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62

p(exc (63 2: _ 1) cs,when L/d 1. (4)

In spite of s remarkable acevemens, owever evene Pry and Bean mode us ou to be o med valdy

essential ecause o its highy deazed caracter. nmcrocysaine materials in fac it s commonl oundat plexc) - la even if L/d [7]-[9 On theoer hand p(m/ shows in genera a nonlnear dependence on1' whc canno be easiy expaned in ems o4) . In he case of sngle cysas or gran-oentedamnations havng L/ the depature o measured osses rom P and Bean predctons has been reaed o varous eecs lke the presence o egulatsn te wal moon domain multiplcation or wal owng[106. As to negraned materals attemps aveeen made o connec excess osses wth Barkausen noser 7 or to atribute them to continuous rearangemens othe doman conguraon 8 However no generaagreemen as to e roe of al tese mchanisms n deer

minng the actual oss eatures o sot maerias has ebn acheved

A new oneptual framewor capae of incudingmst o thee eecs n a uned reament has een proposed receny e author on e ass of a statisticalapproac to the oss penomnolog The theory deveoped in 3 4 9[ and here e revewed inSection I, leads o the concuson tha e largescae behavor o agnec domans can be descried n erms ofe dnamcs o statisticay ndependent magnec ojects (MO) each corespondng to a group of negborngnteracting domain was and reduces the oss pobem ote nvesgaon of the main phsc propees o as afunction o1", Imo and e atera crsructure hsappoach can e successul appied o a varet o differen materials y invesgang the phsca meaning ofthe concept of MO n ach case n parcular has eensown at a sngle MO can be dened w a sngeBloch wal n grin-oriented ateras w arge domains[20, whereas n microcysallne mateas te woedomain srucure inside a sngle gran plas e roe o asinge MO

Startng rom these premses in tis paper we presente results of twood nvestgaton. n te rst pacewe have carried out a sstematc experimenal study oe oss behavor versus Imax and 1 in varous sot magnec materals consstng o measurments o the ossper ccle vrsus f n he range 0 1m 00 or 00 dependng on te maeria peromedat severa

values o peak agnetaon on SFe aloys o diferent texture and gran sie Aco on Ne alosand amopous rbons. B thes resuls reported n Secon II. we have trid to provide a source o nformatonon propeties edd cuent osses n sof materialsas wel as a as or a pper testng of heoreca lossdels n hs connection our second goal as een o

[E TANSATIS O MAGCS. VL 24 O 1 JNUARY 1988

nepret tese expementa resuts n tems of e menoned dynamcs of MOs and to reate te osevedpropetes of e parameeri o te micostucture and thedomain sucture of te nvestigated materials As fulydscussed n Sectons and V severa interestng concusions ave een otaned by ts anass First teteor gves a natura ntepreaton of te genea facttat the dnamic oss per cce is a nonnear uncton of and shows in paticuar that ths nonnearty is appoxmate consstent with a smpe aw (c1 =k2# or a wde variety o mateas Second e eory is aso appcale to nonoened mcrocystalineamnatons having a ne domain stuctue L / d .In this case the absolue vaue of te constant k can ecacuated under reasonabe assumptons drect ntems of the vaues of the seress oss and e averagegran se obtanng good agreemen wt expeimentalresus Fna te theoy reduces e dependence o excess losses on both Ix and to a common mecansmthe competton etween e appled eld and gh inhomogeneous intea counereds goveng te dnamics o te snge MO s s feature of e theor as

mpotant practca consequences since t permits one toextract the dependence o dynamic osses on ot Ix and" from a singe loss cuve at a gven vaue olmx and toexpress ths dependence n closed anayc fo n parcular i wi be sown n Section V at n te case ograinoriented treepercent SFe te knowedge of onytwo poins of a sngle loss cure pms one o predcte loss behavor versus Ia and1 wth an approximatonat for te daa presened n tis paper and n e range

1 0 H s wtin percen

I STATCL IERPRTN F DDY URRN

O

Accordng to e statistical theoy o edd curent ossesdeveloped in [3] [. [19]] e asc pysca mecanism goveng excess osses n sot maerias s idened w te competton beween te extea magneticed apped unom n te sampe and hg nhomogeneous ocal couneelds due to eddy curents and micosucura neractions he asc consequences of thsphyscal nepretaon are uy discussed n the references entoned and can be summared as olows.

or eac vaue o the average magnetation rate i= 41 e magnetation process n a given crosssecon o the magnetc lamination can e descred asanticpated n the intoducon n terms of smutaneous actve magnetc obecs he dynamic ehavorof a snge MO s contoed b an equaton of te fomHe o , were Hc

'\C)/i s e excess dynamc

eld actng on the MO s e magnec ux rae ochang coesponding provided by the MO and te popotonal constant is detemned te dampng eectof edd currens 0 [3 Wen tere are f smutaneously active MOs must e on e average a racon /f o e toa ux rae s imposed o te sampe (Sis the cssseconal area of e amnaon so that a

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BERTO: POWR LOSSS N SOF RROMAGNIC RI

elnhip he Hx< /f i expece whchcly u u be [20]

whee

5)

H(W) aGwlSi = 4aGS/rJm 6

n he vlue he imeninle cecen Gw iGw 4/73Ek 12 3] 056.

2 he fnmenl ppey he uny f ppein n 5 h i i expece be ncin n Hex;{P} he exce el n me e {P} pmee chcezin he micce n ncue ieen eil mnncy inceinwh incein He [20 Nce h, if h uncn iknwn we bin m ,

7)

which cn be ve wih epec Hx h eenn he epenence f he exce px = Hex nHw (ie n

Ixndfm ee 6 n n {P} Hweve,

nce nH {P} i n incein fncn H heepenence Hex n Hw wl be n ene e hnine n ene ce n he exce pe cyclewil be bine. he he ve heefe nlnepen f he c ley knwn in he leen cne by he expeen epte n h ppe,h the pe cycle nly nnline ncn mneizn eency.

3) Seve nbe ly bey he ple lne lw

f(Hx; {p}) = no+ HeclVo 8)whee he mcucl inin nw ce byno whch epeen he limin numbe imu-neuy cve MO' when 0 n by he mneice Yo Eun 7 n (8) le the nnline excel expein

Hex p(exc)/i foV (, + 4aGWsiln - )/2

i 4xfm. (9In he lwin ecn we h unetke enel

uy f he ppee f he ncin nHc; P} inieen mel cliy he el vue n ppic-biliy f he ppe heec ppch mneicl n, n ptcl, he phycl enin n nef vliiy he ine lw (8) ee pin hepeenin f he expeimentl eul, hweve, we

wn ecll ipe n uefu pcee ey p-pe in 20 by which he uncn fHc; {P} cn beiecly bine expeimen. Accn (5) Hw Hexc i eemne by he ve H(w nH Bh f hee uniie cn be iecy evluem expemen, cn be een f hei vey ein. heee i we pl enec cue n ef HwHex veu ine PIm veu fm

623

ulwe h iecy bin he behvi he uncin nHx {P} i ineein nice h uiemi l epeenin h been ppe nue huh n e epcl be n [4 5Accin he phycl inepen mmze in f i expece epen expcly n Hex nly whiehe uniie (e,

Ixhl hve nly n inec

nence huh ince chne he pmee{P} hi men h we my bin vble n-in n he miccl ppee f ieen mel, n he mcn f he n cue be-hvi upn chnn Ix n me el imply byin he ve Hc epeenin exmple if nchne ccu n he mneic min cue venei uncn f I we expec h he lce een ieen vue f Ix hul l e-uce ne cue when epeene in em f ve Hex hi i he pn view h wil be pen he cin he expeenl el epte inhe fwin ecn

II.XPERMENTAL ESUS D ISCUO

Le wee eue n n ee (GO) n nn-ene (NO) heepecen Sie ly Ac n uet, 500 Ne ly n mphu ei le in ble I. w ple emee wee empyein the expeen: n Epein me n iUy wn ibbn he pwe w bine bymen f hih pecn nlc wee peinmeemen cne nuil neic xwve n he ne mnezn eence 4Hz he hyee w eue in enel hhhe blliic eh n he ce NO Se n Acn, hweve whee he e in he blic evlunf he hyee l w fn be cmpble wih hevin ync w m he hyeei w bine by iecly expn he ynmi ce wn ech pe, he behvin he ne 0 : f : 00 Hz 0 m : 400 z hephu bbn ) n evel (u ve) vle pek mneizin w eeine

he bine Pfm vefm cue e epte n i0 (ehn pin ech e) In he hhnp he e, he vey e eul e epte ine (x ; {P}) veu e' ccn he epeenin ce n Secin I. We hll nw exmnehee eu in me eil, cuin u enn n he plce n GO n NO Se, becue hee w ceexhbi me bic ee pwe cmn e exen l he nveie mel

Gr Ortd TrPrt SFi () ept he behv he pe cycle n

ni m P fm ( i he eny he me ) veuf meue ve ieen vue Ix he ce-pnin epeenin in he plne Hec i ven in (b) h epeenn cley hw he c -ey ee in pevi wk 20 h GO Sie i

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624 [EE TRANSACIO N MAGNE. V 24. JNUY [988

BLE I

ateril Popns

Fige yNumbr l03 Kg/m)

2 gai-id 3 % i 65lngidlly cu

gri-d F avesy cu (9

3 noictd % e nnorieted % e c on 76 ea 9 5 N amrphus MEGAS

6 3

ph LS65 CO 756

40r-

(a)

aCndtv Sze(IO'!rm- (1-'

222.2

2

9.3

22

1,88

Fg Los pr e nd ul ma da x wavfm vrumgtizg rqcy i gn hc S dv o pk mg h omnVu bo p o p hr s argerh i mr va, bn a t saaed 2. 3 9 w pam V -i us w (b Rpsao o m emna pn m pr by 5 and 6 vrs dyic HY I n ha h pnta e bm sg o f (8). Thr p i gv b th ntrso wh j x Nua d a a b at ar mh that has ay tt = /, en 1 h 1.7 T 1 a 2 w T

c wh h ln w (8 or h dpndnc o onH cly olowd W pon ou h h rul cn-no b mry npd n m o rodr xpnon o {P}) ound H = 0 c h l Hx I Vo by o wh rpc o cn b y chcd drcy rom Fg b . Th vuo h pmr f nd ocd wh h drn

ample Geotry 50 Les (W/kg)

xperi- acu-c mntl l

Thicss a fm(1 m) (1- m ,) 17)

2.9 8 1.7 3fa3.4 2 L 83.5 1.5 18 9 31 1 21 8 391 1.5 36 6 8 3

wo 1 5 4.5 6 1 3 - rhbons 5

5 15 8

1 L 8 1

o cuv y obnd by qur n ng o h xpm pon n h (H, plnhown by h bn gh n n Fg (b)W obna 015 Am ndpndn o IaX" whr nce rom 1 whnIx T up o 25whn Iax T Th nowdg o o nd V pmon o prdc hough 2) (3) (9) h bhvor o P!vru ndax Th bon n n Fg ( hv bnobnd u by h pocdur. n cn noc h xcn grmn wh xprmnl pon nd pcur h bly o () o dcb h obd lononln Th ru d o r nrng con-con bou h bhvor o xc lo n G SF

Eon (9) mp n c h o ucnly hgh vl-u o! (commony bov w Hz) h xc o prcyc cn b pproxmd

!m : 8I .G(W)SVo/maxf 4 0nd hro bcom nly ppoo o Th h m on oud n h u 2 [,h dynmc o onl r md o ow mg-zng rquc m omwh nccur r ru how on h conrry, h uch nonn ppoxmly oby mp J w n h wholnvgd rng o h dpndnc o h ollo pr cyc !m on ly o h om

P! +

m+

k4 Iwhr h mnng o k, kJ k cn b y dducdrom (2) ) (0) I c b chcd om (8 hn h g wh ! 4, h nmbr ocv M ncr ny Th concuon n good gmn wh h ru rpord n [4]5], 25]

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BTOTT OWR OSSS SO ROAC

e fat tat te ed Vo s oud to be depedet ofIm makes t a itri parameter of te mateal, o-eted to s miorutural propete, rater a a smple tg paramete We sal see at t teretgoluo apples to ost of e material follog telea a 8) t a bee uggested i a peous paper[20] ta te motural tepeato o Vo oudoe a eato of te orm Vo - Hhyst/No beee Vote quastati oee ed H" ad e umberN ofMO aalable or magetato a ge ro etoof te matera. We e meag ad adity of toeto GO Sie eeds furte study ad l beaayed a futue pape a pobe terpretao o tog moysallie maeria le O Se as beereetly popoed 21], 22 ad i be dsued teex ubeto

A to te depedee of o o Iax e eall tat epreets, aordg to (8 te umber of MO ae simutaeousy ae te lmt of lo magegrequee, ad at, te maea uder oderato,ea MO esealy ode t a gle Blo a

s peouly poited ou 25 at lo Ia> a aue of te ode o te umber o all peset teo eo o te esgaed sample i te demage-ted tate T diaes tat a faly reguar ad oeet moto of a all take plae at o I Te pogree ose of eguarte te a motio treasig I s e lealy poted ou by te steadydereae o o do to o 1 oe ate MO at a me,i epeset a qite geera oer lmt fo te aluesof ay material [2 A eeg tet of te pysa meag o o a be made by oiderg e mod-ato i te os beaor oequet to deret po-edues o ampe demagetiato Ea o te osues reported Fg. (a eer o a sample peimary demageted at a frequey o 1 H. e ame

meauremet ae pefomed aer 0 H demagea-o deret euts are obtaed e example epoed Fg 2(a refes to I 0.7 T ad o a detedyam loss derease ater50 H demagetao Tiset progreely dsappeas e ge aues oI ae odered Tese esuts a be expaed quatatey by otg ta by demagetg te saple at50 H e aate doa multplao poee tatodue a ger umbe of doma alls i te sampero eto, a osequet reduo o te exeslos Te ely geerated a oee ae easly a-ated at g dutos ad t expla y e lossbeaor aeed by demageato oly eIa 1 T Hoee ts tepreao does beome really e

dt ad exprssbl quattate ems e e amelos daa are epreseted te plae (Hec' g 2be deree betee te to o ue reuts o a eae of, rom 25 up to o 4 diatgte ge umbe of doma als trodued te sa-ple oss seto e te sope /V o te o ea o aged at al a expeted om te metoedmrottural arate o e ed Vo.

> 7

\+Hexc !aVo0.5A/m

6

10

oLof mH-Z-O O-5Hex c/ m-O(a) (b)

g 2. Md bhavior gr td epce at [ 07 T eqt deret procedues of smple eag-neizao. S capto f Fg 1 fo meanng of mployd psta-tion

A a al remak, e pot ou tat e iea la 8

ttly folloed by GO SFe ee ae exesie past strag or upo e applao of exteal eslerese [20 ad el derbe alo te beao o tree-peet Se (0) [001 gle ysas [9 [20

Nonoriented ree-Percen SiFe and Oher MaealsFoowng he Linear La o H/Vo

g 3 ad repor e os beaor meaured o tolamiao of NO reepee SFe aateed byderet gra se ad oery tee materals teaerage e o mage doma etay maler tae gra e tu, maller ta te lam-ao tes (ee Table A dued e oduto ay model smlar to at o Py ad Bea ouldpedt i ase, o exes o a all see 4 i lear

otradito t te eperimetal data epoed Fgs3(a ad 4(a. We ll so o o i otradoa be reoed by makig use o e teory dsused Seto

A st reut of teret tat, as so by Fg 3bad 4b, e lea la 8 s tll fullled. Hoeeotra o te ae of GO Se te tem Hx/ V opredomat at a aue ofIx ad o terest Teparameter doe o play ay ga ole ad a beegleted. Pysialy t imply mea ta e umbero e MOs beomg ae dyam odos soodetoy ay memoy of te quastat ate derbedby Equatio 8 ad 9 a te be oeiety approxmated a

iH; {p} H/Vo (12)pCexc) = iHCW)Vo= 8G(SVoImaxf3/2. 3

Equatos 12 ad (13 ae a umbe o emarkabeoequees Assumg aaogy t e reult obtaed i GO Se tat V a irs paameter of tematera idepedet oI e expet om 12 ta al

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6266,-00

5 p

--<

m (a)

0

re

"C0 5 1 (b)

Fig 3. Pwr l rid tre e oen t gi alogou f Fig I Fo ti 8 a axiay 2, wic does c amtr D l o ld V td rm (H" rprtti xml in i V 07A / Tw oni gt gmnt n ig ( t htra ccl contbon80

3

_

_

O

0 -++ +

H /Vo,O.12

b)

Fg 4 Se a n 3, f aple whe V 12 A

0

50loss points at dieent values of Imax should educe to asingle staght ine when epresented in the plane H, hs pedicton is well coned, apart fro soescatteng of the data reated to the pecsion of the easueents by Figs. 3b and 4(b. In tens of the behavior of P1 vesus ' this iplies that the singe paratr Vo deteines, through ( (3 3, the copetedependence of dynac osses onx and and, in paticua, that the ecess oss pe cyce follows a siple law The boken ines n Figs. 3(a) and 4a) weecalcuated fo (, 3, and (13 assuing in each casethe xed vaue of V obtained fo the corespondingeo representation: V 007 A in ig (a and 0 A n Fig 4(a.

It is evident tat the fundaental poble at this pointis to justify on physca grounds the absoute value ofthe ed V so as to eplain the icostructua easonfo the pesence of an excess loss contrbution in agneticainations having doains denitely salle than their

IEE TRANSACO ON MAGNC. VOL 24, NO JAUAY 98

thickness A possbe ey to this poble has been poposed ecently n [1] [ on the basis of the foowingscheatic description of the agntiation process in negained ateials Adopting a point of view sighty dfeent fo that of Section I we can equvaently inteet a snge MO as a egon of the ateal cross sectionchaactezed by a faiy hoogeneous oca coeciveed, so that it will becoe active as a whole when theapplied eld oecoes a gven theshod n an annealedne gained anation whee the ain uctuatons ofloca coercive ed ae expected to take place fo gainto gain a sngle MO is then natually identied wth thewhoe doain stucture deited by the cross secton ofa sngle gran o that the total nube of Os pesentn a given coss section of aea S of the ainaton wlbe

4)with equal to the aveage grain size. he statistica distribution of the values of ocal coercive ed at which diffeent MO's wi becoe active can be assued to be toast approxation at with constant densty 1 V(the

eld Va epresents theefoe the aveage iniu sepa-ation between dieent local coercive ed values. Asfully discussed in ] these assuptions ply that indynaic conditions when the applied ed is greate thanits coespondng quasistatc vaue by the aount Hc>a the MO's nsde a potion of width Hexc of the entoned distrbution of local coecive elds wi be siultaneously active Sincc this nube is spy =H Va, 8 is staightfowady obtaned On the othehand, as a consequence of ts vey denition, the eld Vust be drecty reated to the acroscopic uasistatccoecive ed Hhyst of the ateal In fact as shown in[1] [ the vaue ofHhy in the loop of peak agnetiation I is related to by the epession

5whee N is givn by (4 and s > is the vaue of acroscopic agnetzaion when all gains ae satuated eachalong its ost favoed easy agnetiation ais ( < I 0.85/ in a ateria of positive cubic anisotopy having aperecty isotopic distbuton of cystalogaphic ganoentations o 4 ( we obtain

Va= 2SHhyst (l,)/Srax 6p(exC) = 8/axf,. G(W2

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BERTOT: POW LSSS IN SOFT FRMAGNC L

agreemen wth he excess losses observed n he two NOSFe lamnaons considered n Figs. 3 and 4 The vadyand range of aplcaby of 7 have ee esed oeexensvey in [9] [21] 22] whee s shown hat 17s actualy caable of reroducng, o a good aproxmaion a nmbe of oss resuts n NO hree-percen SFeamnaons sannng a mch wder rnge of gran size

vaes (from 30 m to 300 m. I s woh remarkng' however ha he whole ce presened hee s expeced o fa whe he ga size becoes arge ha hesampe hickness Acuay n hese condiions he nhomogenetes of oca coecve ed nside each gan become oe and moe moran Each gan sps ntosevea ndeenden MOs and wih fuher nceasnggran size he maeral rogressivey aproaches he condon where he snge Boch wals rather han the sngegras ac as indvdua MOs

I is naua o as now if ohe materas besdes OSie do behave accodng o 7 gs 5 and 6 eporhe ess of oss measremens on Amco on and Mmea The nceranty n he oss absoue vales s rahe

lage n he case of Mumea due o he vey ow oss ofths matea Anyway i can e seen fom hese gresand he daa repoed ae I ha he consderaonsade for NO Se remain essenaly vad g 7 eosa na case whee he near law 8 s obeyed ha of awound bbon of the amohous aoy Meglas 2605 SC.Alhogh he mcosucal ropeies of his mateiaae comeely deren rom hose of GO SiFe and hedomain scre s extremey tcae we nd a rahersmar behavor of he funcon Hxc; {P}). The edV s ony weay dependen on Imax, nceasng fom Vo 063 A/m when Imx = 5 T up o Vo 93 A/mwhen Imax T.

Mata Not Obyng th naw o Hexc/Vo

Ahogh he lnear aw (8) does apy o que a argenumber of deen cases, we have no a po eason oexec ha should be aways vad Fgs 81 repohee cases (amophous Megas 265 O 5050 NeGO heeecen SFe nsvesay c where (8) is acay no oeyed The Hx> represenao gves evdence however of a neresng feaue common o ahese cases he fac tha he fncton Hx {P}) assocaed wh each maeia, hogh nonnea s apoxmaey ndependen of he arca vaue ofImx. Fgs8b1 b show in fact ha al the oss ons of a sngemaera tend o arrage hemseves aong a sngle cewhen represeed n tems of verss Hx hs rest

has mmedae nteesng pracca conseences, sce mpes tha s posse to obain h dependence of dynamc osses on boh Imx and js from a snge cueofP/f versus f a a xed vale ofIm In fac, hssnge cure s sucen o deemne the funcon H{P}) whch can hen be nserted no 7 By sovng hseaion wh respec o H he deendece of excessosses on H(wl 4uGwlSf (he ecess oss wl hs

0 Armc Irn

1 T0-

0 T

7 T-+--

627

I C. im

LL m z Hex (A)

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6215 M 5 u l iHexC!VO

_ kOL___ 20 m H

()

V"0.8 m

5 He c(A-I-m-) '10b

g K Pwr l i Mtl 2605 CO mu lly Cmm ge g t Fi I ut fr ft tt w xtl wh reprsd t vruH nn wh v i d ppmi i npt Thig w b n m q lw HjVo k i 8( with Vo 08 A/m20r 5CNiFe l

07 T._x-:

)

1 (z) 10

In'c/4 3

b

0

Fi Pw i 00 Ni Cmmt t i l tht Fi. I an bt' w llw polymia a' I +HVo' wt o 8 Am

pd max a 1 ly hg i pd Iaa P} is h ai Tis p s ilsay ss k is shw Fgs a)a).Ea s has alad wih h a 7) 2) r rrspg sgl i f H

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RTOT OR LOSSS SOF FRROAI ATRIALS

o

x ) , [4) (x Ol

, [ x , ] o ] ) [9 (c x)

[

l

Fi. Behavor sus ax f hysteess eld H /4Imaj' ba m ml s o p n g \-0 C-espnnc wee vs symols an ge um (w qek) Tb I i n s Nms wi aes epesen sl acs y w e se f aa as ben mp.

ummazed by Fig 12 where he ame lo daa of Fig a) are aga in repored ogeher wih a pecic iuaion of the dependence on m ofol and hyerei loe and f 50Hz To intepre thee data et uconide what we have ea in he previou ecionabout he behavio of he em which accodng o heeparaon of oe 3) contrbue o he oal o P. Ato he hyerei o we have een (g. 1) thahe hyerei eld l /4Imaf n h ateial apprximatey ppoional to r o hat p Iaf (a mlar eul s epoed n 5 h oudbe a good appxmaon a eat n the nge Ia 5T The exce o (exc on the oher hand decbedin general by (9 Howeve f we l oueve to ufciently hgh agneting fequencie ay

f 20H z

we can ue he approximae mpled expeon 0 anduhe negec the a em oVo/4. Wth hee appoxmaon and akng nto accoun hat he ed V in 10 ndependent of 1" we can therefore expe he oallo per un ma a

72d2 2P/0 : Colaxfm + 6 (/axfm)

)3/2 C Imxf 8

where 2 ha been ued o expre he caical lo andC C are uiabe conant chaaceizing he maeiaSnce C and C ae the ony unknown paamee of 18the knowedge of wo experimena poin ucent o

deermine hei vaue and conequeny o pedct thecompete dependence of P/ on boh and . n hecae of he data o Fg. 2 we have deened the vaueof C and C fom two pOint 0nd f 50 H ofhe o curve meaued at Im 5 T. We have enmade ue of 18 o predc the o behavo n te whoenveigaed ange of Ia and vaue The reu epreened by he e of boen ne n Fg . We can ee

94.Gr d F

50 f (b)

F 1 Gai n -prcen S F Sme g SeC llusan pn eav Ol a hy-ss _ ls pe n mss a = 5 Hz. n ns epes piins 8 with Co 1 X 1" = 0 '4 J . ' g" T' 3/2

hat he agreement beween 18 and he whoe et of expermenta poin i wthin 10 percent when f 0Hz The devaion a high pea magnezaon ma >.5 T are due o the fac ha he expeon we have uedfor the hyteei o becoe a bad appoxmaon wethoe a ow Im ae fm neglecng e em oo/4 of10 Acualy th em become oe and moe importan wh decreang 1 nce o pogevely ncreae whe at e ae e the r em of 0 deceaea :. ncdenay thee conideaion how hat bohthee ouce of eo hould be mal aound 5 otha the vaue of C and C are indeed bet deemnedby condeing a we have done he o cue coepondng o Ix = 1 5 T f coue, 18 could be apped not only to G SiFe bu n genea to any aea

obeying the near law 8 o 1 wh V ndependen ofImax and approxiatey popoonal o [ ee g.36 and 1).

Equaon 18 give evdence o he exence of wobaic conrbuion o he dependence of e oal lo P/on Ima a a xed magnezng fequency one ppoonalto Iax he oher o I The aveage exponen expenghe aw of dependence of P / on Im eefoe expeced to be included beween 15 and depending onhe value of C and C n 18 concuon houldbe compared wh od epca le ofen menioned nte teratue 5J expeng P a P IZ u reamenpvde a hyca nepeaon to thee ue and howhow hey ay ae fm e nelay o he hree em

whc accodng o 3 conbue o powe oe CLUSON

he eoeca nepetaon o he expena eul on power loe in oft maerial pented n hpape ha hown tha he uncon (Hexc; { P } denedin Secon povde a pming convenen too o looknto he connecon beween dynamc oe and cro-

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630

srucur s ms sr ss sg fuon H b ssd wh gn r n wh ss urs drn pmgzions r consdrd nd whns G SF dpndnc f s osrd prids ddion rm h mgc dom sruur.hs rsus suggs usng hricl rs n hsud h prprs of

fin drn phscl su

s Adpng hs pn of w hs prmd s g ur nrpon of h gnr prsn f nnlnris h bhr h ss pr cl f mrl nd h qun prdic xcsslosss n grnd os 1 Hwr n h css whr w r no bl prd h prprs of fm mrosop od hr f h sng uncin H P) n b ssoid wh gn ril hs r pr osquncs. f f h b d rm snglss u msud g lu m" nd hrough h pl dpdn dnmi sss n boh d n h word u B ng us f hsrs nd som dd frmon on h dp

dn hsrss osss on " w h shw So h n GO SF, s possl prd h hor h o oss on Imax nd fr h know dgof on wo pins of sng ss ur wh n pproxo h fr h d prsnd hs ppr d h rg 0 Hz s whn 0 prn Dopnggr rosruur mods h hr H { ) n rius mrs pprs now s h n bjc o fuur gns.

ACKNOWLEDGMET

h uhor s dp ndd Prf G MonPrf A Fr M nd Dr F Fiorlo or hr cs ncurgmn d nrs n hs wo umbr frfu dsussos d ub os d suggsns fr hr ric rdg of h uscrp. Hs wshs h E G A. Go S Rocod sc r h hn ssn i ss sumn

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