed m Ihe `,uperc~mdt, cl,ng filaments 'The maL.,.nellc Iield al Ihe rilamenl surla~e. H,. i, in c~mh,ned Ir(m~ Ihe exlernal I'~eld. Ihal ol Ihe o~upl~ng currenl and lhal ~1 Ihc c.~lernal lield screen,n[: The exper~menl`, described heh~w were u'arr,ed ~)ul ~m exper~menlal ~.'~mp~)`,lle`, wHh ~ne layer ~1 super CoN,dueling. I'llamenl`, F'~r these samples Ihe o~uplin[~. currenl;~ cah:ulal.m wan perh~rmed hy u`,~n[~, Ihe two. l',lamenl model i)l lhe ~.'I)ITIp(I`,II~. lak~ng mh) al.'l.'()IJlll the eleclr,e lield ~n lhe ,,Liperc~mducl,r,~ l'~lamenl`,./~ II In ,~ur s~)lLil,~!,ri Ihe c',,iJphlu.., ctirTenl ~aluc. I.,. can he wnllen an Ihe ,,urn ~fl' Ihe I~flal u'urrenL In-,. ohlained w,lhoul ~.' and w,lh Z~J add,l,~m which ,`, ohla,ned Irom Ihe equullon
Z 'J"~'
( '/i' ')
materials in m a g n e t t c helds • V . A . Altov el al.
where /~ lake,, ~nh~ a~.c¢~unl Ihe IiehJ ellecl ol ~)lher Iilamenls lur Ihe tt,wen compos=le 'The `,olul~on of Ihis equali~m wdh regard I,~ H,. allows u`, I~ delermine Ihe field Ihresh~dd ampl=lude, z~E./~,,the ,ncrease,d whk'h re`,ult,~ in an el'led~ve res~slance I,~ the Iran`,purl currenl We used a s=mflar melh~d when cuns=der,n.e, lhe m%,nehc behav,~ur ,~1 the compcmde superconduch~r In r~dalinL., nia~,~lelu.' fields We h ~ k mh~ a¢¢ounl lhe elle~.'l ,)I C~ml-flln ~, currenls [n lhe matrix and lhe Stil~erconducl,ng I'~lamenls and a `,creenin~, value (~1 Ihe exlernal Iield ~ndticed hy Ihe currenl'~ in Ihe ouler layer ¢~1Ihe slahd=z~nl~, maler=al. We ohlamed Ihe expres,~¢m h~r Ihe Ihreshold ampl=lude ul'a r(daling I'~ehJ liar a c=~mpo`,,le, an increa.`,e ~1 wh,ch led I~ Ihe appearance ~1 an efl'ecl,ve res,qance I~r Ihe Iran`,p~)rl eurrenl Ihal can he pre`,enled a`,
-I ~11,1.1 = ( B I ¢ - B ~ ) i l
+
[ ') 11 .1-o.~r] ) ~/'' ,
I + 4o2"r'~ t ~/z
I * ,.,'~ ~
.
where r~ is Ihe ¢Lirrenl quem.'hlnL.., clmslanl in Ihe i~uler la~er ,d `,lal'~dlztng n|;.ilertal, r~ I', II|e ~.¢~LipllnJ/, current cem'.;lanl helween Ihe malrL'~ and Ihe .`,uperc~.mduclm~, Idamcnls I + I/(I t- ( d r y ) " takes inh~c,m`,iderali*m a I'dumenl screenlngellecl Ihrough Iheu'urrenl clo,~ed =n Ihe ouler layer ~1 the.,,;lah=l=zm~ maler=al The Ih,rd mulHplier ol ItHs expres`,~on take.',; inlo acc(~unl Ihe c~uplm~, currenl elled ¢~n Ihe Ihre`,huld value As at, example, Ihe dependence ~1 Ihe relaltve Ihresh(~ld ampl,lude, Z~l~Bd.,(/)/~kBih(/ = I)), on the rotal,ng I'leh] Irequency h~r a one compunenl (r, = r~) and u rwoo)mp, menl matrLx wHh a hlt~h,~hm,c Ic~ luwc)hm,c nlalrlx rall¢~ equal h~ '~. ,n illuslraled ,n Fl~ I The calculal=on`, are perlormed lur r~ = ~ , IO ~ s(curves I), r~ = 2 . I() ~ ',(tu~'es2) and r= = '~ . I()z .`,(cu~'e,s ~). A`, Ls :,h~wn ~n It,~; I lhe relallve lhreshold amphlude depen denee on Irequem.'y greatly depends on lhe m a l n x ~.'~n ducliv,~, h=gh ~hmle to low.ohmic malrtx compunenl c~mduel,vil~ r a l , , , a n d l~isl length Wilh lhe ~ncrea.se,)l
") /~'~H I U
where/, ~,~ Ihe I~t`,l length and p,, ,',; Ihe re`,i,~lanee ol the mairLx
When
the p e n e i r a l i o n
I]eld v a l u e is s m a l l e r
Ihan
the threshuhl, and Ihe eleetr,c I'~eld al Ihe I]lamenl ,',;urlace can he wrHlen as Ell = /J.J~/rl h (where h ,s Ihe field penelrali~m deplh ,nh~ Ihe I]lamenl and H,. I the ma[~,nel,c field im Ihe I'damenl `,tirlaee) Ihe equalion can he `,olved
as z3J = -
,-= B~I ~'(.,,~ (11"/2/-,)
`,m (cur ~' 'r/)° ' '
('7)
',~ o.~
(n/21,)'Zlj~.l~,pe(oJ~r ~ ÷ I) ~ f~T
The correction h~r lhe couphng currenL I~. ,s imp(~rlanl ~)nlyalsmalllrequene,e`,(~//l m~i)4aloJ' I/r) Allarg, e Irequem.'~es oJ ~'. I/r) ~J/Irr , IS equal Io1) I The c'ondlllOn i~)r elfeellVe res,slanc'e ,n one of Ihe eomp~)`,tle filamenl`, ,n an ose,llalmng rna~.;neltc I]eld ~.'an he presented as
,1
~
(IdH~n'~/4-1.dl
÷A)I = +i,.(I--kl)l~') I/'~
L)
:2
rl
rz
• 5r
I
[ 5 f, I-Iz
L)
~- ([d H~n~/4 + I~(I - k ) i ~' ,I- ~,.,( I -k,)'z) '/~ I = ~ (~' - ~)
=
IO
Fig. 1 Dependence ol Ihe ;elalwu Ihreshold amphludes on Ihe frequency of Ihe samples wdh 'r t = 5 x 10 3 s (curves 1), r I = 2 X 10 " S (curves 2), r I = 5 x 1 0 " s (eurvRs 3)
Cryogenics
1985
Vol 25
May
267
Superconducting materials in magnetic fields: V.A. Altov el al. 03
frequency lhe Ihresht,ld value, ~l~lh , decreases and under the large frequencies ol field rolalion =1 approaches a conslanl value independenl of frequency.
~
Methods of measurement of the oscillating field threshold amplitude Three melhuds ol measuremenl ol fhe osc,llating field Ihresh~dd ampl,lude AS~,, are presented m this Paper I
"
The I'trsl melhud ~,1 measuremenl was as h.,llows 'The specimen slud,ed was included ,n Ihe clused supercnnducltng c,rcull wtlh 'lhe measuring' supercondueling s,.)leno,d ufa km,wn inductance as the sec,,nd elemenL 'T'h~s s,.J,len,L,td served as a 'currenl source' and allowed measuremenls I,L,he laken Irom a ma~leh.~ res~sl,ve hismulh transducer placed tn the solent,~d cenlre. 'The current was exciled in Ihe usual manner by means o1' a Ihermal swtlch. In an osctllaltng exlernal magnel~c Iield al higher Ihreshold o s c d l a l , m ampltlude h)r a gnven currenl and an exlernal magnel,c I]eld, Ihe appearance ol Ihe el'lecltve resislance resulls tn a current decay The Ihresh,,Id a m p h l u d e value was determined I'.,m the Iield amplilude when an increase or resislance P{~ll ~'" I0~" m appeared tn Ihe ctrcutl. 'The second method is hosed on Ihe lad Ihal in a variable magneltc Iield wilh c,.,nstanl b'. Ihe charucler ol Ihe vollage change vaned sharply whet] the I~eld Ihreshold value was exceeded In our opintun [he vollage on Ihe sample m a vat,able field can he divided tnlo Y. Ihe one reduced by Ihe exlernal Ilux change ~., and Ihat due I(, an It|dLt~.'lt,,l'l redts Irihuli,,n./.I, ins=de Ihe superc,,nduclor In lacL Y d,,es nt,I depend on a field dtslrihul,)n ,n Ihe super cc, nduclor Wilhin I h e e x p e r i m e n l by c,,mpensal~ng Ihe w~llage value induced hy Ihe exlernal Ilux change (I)0' ~,ne can delerrrime AB. I[om Ihe expermlenlal dependence U = U ( B J ,~ 'The exper,nlenlal sludy ol ~r./. li',r Ihe case when Ihe sample was dffeclly ji.ned Ii, a d c source was pul inl,) ellecl ,n the h,lh,wmg way 'The sample was placed m Ihe superconducltng s,.,len(,Id cenlre h) create an oscillaling magnetic I~eld wilh a given frequency and oscillalton amphrude A direcl Iransporl current ul a given value was passed Ihrough Ihe supercunducling sample. 1'he vollage I rom the sample tn the (,sollaltng magnelic Iield was led hi Ihe mlegrah,r tnpt, t. A S . was delermtned experimenlally rrom Ihe ¢naxJmurn field amphlude, Bma,~-Bmm, under which Ihe Ilux value, ~ = § I' el/, remained equal It, zen, I',.,r several field change cycles•
02 '
l-
J
i.~
(')~ (,,
• ,~
".~.
"~,~
I 05
(')()
113
//io Fig. 2 Dependen(.:e ol lhe o~c,illalmg held ll"ireshold amphlude lur ~amples ol dtamele,,r 0 . 0 8 turn (,'ui-ve I, B -- 0.3 T; curv~ 2, B = 0 55 1") arid dlameler 0.22 mm ((:urve 3, B = 5.0 1")
'The model ct.,mpuslte samples had a layer (,I superconducltng I]lamenls 6()p.rrL nn dnarneler nn a copper malrLX with an exlernal dtameler o1'11 '~t mm 'The I~rsl compustle sample had a Iwtsl lenglh ,,I 2t) mm, Ihe see,rod a rwml lenglh ~H'6() mm The Irequency dependence ABe,. h,r bulh sludted samples ts shown in Fl~. '~',Ihis shows thai Ihe field Ihresh,.dd ampl,tude decreases will, increasing frequency H(,wever. l h e c o u p h n g c u r r e n l s , n l h e s e c t , n d sample which had a large rw=sl length are larger Ihan Ihose tn Ihe Iirsl sample, and Ihey are closed tn Ihe supercunducltng filamenls which resulls in Ihe tnduclt,.,n redmtrtbul,,n m Ihe filaments and tn a reduclion ,d'lhe field Ihrest, dd value. A8~ With an ,ncrease ul Ihe Iield osctllaliun Irequency Ihe filament screening ellecl gr,,ws due Io Ihe currenls in Ihe t,uler slabiltz.=ng malrtx layer causing Ihreshold value t,., mcrease AI ,~, '.. I/r. ABe, ts constant and =ndependenl ,,f Ihe held (,scillalion frequency 02
• 25
T
I
]-
Oscillating field threshold amplitude and losses FIR 2 tllustrales Ihe exper,mer, lal dependences ,)1 Ihe osctllaltng I~eld threshold amplilude measured m Ihe exlernal field B e = B0 s,n oJ/ + B at an ,)sc,llal,t.,n Irequency / = ()l Hz Ior two m,,n,)lilament samples wllhoul a slah,hz,ng ci.,pper c,.,al,ng 'The expertmenlal results. AB,., were ()brained by the Ihree ahtwemenli(,ned meth,,ds h,r Ihe Nb-.-'T'l alloy samples, w,lh a d,ameter(,l'l)llX m m ( c u r v e s l ar,J2, t'L~ 2) and,'ltameler ,,I 022 mm (curve 3, Fig. 2) 'The exper,rnenlal dula uhla,ned using the lirsl mell],~id are marked by circles, Ihuse by Ihe sec,,nd melh,,d by cr,.,sses and Ih~,se hy the lhtrd (,he by Ir,angles
268
Cryogenics 1 9 8 5 Vol 2 5 May
¢j~ ot ,:1
" ~ c ~ c ~ " " ~).--cJ
o
(.)
I
I0 ~.~0 f ,Hi Fig. 3 FruquHncy depHnde, ncP ,)1 Ihe oscdlalmg Imld Ihreshold amphlude lot Ihe ,..;ample'= wtlh a IWlSl lenglh ol 2(') rnrn (curvH I) and 60 m m (¢:urve 2)
Superconducting 0 C~
materials
#n m a g n e t i c
fields ." V . A . A l t o v el al.
h (see /'/g
'~) T'he =nve.,.,Imgall,m wa,, carrted lILll in a I'lehl w,lll Ihc tl)riMillll tJ.lrllplmC'l|l L~ ]"ilL' vechlr iII Ihi!, c ( i m p l m e r l l ~a:, dtrecled parallel hi the aXl~ cd' Ihe e ~ p e r i m e n l a l spectmen a~ a n l l n - l n d u c l s v e wife coll. The I'ffsl e x p e r t m e n l a l .~pecilnen was Ihe lille u~ed previl~u'qy h~r Ihe .~lLtd~ i~1 Ihe erlecltve re.~i.~lance in i).~cdlalln~. ina~,nelic rleld,s,' 'The ,'..ample wa,~ a layered b t h l a r cud ~)1 an Nh-'T't-ha,.,ed alhly rncmld'flamenl c u n d u e h l r w l l h a d i a m e t e r 111'() I '~'~ m m 'T'he sludles p e r h l r n l e d have sh,lwn Ihal hlr hlqtl the riilaLin/,:.,, rteld and the o s c i l l a l l n ~ I]eld Ihere ext.sls a Illre,,,hlfld aitIpltlLidL' OI IIi(' rl)l;llllll~ riehJ an iiicrease iiI w h i t h cause.,., arl ellecltve reSl.'.,lance Ii) lilt" Iran,,,pl~rl cLirrerll rh)wmL.., ah_mg lilt' .``,'.,ample T h e ellecltve re~t.~lance resull.,., in Ihe l a d Ihal parl ol Ihe enerE'y dt~.',,Ipulln~, in Ihe .``,'.,ample i['~ Ihe rlllaltr'~L.~ ma,t.'neltc I]ehJ =~ hetn~, p r l w l d e d by Ihe eurrenl .'.,Lmrce (in Ihi.s ca~e due hi Ihe a c c u r n u l a l e d r'nert.,~ In Ihe sldemlld), and Ihe current trl Ihe etrCLitl specirnen ,sldem~td he~.,trls hi decay In our expertmerllS I he I h re,'.;hl dd a m p l l l u d e ul I he rol all n.~, held t~ l a ken as I he held value al w h i c h ,o{,tl = I() ~ ~ m appear,'.,. t'q, t h(u) tllu",lrale'., Ihe e~,pel [ m e n i a l dependerlce ~ll Ihe rlqalln/:.,, I~eld Ihre,,llldd valLle, ,~i~'ll ,, llri the cLtrrerll//I. m Ihe sample lur Ihe value t)1' tile mean rieht B = ()¢-~ T T'he a p p e a r a n c e i~1 st'reentrlL... , currents tn Ihe malrlX Cl)lnphc.'He,'., even m(~re Ihe hehavi(:.ur i~1 a m u l l d ~ l a m e n l c l m i p o s i l e tn a rl~laltn~, magnel=c I]eld We have exam=rled Ihe w o u n d Nh-'T'I- ha,,,r'd n~LilllrilarnerH c~mduehlr w i l h a cc~pper and a m i x e d (.'Lt-L'uNt i n a l r i x A N , i r n a x 'T'C' 13'pe c~mduchlr(Irl~m I M I I_JK) was laken as Ihe,',.;ample w l l h a m i x e d malrtx exlerrlal d t a n l e l e r i~1 ()~ rllnl and ~Ltper c l m d l l t l t n ~ . I'tlamerlls iiI I(I p rn dtarrleler I~lsled eve~' I f =nrrl Ill Ihe ;.,ilml'~h' wtlh ~.i rlq'q'~er m a l r l x w l l h art e~.lertl;.ll dl;irllelCr ~ll l) '~ rlllll ~lll~i .'.,ul~crciH1dlJclln~., ltlamcnl,., ~I d i a n i e h ' r 2", /.irn Iv,,i'.,led ever3, 2", man. lhe c()ppcr hi ,,uperc'imdLichlr rallo wa,., I I [ h e re,.,Ltlls h~r lhe lllresll~dd a m p l t l u d e ill lhe r u l a l i n ~ liehJ Irlmi lhe Iran.'..,pim CLirrenl ~,alue are l~re'.,enled irl ft~_~ hh T h e rlleasiJrell-letll~ ~ere carrted lILtl at a r~qalnn[., held Irequem.'V ill () I Hz II1 a CIHISIalll l'whJ B = i)h T These e x p e r i m e n l ~ have .'.,tll~wn Ihal tl Ihe Iran~porl t Lirrerll increases, Ihe t h r e s h u l d arni:,hlude iiI Ihe rlflalin~, I]eld decreases Llnder ~rnall Irequencte,,..id'p, l l u l , m Ihe sc'reenln[.., currenl ellecl,,,, in a rnalrtx are small, In lht,',, ca',ie ~ne can c~mslder ,~eparale I ] l a n l e n l s tn a cl~rnp,o~lle as isldaled llrle,~ ~lnce Ihe clmducllm~ Lttlder study have Ihe '.,arne crtflcal current derl,stty. Ihen Ihe r u l a l t n ~ rteld lhreshuhJ a m p l t l u d e Is dtreclly prlip~)rli(mal l~,~, lhe I'tlamenl diarneler a.',, vvtll he dern~m.,.,Iraled beh~w At all increase ~I file l,'hJ rolali~m Ireclueilt~' ,,~i.Bd,. the '.,creentn~., cLtrrenl.'., chased in Ihe m a t r i x he~lri Io [',rew.lll r(lll.lllllg
()()4 It
/'
[l')
;
I'l#'l I'~'I'l
j l . )
(.)
IJ
/
/I.) ,
i
O()
05 IO ,", I-~ Fig. 4 FrHquer,:y dependenl:e lil the .'.;pe,"ihc h.is.,.~e~=,Ir~,r the {,l.lmpLl',,lll-' ',,dm[Elh-H; wtlh a Iwl!=,l lerlglh 13160 turn
I t,lf ,4 ,.,hliv,'s e x p e r t l n v n l a l dependem.'e.',, i)1 Ihe hHal h~ssvs up~)n I l e q u e n c y ineasured by Itle cah~rtrrlelrl~,.' m e l h o d hlr Ihe seclmd curnpl~.'.,tle Wtlh all tncreased Irequencv. U sharTd',' I'alls, and ~..'cm.sequenllv tly.,.,lere~ls his.ses l..~rlll,v alli/ a Ilit'al ma~.llnum lit'curs
Rotating field threshold amplitude I h e e.~l~erlmenl w.i:., c;irrled (~=tl Irt Ille hdh~w=rG;, wa~ 'The h i l ] l a r .%lmple. 2, i r i t l u d e d in itle ctrcull ~ll the '.,uper t'lmiJili.'llll I" ",l_llClllild. I (',el" tl~t ~) wa,, l~l;.il.t'll tn Ihe i-lille (il iJ ~,uperi.'lml/UCllli~. hlur pl~le Uilll windlli~. II had ,,iril.I;,llidal vvlndlrlQs hi l.'reale a r~ilalinl7 iTi.iQnellC Ileld [ v v l l pair,, iiI ;~,l.lllerl.'lirldUcllnl.~ ~liidlnl~.~i were led I'lv I~,,,/ll c l l n l l ~ i l l e d ,.,iiLl Ice.% ill' allerrialinl., currenl. ,-I, Ihe .~i nu.sllldal Cl.lrrerll IreqLlerit'V arid iI.s anllL'llllude wl're l l h l a m e d hy Itltqalld,Jrd ',;l[.',nal tJelierahir, ~ T h e a m p l t l u d e ~alue ill Ihe a l l e l l l a l l l l [ 3 l'lJrrelll in Ihe Wllldln~2,~ was iTll'asured hy I~t,,li aln ml~lel ~. A Ill lhe s a m p l e sl)lemqd a t'llrrenl i~I given value was shlirled lJSln~, a lherrrial swtlch T h e curTenl rhlwln{., in the t'llCUll was mea,.,urecl hv lhe maL.meh~re.sislt,,.e Iransrlu,.'er.
02 )
~.l
I-
I~S ()1 ,J
() (.)
, Ftg. 5
I
1
D,aqram I)l Ih~ Pxpurirr=~,r=l.4 trlfslallaltorl
~
O6 T
f
(J I Hz
\%,., ,
C)6 I"
1.-.
~a'~()(' ,I
,
Z I (J
05
IW~
OI Hz
()1
b
L)
//1¢
t
i
5( )
K)( )
I,A
Fig 6 Threshuld value ol Ihe rulalmg compurlHnl amphlude, i~1 Ih~ exlerrlal h~.ld as a hJn¢:l,)n rd currenL a, Fr)r a munuhlamerll (',t)nduclur, Ih~,I',orlsldnl value qJI Ihe exlmnal he,ld t,~B = 0 6 T, b, lur Ih~ ,.,drnplm., wtlh a q:llpper c:l)rll]ul'.lflr (Z~) arid a mt~ed Cu-CuNI mdlrtx N,)max TC lype c:orlducllff (('))
Cryogenics
1985
Vol 25
May
289
Superconducting
materials
in m a g n e t i c
C)U(:~
f i e l d s ." V . A .
A l t o v el al. I i l a m e n l '~vr*.'enlnE, beE,ins h~ prevail due h.) Ihe +,'l~upling currenls tn Ihe ouler 'dahdnzt nj..; copper layer ol Ihe m a l r t x T h e ca h.'ulaled dependences ~ll Ihe r¢)lallng Ileld I hresh,dd a m p b l u d e h)r two comp¢i.sile samples under sludy arc presenh.'d by sillid lln4:.s ,n t'),t: 7 II Ls evtdenl Irl)m Ihls F'tglJr¢ Ihal Ihe cah.'ululed ~.'urve,,; agree q u a l l l a h v e l y w l l h e x p e r i m e n t a l resulls in Ihe i r e q u e n c y range i n w d v e d
/~ " Ob T ~ 50A
('104 I-
L .,1
Conclusions 'T'he resulls (pblalned can he (d praclieal tnleresl h.)r s u p e r c o n d u c l m g eleclrtcal m a c h i n e s wtlh a super c, m d u c t l n g =nduclor u p e r a l i n g tn a I'r,)zen Ilux regime, and l'~r the c a l c u l a t i o n ol h y s l e r e s l s and m a l r t x h ) s s e s in
UU~? I )
(i)
I.)
l.l
f,.'()m p< ~,st I~+."m a t e r i a l s .
I
C)(,
I
5
IO
I
t ,Hi
Fig. 7 Threshold value ol Ihe rolalmg compcmenl amphlude ill Ihe exlemal held as a luncllon I")1 Ihe h'equency lot Ihe sample wHh a copper conduclor (Ix) and a mixed Cu.-CuNi malrlx N.'imax TC rye.' i:onduclor (<:)). The solid hnes represenl calculated values ~k~'~ll- I
dependences
ol
rolalion
c
in
veluclty
Ior
Cryogenics
1985
Vol 25 May
Andnanov, V.V., Zenkemch, V.B., Kurguzov, V.V., Syl¢'hev, V.V. and 'T'ernovsluv, F'.F. F'.llecltv¢' reSlSlunee ol nun ideal supez
~.'Imduc.h)[ ~)1 the II I~'pe [n Lt,,i;lllallrl l, ITl,.ll,nc.Jtlt IlehJ Zh t/~ ',p Te, e t1." ( Iq71)) ~8 1',2~, .5'or Phl'~ .lt TP I IqTI)) 31, NI'~
2
Zenkevilch, V.B., Andrianov, V.V., Kurgazov, V.V., Svlehev, V.V. and 'Ternovskiv, F.F. Apparenl resl,~lanc'e ol nun-udeal ITp¢ II
nuperconduch~rs ('rv,g+'m¢'.','(Iq72) 12 42,4
(.)gasawala, T., Yasukochi, K., Nose, S. and Sekizawa, FL
[~()
t"/g 7 W H h l n Ihe
s m a l l Irequem.'y ranges Ihe svreenlng currents closed m s u p e r c o n d u v t i n g I'daments c o n s i d e r a b l y i n l l u e n c e Z~/~h, however, w i l h an increase in the r o l a l i o n I'requency
270
References
4
E.II,:cl we [e,,P;lance ol cunenl car rymg .'.,uper+.'ondu~.'llngwin.+ m osL'dlaling magnet.: I'wld,~ I, Cn,ugemc'.~'(Iq'7h) 16 1t Mm'gan., G.H. T'heoreltcal behawour ol rwi.,,led mullic¢,e supcrcl)nducllng, wile in a lime varying unllorm magnell,.' I'tehJ .I ,4ppl Pht,~ (Iq70) 41 th7t