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MET06oA'; TijC; 6lovoJjijc; TC,V KuAIV6pIKOV …library.tee.gr/digital/techr/1969/techr_1969_7_433.pdf4JJ MET06oA'; TijC; 6lovoJjijc; TC,V EIC; • KuAIV6pIKOV KtAucpoC; uno T';V tni6paolv

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bull bull

4JJ

MET06oA TijC 6lovoJjijc TCV bullEIC KuAIV6pIKOV KtAucpoC

uno TV tni6paolv PEUJjOTC)8OEC)C E Kplpoundi~

MllXtOO ~ HiEKtpOJtYyOU

1111 T I1 JW(O ~ fT lC iQaaiu kuoHuX811 l] ciie~ (I rijr itETOshy

loA i et Til l Oo1Opir til 7lVX ~oT1rro~ QOijr to)1 ono((w-HishyTWP -rO 1-~1J(5elXOV ~fAIq(W Qto rry~ brioeaal1 l1La ~ (wshy

lJanJ)87(f6 (iJ ~ To xvhvoQl1Ittl v l(i)~1ltp (J O~W iTit t I(d)ov nd shyXOt ~ai d7rriQov [lj llt ftt( iv (iJ r YJappr ala Tij~ onoiar rJdgshy7CTat r] Qe1JwTWfhjat fhwe-eITW (h e t v(dm~m brl wiJ aoshyVO( wv ~v)(~middotr5~HXOlj X1)VlPfi U H u vw-rilw ouira~l n(oeJa(shyurnm 7lQor rei OlOnoAIyen O ltadoICl find flQvoiOtJ H ( wpashylJI COflh or1 ~teyiarrl TIPf] T1j rVXVoT1rro emir fafaral i x -rif otu()xfia r QCl jwtwOrj(]pound([)r b rjJ 6 Xgovo xa-ra TOV dorOlOV uWUWt 1) Jt1JXV6rl1 eoii ri (~ GIr)lJil OV noaoGtov fllU neoshy~u8oetU(J lf (01] ~owfj HWI uluopoQa tf] nv(vOT1]W (Ufr elvat dVt~deTlJTo rfj btugxeiur r fj ppound1lJlarwBfjoewc

I EloaywYll

To 1tp6PATlJW tfl~ OtavO~Lil~ TroV olvoppwllcmov tvt6~ troy 1(Yooshyyiwov UI~lKroV jleuroOwv uvnjleuroTIJ)-t i ~ttal ds 6Aalt Talt ~ )Ft( jJOTeuroshyXVlKalt KllTaaKeuroOO~ poundvOu oCP1(5tlLvtn l jluyvTltlKa 1tEoilJ OTlJlLOOPshyYOUIleuroVa lm6 PCUjlUtwv jl eurotapa) J oIlEvWV ttl rpolt tOY xpovov H aKplPnlt 1vwQtlt 1ijlt owvoll fll O tautTllt 68Tlyeurot ELO OlatDSeurolO at 61tOlUI Eitc lJatwvoov tao n1twEIao gK OLVOPPEUjlDtWV EiTeuro ltEpwpiouv TTlv cltiopuolV TOU 1tEoioo ToD ltPOEPX0jltvou n ubtampv

To JtP6~ATllla WUTO JtupoocrLa~ETUl eurojlCPUVEcrtEPOV Ei~ nil KUtashycrKeuro OOJ ~teurolvu~ u[ 61tOrUL oEv euroIVaL oovatOV va OLUjlOPOPWOoov Es gAClC1J1 LnWV 61t01euro f] OLUOP0jlll rampv OIVOPPEUIlDtWV OeuroV euroIVai OOVUtOV va 1tEPLOPlO9~

Ta OIVOPpEUjlaTCt Tel euro1tuyOjleuroVCt t Vt6 tampV aYWYlllWV 0IKroV jlgcrwv OTljlLOOPYOOv euroV Jteurooiov To) 6no lov jleuro1UIXtAAeurol TO apXLshyKOV nEoiov TO 1tPOEPXO)lpoundVOV tK rfllt 7rQyij t OTlAaOn tOO K) K~rbjlUt~ toD oLuPPIOjlEVOO un) 100 PeuroUjl DtOO npoX(jlpoundVOIJ va ttpocrOtOpicrWIlpoundV lrlV t7tiOpacrlV ~OU OEU tr PEUOV TOgt wonlo 1tcoioo avaxwpoDjlEv tK jlla Ku8oplO9euroicrTlO OLaVOjlij~ OIVOP PWjlCltWV tV1O TOO UAlKoD ~tOo o Onola rupUKtTlpirHll (mo 1nnVOtTl1OO poflo J

Kat01tlV 1tPOcrOIOPl~ETcn TO crOVlcrtUjleuroVOV nEbiov 0Tl uoi] to mofov T6 01tOlOV unUtteurol1Ul crOVO~IKWo 1tpO ~ JWYWlflV 1flo anapultlltOu elva jlova 6u jlTlKOOO tlAc KTP1Kflo taffro~ Ola TrlV 0TllllOupyiav taD moiol) wD oVtlcr1OlXt~OjlEVOU 1tpolt 1Tlv OIUshyVOjlnV taUTTlV tWV OLVOPPElljlcLtWV EivUl Ttpoopuvtlt OTt 010shyopopa tampv moluJ((i)v jlEyeuro9(i)v t(r 6noiu nEprypaopouv 10 nvwshytEPW 800 moiu ali crotn nl jl l 10 neuroOlUKOV jl tmiddot([ 90~ ToD oPXlshyKroo eltl~UAAOjlpoundVOU eK tio 7tTlyljlt neuroOloo

E[lt TTjV 7tCLPoOOUV t pyacrllV t~erweuroTUl i] ~uta t3oJil die ~mr VeurojlTljlgVTlO eurov to tva o KUJl vft rlL tw() KeuroAUopOll C JtUKVOtTl1O poiJ ~ trov OLVOPPEUI-lD1WV 01(11 1 OIUVOI-li] 1tPOEPX61 ctL b 1l1a~ ypUjlshyjli]o T01t09Etl l~t VTl~ r-rrl toO UIoVQ t uu KOLVampp L ~ )i) KEAUqJOUlt TOiJ 61toiou TO tcrWTeuroPlKOV nATlPOUTUl 010 jlOVWtLKOO jlpoundrwo H jlpoundTUPOJTj aUTTl 1tPOgPX8tul 8K 1ijo EcpapIlOYflt gVO J-l8Ushy

jlaTO~ tvtocrEW~ 1 (L) hoooTlO tilv jloPCPliv 6p90y(J)VlKfl~ PEOshyjlatw9liOEWlt

H JteuropiJtTU)crl~ oGtTl EivU OOVUtOV va Esollolw8fjnpo~ tv KashytWOIOV jleuroTO IlUVOUOO 010 toU aywyoO toD Ono(ou OlEPXEtaL Il[a owooxil pwWltoJfTlcreuroWV JtPOI tPOqlOOOtTlOlV gvO~ OoOtl1shyjlUtoo 1TlfEcrTljlOVOtW 11 tTlJEXEljJlOjloD

610 tllV tOPEOlV TampV jleurofE8rov tOO nEoiou KU~ croYKeuroKPIIlEvwlt TOO IlUYVTlTLKOO olUvucrjlanKOU OOVUjllKOiJ XPTlcrlll0ltOlOuvtat a[ OIUopOPeurottKUi eslcrwcreuroL~ IOU Maxwfll a[ m~plypncpoucrU to tlAEKtPOjlUVTltlKOV lt80iov 0 Ka90plO1l0~ tflo jleurotaPOf1lt dx JtPO~ tov xpOVOV tflo TtoKv6tTltoo poflo tmv OlVOPI=euroOllntWv yivEtat Ola tflo XPl1crEWlt tOO IlEtacrXTljlUtlcrlloO Laplace

1 YTToAoYIOlC)I T~t lETapaA~c T~t TTUKYOTlT0C pof1c TWY ~hyapptuj1CnWY

21 AVU)OtLKO imoAoy~ollo

vEOroo eurovu KOALVOPlIt OV poundIOcpOlt IlcyaAOD 1taXO ~ tcrWtEPIKflo a KT~volt u KUTD JJ 0lt TOO (i~l) VO~ TOU l crooTEPI1W O KO)WOplshyKoD avoiYjlawo TOO KEJlXPOOlt UmipXeurol Ilia ypalljlil 11 61toiu OlUPPeuroeurotUl 07to pEtljlUtOlt tVTocrEWlt l(l) (crX 0 To Keurofocpo~ a1t01euroAcltal ts oywyljlOU UAIKOO dOLKi]o uvncrnlcreurowo g KUt jlayvTltLKijo 0IU1tEPUt6TTlTOO jl crm9Epfilt

6lO TOV Ku90pwjloV IOU jlayvTl1IKOO OlUVOOjlUtLKOiJ OOVUjll~ KOU euro1tl tOO KEAUcpOOO 9a 6]0KiTlPWaWIleuroV tnv KUT(J1pound~W OICtmiddot

Ai ip I) A (I)

bull Mrllavo6o- HJ6KTP0OOC 6100KTOOP EMIl t hOXIODxo TGW MOO1)latIKOOv TOO n avClflorl)llolJ 0EcrvIKlC M1XQVIKOpound de ttjv oliJocr1avErnxEfpT)middot crlV HEKTPlOJ LOU

bull bull

bull bull

middotIu~o~ 19694J4

cpopucfV t~(OU)OtV T orcoia npOampPXampTflt tIC t~V t~laroaEwv u )il Maxwell

1 Ir t)= a~lr I I (211)V Ie ill

EVen A Cr t) to ~flyv TlTlK6v amptUVUltJ1 IU tl KOV blJvu~u6v hi tOn 1gtt)(qIOU( A6yIgt tamp bcptG11ljJCv1lt (JUJJJJ lTpl~ fJ JJ) II11 OUVt~

ltJl6)aa TOO A ad amp(vcu I 1(016 t1)V otEu6uvcrtv ToD 6~OVtl( re Z rrfOl Aor t) = AIICrt) middot Z 6rc6tt 11 (211) (LJl~ tiVet flv IlO PltJlv

1 (r t) + I a (1 11 _ middot( 11 (112) cJ l~ r Dr if ( t

6 ui tTW )UO lV t fi~ Ot Qlpopucil t~I OtixrC(J~ ( 2l2) lJH10IjlOnOI E Ishyt (U ItQ apxll v 0 1J strtlt1gtT)Jl [t I O~to LnpIClCt H jlcwOXl1jIl shy

tlOIJt 1 ~ ltp6 toV Xpovov l (Juvnpt l1ol r t~ A(r l) eCJl~ 6u dVUl i CSlo(rl) ) Ao(r L) K (ltOItL v f(IUOU + (21 2) CljIPUVU TflY llopcpiroJ

d1 r I t [ r ltI _ I I (213)drZ r dr - K l

fcp 6crol oEx61-Ul Oa On 01(1 t =- 0 n A 1o) 0 5TlA(iSr 6[1 KUCU tTl v apxnv toO )0 101 f1 JtOK VO Tll~ porc T6)v OIVOP(1) shy~ILt(J)I htl TO C KpoundMtqIo~ d VClI jlT) 5e

H 01UltpOP1KT] U(OfOO l~ (213) ~ ~iOOOatC Il esse l Sci htl TtlV YEVUCT]V AoolV

eVaa KI - ~ Enclo rl oui r ~ 00 tl Olvoptl1OL Jje68~iI g

Ig 1(1 Sexojleuro9a on E = 0 Kat t) YeuroVIKr) AUm Jltjl6ltivct niv 1Opltp~V

9 (r l) = EKlkr) (214)

S o t TltnaOOjlEV va ~QaOoaOOJlE rllV Otaaopciy Eo npo to ntO futOAOYUOJiY to jlUYVTltlKOV lIlQVUO)IUttKOy OOYU)Il shyteOY A(p t) to n pOepx6 jlEVOV tc T1 ypaJl)l fc nit t 6 aootepI shyKOY t o) a)urpo~ T OOTO Elval bull

Adpl) = ~ (t) lnp ~

H J1IitoOln jlQt I~ItVTl w itp6 TO XpOVOY l (JUvapTl1CJ1C Tf~ A(pt) raToo 1St( dval PI(PS) gtA(pt) ~uI T6v (trohoyWl6 v cplps) clJWu fml vel Ku90plCJ9a n O1JvoptTlal~ let)

6poundX0JlpoundOa on i] JleuroClpo lt tih~ EVlUOeuroOO r I(t) na phJtcuut uno JI~a PIl9JJi)0lt (ax 2) 6n6[euro fl JlntaaxnuuncrJl EvTl aUVujltll shycne q(ps) yivnm

9 pS)=$ JI t

i-o l -- Inp (215)1

-1afco 6n r (1)wIPt11UlI J (rU llapl01Q tiJv IWKvOtfltll DoTi t6)1 5 l1oPPEUJj6TOl V t-n l f OC Kex0ql OOt H jlETOCT(T] IJfl ttOIlCVTI ilic 1t~ t Ov XpO vov cruvirPll(J~ tIllJtlr fI i(rS) gt J(r t) Sd 1PQ( JLav i5 m o pltf1V Eli crmCflv ttap-D j lO[av t il O (2 1)) pc YampV1 JorV Al)(JlV fix 1 (214) H AU(n~ aun1 aa poundIvui

i(I) = CK(k r (216)

610 tOv KaOOpLcrliO V tit~ (JWOcpOr Co llptTr L va )Il~ til[ 6VlV tTr ~ pom f1I~ olovoll t61v OlVOPPEUJJtlWV fi r f OY xampPOv tov poundv16( coO Kll~I) OOu Eov aeoopil cHIlUv en Ao(p U poundIval 16 jlaYl t lK6v SIQVI)OJJanlCOV ouva~mov t6 npospxo shyjLEVOV b e til OWVO Jlto [611 li IVOPPeUIl((1WV rote [0 jlalvlln~ KOV SIUVlJOj ottK6v OUVUjltKUV d T6 ecrooTEplKOV t Oa KE~~Ushyltpou sa poundtval AI _ Al - Aa il BUl [0lt jLpoundtaOXllIlOtlOPtW C OlVoptLiapoundlt ltPI = lJll - Po bull

r

1 L

o I

~f lOYLJtooyt crp6v t~ Aa(p t) npklVOIlpoundV to 6AoKAlpro~a

11 IIC

AOI PL )= l l r LJln Rmiddot rdrdl

z~ ~

le (P)= f l(rs) ln Hmiddotrdr dltgt

lnR - lnr - 1 (P ) ( COSIll9 middot cosm6 +n sinmO)D - - m~ middot m III r

6 oJna 1 ]9IPB) - L -k- kdka) - To klka) (2171[

TlIK~ ~ ~I (p S ) Oil elvol TO 6Bpo~a T~ (21S) Kat (217)

iJ- 1 raJna 1 19 (p) 2~ np ot I - k - k l kOI-k (ta ) (2 1 8)

Eav tCj)(lp~6(JoJul nv plav OlIlthi lITll ~E[a(u TfI (214) I(o i (218) O1iIl~I(m iJptJlj tf)v 6roiClY1) n jl middottf lJ avTlTlUlO adla tvul(JIW)t tPti n1i otaxmpunni1t t 1tlqK11Eioo el4 0 rdtJ)tamppu~6v toD KeAlJqOU SllAaoil Sui P Kam [lv tqNUtTO~ jl llvt lCTV ottOOuV(Jl V ftXEI nlv Ulrtlv nJII1 v tll toU iryory tOI) 1(~IJ q)(J u Im l lOG tcrtL)tEpncoCi lJovwtuoO ltpcxrihopl~o~Evfru OaOe p~ Eo (o CoO at 61toTal (JJolliotovmt 8m 1fie axshy

nwgto g1 ~ ~( TE~ltK~ ~ mJvrrptT)ltT i(r 8) 1pil~ETa 1 bull k krlI Ibj== -- (219)

2bullbull k (ka)

AI(l Tli v rClpur lV ttJ t auVUprt1oE~ Jfr t) tCflap~(~~uy bi til (19) t6 6)o~~pIJ t oO Fouri Imiddot 61lt6

y-+jOr

~1tj - shyIfmiddot (2110)

61Q niy 6joK)fl pwatl fftr (2110) Oe Po()JBV t ampv ~oo trtoshy~evooY cruvapopound6)v

I k(~8(8)=$ Koi g la) k (ka)

loUAlo~ 1969 TpoundXYIKO XPOYUCO 4]5

tae avnOtp6qJou~ a))twv f)t Ot

L-[gi)J= holt) Kal L- [g Is) J = hlt)

onon Kata to 9EOOPTlJlO tOO Borel J- [ g()middotgIS) 1 f= h(r)h ltr)dr (211 1)

o

L- [g() J = L- [ sIJ = 11~t

Kal y+Jeo

L- [g (5) J= 2 ~J Se k+ih-kc-r)~ ps = Sresidus k(k) -J ~

Kat On to 6epOIO~ t(bv O)oKA~rIKGlv lmo)oimov Ol(~ tOe ovrotepw cruvaptTOElI Bessel O(OEl

SreSidus=1- 2lJ6- ~(I~t J o(t2npr ) J (n po)

v9a llu O[ plCat tl1 (J)vapt1iOE~ Bessel J a Kol P = J Ton g

to o)odiJpro~a (2110) fXEI tiJv fKcppaOlv

J ( r t )

KaL oLoel tnV ~EtaaOAJ1V tfllt Otavo~i1~ tuv OlVOPPEU~Qtrov oUl tJ1v 6v-rlltrtOIXOV toO aX 2 ~Etapo)v 1flt ~V1UOEIDI 1(t)

Eav 1oopa 8ekriOro~EV va (mo)of(arolle v tTtV ~Etapo)ilv tflt olovollfle tiDv olVOppeUIJUtrov J(rt) 01Ct dav 1Jpoundtapo)]v t1e I(t) QVnotOlxoooav 1tpO~ )l(av peu~atffi8fOlv olapKeicu l

(OX 3) ed 1tpE1rEa nporlyou)ltvrolt )Icl Ei5pUgtJJpoundv tnv 1Jpoundtal3o)itv F(rt) fltll avtleJtOlxet npoe ~lav JJpoundtoJlo)ilv tPl c J(t) noplshyOta~EVl1v SuI tfJlt jkl91l1ooc toO ax 4 H yea autf )lpoundtopo)1l tflc F(rt) 96 hu tiKpl~Ggtc tflvaa)lilv ava)utlKnV bcppOOlV roc 1 (2 11 2raquo)I jJ6VI1V tTlv SIQqJOPclV Otl n OuvaptTlOlI 80 Xl] qJuOIKnV ftvvolav 0111 xpovov 1000v fI )leya)utepov toO t eV(J Stv 80 ()cplOtataL oHi xp6vov ~uepotfpov toO 1

H OtolaquopopO tiDv 060 bqgtpaOerov 86 000l] tflV )letal3o)nv t1c OlQVOIJflc t6)v 0IVOPP8U~Utrov tflv npOepXO)lEVI1V h t 1c peushy~atro80poundwc toO Ox 3 fltot

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into tnv npotgt7t09poundOlV Ott 0 OeuroUtfpo~ opolt tvt6e t1lt 6YKU)I1e 6nOKt) CPUOlKflV tvvOlav )lOvov Ola t t tvcent oU1 r lt t otv 6qgt(Otatal 6note Kat oev fa)l~avetQt (m ~4IW KOtcl tOV 6noshy)degY1O)lo v

z z Ape~qn~ bnOMr(lltJ)lO

61Q 16v apI8~fnt(ov lmo)0flO)l6v t1Jc ltapaOtaOErot (2113) typdCPTl EV rcp6YPltlIJIlO 01 flMKtPOVlKOV intO)OYlOtnv KOta lilv I(WOIKOTCOfOW ForLran toO onoico to ol6ypa~~a pofllt t~shyqmVICEtal eu to ox 5 0 6rcO)OflOjJ6lt SlaKOmElOl el~ euroKElshyvov tOV XpOvo Kata tOV 61t0ov 1l tl~n t1J~ ((rt) Ka8(0tOtOl to tv hatOOtOv t1e nfJfl~ 1tiv ono(av )aJ1PaVel 1l (rt) KatO tOV np6ltov XOOVlKOV Jlfl~ toO ()1tOAoYLOIl00

)llvlou jJt 6l01K1v oV1(OtOOIV g = 02810- 7 OM Kat )layvl1shytLICTl V OLa1tEpotOtftO )I = 4n middot 10-- n seem- i

Ele to Ox 6 nop[O1OtOl n )leto~o)fI t1J~ 1lOKVOtntOc pofc Olo )l(av pEU)lat(06fOlv oLapKdalt OOO J sec H OKttlt toO K(8)6shylaquopOUlt t)fcp8Tl J em A eiKovl~O~Ev(U tpEf~ IlStoj3olat dVtl

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Etc t6 err 8 Q1tpoundIKovltetQ 1 )1Etal3oAn tfc ItUKVOtTltOC poflt fila ppoundu-Wtdl9TlcW olaplCdw 0001 sec Kat Sui dJulpoC oKttvoC lOcm At 600 KQjl1CUMrt aVnatOl1ttoVtUI ftp6r to Ma laquo1tshyv~ r = 100 em Kat r = 105 em E~ t6 ax 9 tl1t8LlCovttat(t1 1JpoundlapoAr TflC mlKVOtrftOt poflc Sui QUiplCpoundlav PBu)JQt(f)9iJCJWlt 0005 sac Kat oui d)ucpolt nlCTvolt 10 em Avl$ 01 OlIO lCa)11tUMrl avtunolxltovtal ItP~ to avrodpm PMT)

E~ lSlac fit avrottpoo Jtepllttroae~ 6 ()ttoAo)La~61 heveto 05ui ppoundi)1JCl AvtaOpoundrot I = lOOA Kal Kattl XPovLKf Pfl)JQta O5msee

H 1tQPOUOlQO~Vn ell tJiv JtQpQ)PQcpov 21 ~tQSolTt tll OLQVolll1 tbv oWOPP8UIl(ltWV ttPOEKUjEV AK t11I aVQ)uCucflt )ooampWt rfll OlClqlOPLKfj~ A~LOroOuo l 6ttoia nept)pacppoundL tflv rtUKv6rlrQ POfl1 Cl()v OwoppWllarCOV ~vC6t roO tl)w-yi)Jou 1C8shy)UqlOUt AutTt KaO taul1lV fl 5~Qvo~Tt Iflt 1CUKv6ll1COI pofjl t~QPrdCQl tK lll Evduewt lOI) peU1JCllol C1t 1tl1)It poundK tll dSlK11 6vnCJlaOeoolt roO U)KOO Col) K8AOiJOOt lCat AK tfl~ )JQ)VlTIKIt 81a1[EpaCot1lCOt QUroO OewpOu~eVl1lt Otagepdlt H )JpoundlQ~Afl tflt lhavo)Jft poundIvaI tlVolorOt tlt leuroCPQ)WV~Kf~ plC111 Col) xp6vou ICat Av6t Rap6-yoVtolt 6 6Tto10~ t~QPtdCal EK clt OlvaplilOampWt Bessel Jo AveaptfJCrot rfit IhapKdat rfjlt peu)Jaroo9Jicrampmt l llelOlOll r)lt 1tUKv6l1rot POfl1 ellt r6 lv tCaroot6v l1t tl)Jft nv 61[oiav Aa)JS6veL afir1 elt ~va roPIO~VOV Xp6vov tl1[6 rflt 6vtlp~eoot rOO cpatVOlJevou Ttpashy))JQto1[olpoundhaL Elt C6v aUr6v xp6vov 6 61[otolt ov-nCrmXEl 1[EplTtou poundit 01 sec OU10llt l XP1cl)Jonoi1oLt 111Kpotepru il lapshyKdat ppoundu)Jar09flc~ clTtMJ)t l1eLOOvpoundl nv )JEyLCTI1V AjJcpavlshyo)Jhrlv TtuKv6L11CQ PO)I 1ampV oLvoppeujJlhoov KUl lXl t6v xp6shyvov tlTtOOPpoundCeOOI Qor(l)v Au~avojJEvou 100 p66oolt tvC6t Cou ICSA6qlOUlt jJE100tal fl ml1CV6111t pOflt tv~ fl I(U)mUAl1 )Juashy

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A 1100 Ant tOU KElUcpOtx wbm- AI jJ505 ampit t6 EcWteplK6v toO KeAUlpoult wbm- I

a ACOOtpoundP1Kr UKtllt KEAUCPOUlt m C otQgepo Am-middot E cta8epo wbm- l

J nUKv6t11t pOIlt Am-t

1 ~vtact~ p8u)JatOt -ypal1l1fllt A I CUv6Pt11CIt Bessel J OUV6ptrICLlt Bessel K OuvCtPtIlOLlt Bessel r JlBtpOV J(UAIVOPUC(l)V CUVtEtIlY)1EVWV (oICti~) m t Xp6volt sec an pU~at (JUvQPCioemlt J o 8 lplOJla KUAI5plJ((l)v CUVtEta)I1fVwv (ywvia) r ad

JlQ-YVl1tlKTt 0IanEpat6Cllt 0 secm- l

~ Jla)VltlKTt OlunEpat6tlllt oepoc n socm- l

g ElSllCfI avt[CraCIt om p Ilhpov ICUAIVOP1K(l)V auVtElQ-YJl~voov (aKttlt) m ~ optcJla KUAIOPIK(l)V OJVtECQ-YlJivoov ()wv[a) rad BJ1 OlVapt11Ol~ Jo 5ui at (Koo5tJ(01[0ncl~ Fortran) BDJI CUgttlPt11Ol~ Jo ilui U1

BJ2 cmvQptl1Ol~ Jo OICt a BDJ2 OJVtlPtl1Ott J o Oltl a FTI TtuKv6r11t poft J 0t6 a FTI TtuICv6C11~ po1~ J lila t ~ r FT ~uKv6c11~ pO~~ J (~~[CWOLlt 2113)

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01

5 He-rlilz 1 Erzeugung von Stato nl ren Magne tfeldern In elnem elcktrlsch lcllcnden MaterI aL ASE A Research 9 p 7 1966

I Cars law H Tuc()e) J Operatlonal Method s in APplied Ma shy 6 Paerson R Tbe FIeld Induced by E dd y - Current In a Scm-shythemati cs Dove r 1963 Intlnlte Solid ProceedJngs or tb e IRE p 88 January 1962

2 DerusPapin Kallmann COUlS de Ca lcul Operatlonnal EdlLion 7 Sabonnadere J Method es nUTTi tr lqu es d lllYerslon de la transshyAlbin Micbel 1963 fOITTlation de Laplace R evu e Genra l de I E lec tricite p 201

F6vrler 191)73 McLachlan N Bessel Funetlons (or Engineers Ox rord 196 1

8 K(ll~ E 1I1volln ampIVOpptUIUlTpoundOV ISle IUl)lv6pn6 JB)Ofllll )6YQl tt~ovshy4 Smlllhc N S tatic a nd Dy na mi C E lec lrlltily Me Graw-HiII 1939 VlltGlV peu~6t(j]v dlOtpL13n tilt dlOOlttOP[fI 1968

Transient eddy current distribution in a cylindrical shell due to a current impulse BV E Klezl

lummarv

in the present paper we are considering the transient eddy current distribution in a cylindrical shell due to a current impumiddotise in a conductor located on the axis of the cylindrical shell The maximum calcu lated trans ient current density lor a given amplitude depends only upon the duration 01 the impulse The time in which the value of the curren t density decreases to one hundredth of its value at a given

instant is independen t of the time of the impuJse

Finally the maximum calculated value is les8 than that of the current density which has been calculated for the s teady state or the same a mplitude and of sinusoidal shape

The dis tribution or the current density depends upon the resistivity of the cond ucting material of the shell and the magnetic permeability which is assumed to be constant

bull Mecbanlcal-Electrl cal E ngIn eer Doctors degree of the Technical UnIversity o r Athens Gr adlLa t e o f Ma 1bem a t ic6 of Un [yersll y o f Tbell Balonllii EngIneer at lbe Publi c E lec tricIty En Lerprise

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middotIu~o~ 19694J4

cpopucfV t~(OU)OtV T orcoia npOampPXampTflt tIC t~V t~laroaEwv u )il Maxwell

1 Ir t)= a~lr I I (211)V Ie ill

EVen A Cr t) to ~flyv TlTlK6v amptUVUltJ1 IU tl KOV blJvu~u6v hi tOn 1gtt)(qIOU( A6yIgt tamp bcptG11ljJCv1lt (JUJJJJ lTpl~ fJ JJ) II11 OUVt~

ltJl6)aa TOO A ad amp(vcu I 1(016 t1)V otEu6uvcrtv ToD 6~OVtl( re Z rrfOl Aor t) = AIICrt) middot Z 6rc6tt 11 (211) (LJl~ tiVet flv IlO PltJlv

1 (r t) + I a (1 11 _ middot( 11 (112) cJ l~ r Dr if ( t

6 ui tTW )UO lV t fi~ Ot Qlpopucil t~I OtixrC(J~ ( 2l2) lJH10IjlOnOI E Ishyt (U ItQ apxll v 0 1J strtlt1gtT)Jl [t I O~to LnpIClCt H jlcwOXl1jIl shy

tlOIJt 1 ~ ltp6 toV Xpovov l (Juvnpt l1ol r t~ A(r l) eCJl~ 6u dVUl i CSlo(rl) ) Ao(r L) K (ltOItL v f(IUOU + (21 2) CljIPUVU TflY llopcpiroJ

d1 r I t [ r ltI _ I I (213)drZ r dr - K l

fcp 6crol oEx61-Ul Oa On 01(1 t =- 0 n A 1o) 0 5TlA(iSr 6[1 KUCU tTl v apxnv toO )0 101 f1 JtOK VO Tll~ porc T6)v OIVOP(1) shy~ILt(J)I htl TO C KpoundMtqIo~ d VClI jlT) 5e

H 01UltpOP1KT] U(OfOO l~ (213) ~ ~iOOOatC Il esse l Sci htl TtlV YEVUCT]V AoolV

eVaa KI - ~ Enclo rl oui r ~ 00 tl Olvoptl1OL Jje68~iI g

Ig 1(1 Sexojleuro9a on E = 0 Kat t) YeuroVIKr) AUm Jltjl6ltivct niv 1Opltp~V

9 (r l) = EKlkr) (214)

S o t TltnaOOjlEV va ~QaOoaOOJlE rllV Otaaopciy Eo npo to ntO futOAOYUOJiY to jlUYVTltlKOV lIlQVUO)IUttKOy OOYU)Il shyteOY A(p t) to n pOepx6 jlEVOV tc T1 ypaJl)l fc nit t 6 aootepI shyKOY t o) a)urpo~ T OOTO Elval bull

Adpl) = ~ (t) lnp ~

H J1IitoOln jlQt I~ItVTl w itp6 TO XpOVOY l (JUvapTl1CJ1C Tf~ A(pt) raToo 1St( dval PI(PS) gtA(pt) ~uI T6v (trohoyWl6 v cplps) clJWu fml vel Ku90plCJ9a n O1JvoptTlal~ let)

6poundX0JlpoundOa on i] JleuroClpo lt tih~ EVlUOeuroOO r I(t) na phJtcuut uno JI~a PIl9JJi)0lt (ax 2) 6n6[euro fl JlntaaxnuuncrJl EvTl aUVujltll shycne q(ps) yivnm

9 pS)=$ JI t

i-o l -- Inp (215)1

-1afco 6n r (1)wIPt11UlI J (rU llapl01Q tiJv IWKvOtfltll DoTi t6)1 5 l1oPPEUJj6TOl V t-n l f OC Kex0ql OOt H jlETOCT(T] IJfl ttOIlCVTI ilic 1t~ t Ov XpO vov cruvirPll(J~ tIllJtlr fI i(rS) gt J(r t) Sd 1PQ( JLav i5 m o pltf1V Eli crmCflv ttap-D j lO[av t il O (2 1)) pc YampV1 JorV Al)(JlV fix 1 (214) H AU(n~ aun1 aa poundIvui

i(I) = CK(k r (216)

610 tOv KaOOpLcrliO V tit~ (JWOcpOr Co llptTr L va )Il~ til[ 6VlV tTr ~ pom f1I~ olovoll t61v OlVOPPEUJJtlWV fi r f OY xampPOv tov poundv16( coO Kll~I) OOu Eov aeoopil cHIlUv en Ao(p U poundIval 16 jlaYl t lK6v SIQVI)OJJanlCOV ouva~mov t6 npospxo shyjLEVOV b e til OWVO Jlto [611 li IVOPPeUIl((1WV rote [0 jlalvlln~ KOV SIUVlJOj ottK6v OUVUjltKUV d T6 ecrooTEplKOV t Oa KE~~Ushyltpou sa poundtval AI _ Al - Aa il BUl [0lt jLpoundtaOXllIlOtlOPtW C OlVoptLiapoundlt ltPI = lJll - Po bull

r

1 L

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~f lOYLJtooyt crp6v t~ Aa(p t) npklVOIlpoundV to 6AoKAlpro~a

11 IIC

AOI PL )= l l r LJln Rmiddot rdrdl

z~ ~

le (P)= f l(rs) ln Hmiddotrdr dltgt

lnR - lnr - 1 (P ) ( COSIll9 middot cosm6 +n sinmO)D - - m~ middot m III r

6 oJna 1 ]9IPB) - L -k- kdka) - To klka) (2171[

TlIK~ ~ ~I (p S ) Oil elvol TO 6Bpo~a T~ (21S) Kat (217)

iJ- 1 raJna 1 19 (p) 2~ np ot I - k - k l kOI-k (ta ) (2 1 8)

Eav tCj)(lp~6(JoJul nv plav OlIlthi lITll ~E[a(u TfI (214) I(o i (218) O1iIl~I(m iJptJlj tf)v 6roiClY1) n jl middottf lJ avTlTlUlO adla tvul(JIW)t tPti n1i otaxmpunni1t t 1tlqK11Eioo el4 0 rdtJ)tamppu~6v toD KeAlJqOU SllAaoil Sui P Kam [lv tqNUtTO~ jl llvt lCTV ottOOuV(Jl V ftXEI nlv Ulrtlv nJII1 v tll toU iryory tOI) 1(~IJ q)(J u Im l lOG tcrtL)tEpncoCi lJovwtuoO ltpcxrihopl~o~Evfru OaOe p~ Eo (o CoO at 61toTal (JJolliotovmt 8m 1fie axshy

nwgto g1 ~ ~( TE~ltK~ ~ mJvrrptT)ltT i(r 8) 1pil~ETa 1 bull k krlI Ibj== -- (219)

2bullbull k (ka)

AI(l Tli v rClpur lV ttJ t auVUprt1oE~ Jfr t) tCflap~(~~uy bi til (19) t6 6)o~~pIJ t oO Fouri Imiddot 61lt6

y-+jOr

~1tj - shyIfmiddot (2110)

61Q niy 6joK)fl pwatl fftr (2110) Oe Po()JBV t ampv ~oo trtoshy~evooY cruvapopound6)v

I k(~8(8)=$ Koi g la) k (ka)

loUAlo~ 1969 TpoundXYIKO XPOYUCO 4]5

tae avnOtp6qJou~ a))twv f)t Ot

L-[gi)J= holt) Kal L- [g Is) J = hlt)

onon Kata to 9EOOPTlJlO tOO Borel J- [ g()middotgIS) 1 f= h(r)h ltr)dr (211 1)

o

L- [g() J = L- [ sIJ = 11~t

Kal y+Jeo

L- [g (5) J= 2 ~J Se k+ih-kc-r)~ ps = Sresidus k(k) -J ~

Kat On to 6epOIO~ t(bv O)oKA~rIKGlv lmo)oimov Ol(~ tOe ovrotepw cruvaptTOElI Bessel O(OEl

SreSidus=1- 2lJ6- ~(I~t J o(t2npr ) J (n po)

v9a llu O[ plCat tl1 (J)vapt1iOE~ Bessel J a Kol P = J Ton g

to o)odiJpro~a (2110) fXEI tiJv fKcppaOlv

J ( r t )

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Eav 1oopa 8ekriOro~EV va (mo)of(arolle v tTtV ~Etapo)ilv tflt olovollfle tiDv olVOppeUIJUtrov J(rt) 01Ct dav 1Jpoundtapo)]v t1e I(t) QVnotOlxoooav 1tpO~ )l(av peu~atffi8fOlv olapKeicu l

(OX 3) ed 1tpE1rEa nporlyou)ltvrolt )Icl Ei5pUgtJJpoundv tnv 1Jpoundtal3o)itv F(rt) fltll avtleJtOlxet npoe ~lav JJpoundtoJlo)ilv tPl c J(t) noplshyOta~EVl1v SuI tfJlt jkl91l1ooc toO ax 4 H yea autf )lpoundtopo)1l tflc F(rt) 96 hu tiKpl~Ggtc tflvaa)lilv ava)utlKnV bcppOOlV roc 1 (2 11 2raquo)I jJ6VI1V tTlv SIQqJOPclV Otl n OuvaptTlOlI 80 Xl] qJuOIKnV ftvvolav 0111 xpovov 1000v fI )leya)utepov toO t eV(J Stv 80 ()cplOtataL oHi xp6vov ~uepotfpov toO 1

H OtolaquopopO tiDv 060 bqgtpaOerov 86 000l] tflV )letal3o)nv t1c OlQVOIJflc t6)v 0IVOPP8U~Utrov tflv npOepXO)lEVI1V h t 1c peushy~atro80poundwc toO Ox 3 fltot

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z z Ape~qn~ bnOMr(lltJ)lO

61Q 16v apI8~fnt(ov lmo)0flO)l6v t1Jc ltapaOtaOErot (2113) typdCPTl EV rcp6YPltlIJIlO 01 flMKtPOVlKOV intO)OYlOtnv KOta lilv I(WOIKOTCOfOW ForLran toO onoico to ol6ypa~~a pofllt t~shyqmVICEtal eu to ox 5 0 6rcO)OflOjJ6lt SlaKOmElOl el~ euroKElshyvov tOV XpOvo Kata tOV 61t0ov 1l tl~n t1J~ ((rt) Ka8(0tOtOl to tv hatOOtOv t1e nfJfl~ 1tiv ono(av )aJ1PaVel 1l (rt) KatO tOV np6ltov XOOVlKOV Jlfl~ toO ()1tOAoYLOIl00

)llvlou jJt 6l01K1v oV1(OtOOIV g = 02810- 7 OM Kat )layvl1shytLICTl V OLa1tEpotOtftO )I = 4n middot 10-- n seem- i

Ele to Ox 6 nop[O1OtOl n )leto~o)fI t1J~ 1lOKVOtntOc pofc Olo )l(av pEU)lat(06fOlv oLapKdalt OOO J sec H OKttlt toO K(8)6shylaquopOUlt t)fcp8Tl J em A eiKovl~O~Ev(U tpEf~ IlStoj3olat dVtl

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Etc t6 err 8 Q1tpoundIKovltetQ 1 )1Etal3oAn tfc ItUKVOtTltOC poflt fila ppoundu-Wtdl9TlcW olaplCdw 0001 sec Kat Sui dJulpoC oKttvoC lOcm At 600 KQjl1CUMrt aVnatOl1ttoVtUI ftp6r to Ma laquo1tshyv~ r = 100 em Kat r = 105 em E~ t6 ax 9 tl1t8LlCovttat(t1 1JpoundlapoAr TflC mlKVOtrftOt poflc Sui QUiplCpoundlav PBu)JQt(f)9iJCJWlt 0005 sac Kat oui d)ucpolt nlCTvolt 10 em Avl$ 01 OlIO lCa)11tUMrl avtunolxltovtal ItP~ to avrodpm PMT)

E~ lSlac fit avrottpoo Jtepllttroae~ 6 ()ttoAo)La~61 heveto 05ui ppoundi)1JCl AvtaOpoundrot I = lOOA Kal Kattl XPovLKf Pfl)JQta O5msee

H 1tQPOUOlQO~Vn ell tJiv JtQpQ)PQcpov 21 ~tQSolTt tll OLQVolll1 tbv oWOPP8UIl(ltWV ttPOEKUjEV AK t11I aVQ)uCucflt )ooampWt rfll OlClqlOPLKfj~ A~LOroOuo l 6ttoia nept)pacppoundL tflv rtUKv6rlrQ POfl1 Cl()v OwoppWllarCOV ~vC6t roO tl)w-yi)Jou 1C8shy)UqlOUt AutTt KaO taul1lV fl 5~Qvo~Tt Iflt 1CUKv6ll1COI pofjl t~QPrdCQl tK lll Evduewt lOI) peU1JCllol C1t 1tl1)It poundK tll dSlK11 6vnCJlaOeoolt roO U)KOO Col) K8AOiJOOt lCat AK tfl~ )JQ)VlTIKIt 81a1[EpaCot1lCOt QUroO OewpOu~eVl1lt Otagepdlt H )JpoundlQ~Afl tflt lhavo)Jft poundIvaI tlVolorOt tlt leuroCPQ)WV~Kf~ plC111 Col) xp6vou ICat Av6t Rap6-yoVtolt 6 6Tto10~ t~QPtdCal EK clt OlvaplilOampWt Bessel Jo AveaptfJCrot rfit IhapKdat rfjlt peu)Jaroo9Jicrampmt l llelOlOll r)lt 1tUKv6l1rot POfl1 ellt r6 lv tCaroot6v l1t tl)Jft nv 61[oiav Aa)JS6veL afir1 elt ~va roPIO~VOV Xp6vov tl1[6 rflt 6vtlp~eoot rOO cpatVOlJevou Ttpashy))JQto1[olpoundhaL Elt C6v aUr6v xp6vov 6 61[otolt ov-nCrmXEl 1[EplTtou poundit 01 sec OU10llt l XP1cl)Jonoi1oLt 111Kpotepru il lapshyKdat ppoundu)Jar09flc~ clTtMJ)t l1eLOOvpoundl nv )JEyLCTI1V AjJcpavlshyo)Jhrlv TtuKv6L11CQ PO)I 1ampV oLvoppeujJlhoov KUl lXl t6v xp6shyvov tlTtOOPpoundCeOOI Qor(l)v Au~avojJEvou 100 p66oolt tvC6t Cou ICSA6qlOUlt jJE100tal fl ml1CV6111t pOflt tv~ fl I(U)mUAl1 )Juashy

r J

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Polfilt napouaui~poundL IlKPlfWat tlv autflv JJoplpilv 6gtlt lCa~ tilt tli lilla OtpooJJata H TtapOll(JlaCO~Vl1 JJpoundy[at11 1t)J(v6tl1t pOfilt elval TtCtvtffil )1tKpodpa tfll TtUKVorrpolt poflt fl 6Ttoia AJllpashyvKuQ Elt t6 116V1JlOV cpalv6J1poundvov JJ~ 1lJJtTovoeaofi JJEtaSOshyAflv tflt AvtaCewl J(L) tflt Rl1i fllt lhQV 1l ~vmol( ai1tIl euroxSl tTiv Q6tTtvlJpound)lcujv tlJl~V Kat TtFp(ooov 002 see[S] 0 xp6vo~ 6 6Ttotot a1tQltpoundhat 51a tJjv Jleloomv tft~ 1traquocv6tntolt pofl~ l1eshyXPLI v6t npol(aOroptol1poundVOU 1tooootOO poundlvQ 5uvat6v va ICa90shyplcro tov AvolajJeoov lPOVOV JlEta0 000 05laOOXIICclIV PEUI1Qshytoo9fOpoundoov dl0tE fl jIe)iOtl1 RUICV6t11lt poftt va I1fl ()nep~f JI[av TtapaSeuflv CllJfv

A 1100 Ant tOU KElUcpOtx wbm- AI jJ505 ampit t6 EcWteplK6v toO KeAUlpoult wbm- I

a ACOOtpoundP1Kr UKtllt KEAUCPOUlt m C otQgepo Am-middot E cta8epo wbm- l

J nUKv6t11t pOIlt Am-t

1 ~vtact~ p8u)JatOt -ypal1l1fllt A I CUv6Pt11CIt Bessel J OUV6ptrICLlt Bessel K OuvCtPtIlOLlt Bessel r JlBtpOV J(UAIVOPUC(l)V CUVtEtIlY)1EVWV (oICti~) m t Xp6volt sec an pU~at (JUvQPCioemlt J o 8 lplOJla KUAI5plJ((l)v CUVtEta)I1fVwv (ywvia) r ad

JlQ-YVl1tlKTt 0IanEpat6Cllt 0 secm- l

~ Jla)VltlKTt OlunEpat6tlllt oepoc n socm- l

g ElSllCfI avt[CraCIt om p Ilhpov ICUAIVOP1K(l)V auVtElQ-YJl~voov (aKttlt) m ~ optcJla KUAIOPIK(l)V OJVtECQ-YlJivoov ()wv[a) rad BJ1 OlVapt11Ol~ Jo 5ui at (Koo5tJ(01[0ncl~ Fortran) BDJI CUgttlPt11Ol~ Jo ilui U1

BJ2 cmvQptl1Ol~ Jo OICt a BDJ2 OJVtlPtl1Ott J o Oltl a FTI TtuKv6r11t poft J 0t6 a FTI TtuICv6C11~ po1~ J lila t ~ r FT ~uKv6c11~ pO~~ J (~~[CWOLlt 2113)

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01

5 He-rlilz 1 Erzeugung von Stato nl ren Magne tfeldern In elnem elcktrlsch lcllcnden MaterI aL ASE A Research 9 p 7 1966

I Cars law H Tuc()e) J Operatlonal Method s in APplied Ma shy 6 Paerson R Tbe FIeld Induced by E dd y - Current In a Scm-shythemati cs Dove r 1963 Intlnlte Solid ProceedJngs or tb e IRE p 88 January 1962

2 DerusPapin Kallmann COUlS de Ca lcul Operatlonnal EdlLion 7 Sabonnadere J Method es nUTTi tr lqu es d lllYerslon de la transshyAlbin Micbel 1963 fOITTlation de Laplace R evu e Genra l de I E lec tricite p 201

F6vrler 191)73 McLachlan N Bessel Funetlons (or Engineers Ox rord 196 1

8 K(ll~ E 1I1volln ampIVOpptUIUlTpoundOV ISle IUl)lv6pn6 JB)Ofllll )6YQl tt~ovshy4 Smlllhc N S tatic a nd Dy na mi C E lec lrlltily Me Graw-HiII 1939 VlltGlV peu~6t(j]v dlOtpL13n tilt dlOOlttOP[fI 1968

Transient eddy current distribution in a cylindrical shell due to a current impulse BV E Klezl

lummarv

in the present paper we are considering the transient eddy current distribution in a cylindrical shell due to a current impumiddotise in a conductor located on the axis of the cylindrical shell The maximum calcu lated trans ient current density lor a given amplitude depends only upon the duration 01 the impulse The time in which the value of the curren t density decreases to one hundredth of its value at a given

instant is independen t of the time of the impuJse

Finally the maximum calculated value is les8 than that of the current density which has been calculated for the s teady state or the same a mplitude and of sinusoidal shape

The dis tribution or the current density depends upon the resistivity of the cond ucting material of the shell and the magnetic permeability which is assumed to be constant

bull Mecbanlcal-Electrl cal E ngIn eer Doctors degree of the Technical UnIversity o r Athens Gr adlLa t e o f Ma 1bem a t ic6 of Un [yersll y o f Tbell Balonllii EngIneer at lbe Publi c E lec tricIty En Lerprise

loUAlo~ 1969 TpoundXYIKO XPOYUCO 4]5

tae avnOtp6qJou~ a))twv f)t Ot

L-[gi)J= holt) Kal L- [g Is) J = hlt)

onon Kata to 9EOOPTlJlO tOO Borel J- [ g()middotgIS) 1 f= h(r)h ltr)dr (211 1)

o

L- [g() J = L- [ sIJ = 11~t

Kal y+Jeo

L- [g (5) J= 2 ~J Se k+ih-kc-r)~ ps = Sresidus k(k) -J ~

Kat On to 6epOIO~ t(bv O)oKA~rIKGlv lmo)oimov Ol(~ tOe ovrotepw cruvaptTOElI Bessel O(OEl

SreSidus=1- 2lJ6- ~(I~t J o(t2npr ) J (n po)

v9a llu O[ plCat tl1 (J)vapt1iOE~ Bessel J a Kol P = J Ton g

to o)odiJpro~a (2110) fXEI tiJv fKcppaOlv

J ( r t )

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Eav 1oopa 8ekriOro~EV va (mo)of(arolle v tTtV ~Etapo)ilv tflt olovollfle tiDv olVOppeUIJUtrov J(rt) 01Ct dav 1Jpoundtapo)]v t1e I(t) QVnotOlxoooav 1tpO~ )l(av peu~atffi8fOlv olapKeicu l

(OX 3) ed 1tpE1rEa nporlyou)ltvrolt )Icl Ei5pUgtJJpoundv tnv 1Jpoundtal3o)itv F(rt) fltll avtleJtOlxet npoe ~lav JJpoundtoJlo)ilv tPl c J(t) noplshyOta~EVl1v SuI tfJlt jkl91l1ooc toO ax 4 H yea autf )lpoundtopo)1l tflc F(rt) 96 hu tiKpl~Ggtc tflvaa)lilv ava)utlKnV bcppOOlV roc 1 (2 11 2raquo)I jJ6VI1V tTlv SIQqJOPclV Otl n OuvaptTlOlI 80 Xl] qJuOIKnV ftvvolav 0111 xpovov 1000v fI )leya)utepov toO t eV(J Stv 80 ()cplOtataL oHi xp6vov ~uepotfpov toO 1

H OtolaquopopO tiDv 060 bqgtpaOerov 86 000l] tflV )letal3o)nv t1c OlQVOIJflc t6)v 0IVOPP8U~Utrov tflv npOepXO)lEVI1V h t 1c peushy~atro80poundwc toO Ox 3 fltot

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into tnv npotgt7t09poundOlV Ott 0 OeuroUtfpo~ opolt tvt6e t1lt 6YKU)I1e 6nOKt) CPUOlKflV tvvOlav )lOvov Ola t t tvcent oU1 r lt t otv 6qgt(Otatal 6note Kat oev fa)l~avetQt (m ~4IW KOtcl tOV 6noshy)degY1O)lo v

z z Ape~qn~ bnOMr(lltJ)lO

61Q 16v apI8~fnt(ov lmo)0flO)l6v t1Jc ltapaOtaOErot (2113) typdCPTl EV rcp6YPltlIJIlO 01 flMKtPOVlKOV intO)OYlOtnv KOta lilv I(WOIKOTCOfOW ForLran toO onoico to ol6ypa~~a pofllt t~shyqmVICEtal eu to ox 5 0 6rcO)OflOjJ6lt SlaKOmElOl el~ euroKElshyvov tOV XpOvo Kata tOV 61t0ov 1l tl~n t1J~ ((rt) Ka8(0tOtOl to tv hatOOtOv t1e nfJfl~ 1tiv ono(av )aJ1PaVel 1l (rt) KatO tOV np6ltov XOOVlKOV Jlfl~ toO ()1tOAoYLOIl00

)llvlou jJt 6l01K1v oV1(OtOOIV g = 02810- 7 OM Kat )layvl1shytLICTl V OLa1tEpotOtftO )I = 4n middot 10-- n seem- i

Ele to Ox 6 nop[O1OtOl n )leto~o)fI t1J~ 1lOKVOtntOc pofc Olo )l(av pEU)lat(06fOlv oLapKdalt OOO J sec H OKttlt toO K(8)6shylaquopOUlt t)fcp8Tl J em A eiKovl~O~Ev(U tpEf~ IlStoj3olat dVtl

Tllr)

I

~l6 IOUALO~ 1969

J

I

) J a U JO I MJ 0 ~ ItO

crTOIXiCOVTQ Kp6C tpla omrpopetllco pael TO) Ke)UIpOUt fltO~ np6i tfit petc OK(vac r = 10 em r = 15 em r = 20 em El~ to CX 7 napiOt(llQl 1 ~poundtaao~~ tfllt 1tuKvb111tOl poflc oul Illav PEUI-lQtro9110W 81apKela( 0005 sec Kat oui KUoqlOlt nilA1V alClrVO~ I em sv4 a[ tpEle )JpoundlQ6oMll avnato~xtCOvtQ np6c ttl abta ~a911 d)~ lCat TtpOTlYOU~v~

Etc t6 err 8 Q1tpoundIKovltetQ 1 )1Etal3oAn tfc ItUKVOtTltOC poflt fila ppoundu-Wtdl9TlcW olaplCdw 0001 sec Kat Sui dJulpoC oKttvoC lOcm At 600 KQjl1CUMrt aVnatOl1ttoVtUI ftp6r to Ma laquo1tshyv~ r = 100 em Kat r = 105 em E~ t6 ax 9 tl1t8LlCovttat(t1 1JpoundlapoAr TflC mlKVOtrftOt poflc Sui QUiplCpoundlav PBu)JQt(f)9iJCJWlt 0005 sac Kat oui d)ucpolt nlCTvolt 10 em Avl$ 01 OlIO lCa)11tUMrl avtunolxltovtal ItP~ to avrodpm PMT)

E~ lSlac fit avrottpoo Jtepllttroae~ 6 ()ttoAo)La~61 heveto 05ui ppoundi)1JCl AvtaOpoundrot I = lOOA Kal Kattl XPovLKf Pfl)JQta O5msee

H 1tQPOUOlQO~Vn ell tJiv JtQpQ)PQcpov 21 ~tQSolTt tll OLQVolll1 tbv oWOPP8UIl(ltWV ttPOEKUjEV AK t11I aVQ)uCucflt )ooampWt rfll OlClqlOPLKfj~ A~LOroOuo l 6ttoia nept)pacppoundL tflv rtUKv6rlrQ POfl1 Cl()v OwoppWllarCOV ~vC6t roO tl)w-yi)Jou 1C8shy)UqlOUt AutTt KaO taul1lV fl 5~Qvo~Tt Iflt 1CUKv6ll1COI pofjl t~QPrdCQl tK lll Evduewt lOI) peU1JCllol C1t 1tl1)It poundK tll dSlK11 6vnCJlaOeoolt roO U)KOO Col) K8AOiJOOt lCat AK tfl~ )JQ)VlTIKIt 81a1[EpaCot1lCOt QUroO OewpOu~eVl1lt Otagepdlt H )JpoundlQ~Afl tflt lhavo)Jft poundIvaI tlVolorOt tlt leuroCPQ)WV~Kf~ plC111 Col) xp6vou ICat Av6t Rap6-yoVtolt 6 6Tto10~ t~QPtdCal EK clt OlvaplilOampWt Bessel Jo AveaptfJCrot rfit IhapKdat rfjlt peu)Jaroo9Jicrampmt l llelOlOll r)lt 1tUKv6l1rot POfl1 ellt r6 lv tCaroot6v l1t tl)Jft nv 61[oiav Aa)JS6veL afir1 elt ~va roPIO~VOV Xp6vov tl1[6 rflt 6vtlp~eoot rOO cpatVOlJevou Ttpashy))JQto1[olpoundhaL Elt C6v aUr6v xp6vov 6 61[otolt ov-nCrmXEl 1[EplTtou poundit 01 sec OU10llt l XP1cl)Jonoi1oLt 111Kpotepru il lapshyKdat ppoundu)Jar09flc~ clTtMJ)t l1eLOOvpoundl nv )JEyLCTI1V AjJcpavlshyo)Jhrlv TtuKv6L11CQ PO)I 1ampV oLvoppeujJlhoov KUl lXl t6v xp6shyvov tlTtOOPpoundCeOOI Qor(l)v Au~avojJEvou 100 p66oolt tvC6t Cou ICSA6qlOUlt jJE100tal fl ml1CV6111t pOflt tv~ fl I(U)mUAl1 )Juashy

r J

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Polfilt napouaui~poundL IlKPlfWat tlv autflv JJoplpilv 6gtlt lCa~ tilt tli lilla OtpooJJata H TtapOll(JlaCO~Vl1 JJpoundy[at11 1t)J(v6tl1t pOfilt elval TtCtvtffil )1tKpodpa tfll TtUKVorrpolt poflt fl 6Ttoia AJllpashyvKuQ Elt t6 116V1JlOV cpalv6J1poundvov JJ~ 1lJJtTovoeaofi JJEtaSOshyAflv tflt AvtaCewl J(L) tflt Rl1i fllt lhQV 1l ~vmol( ai1tIl euroxSl tTiv Q6tTtvlJpound)lcujv tlJl~V Kat TtFp(ooov 002 see[S] 0 xp6vo~ 6 6Ttotot a1tQltpoundhat 51a tJjv Jleloomv tft~ 1traquocv6tntolt pofl~ l1eshyXPLI v6t npol(aOroptol1poundVOU 1tooootOO poundlvQ 5uvat6v va ICa90shyplcro tov AvolajJeoov lPOVOV JlEta0 000 05laOOXIICclIV PEUI1Qshytoo9fOpoundoov dl0tE fl jIe)iOtl1 RUICV6t11lt poftt va I1fl ()nep~f JI[av TtapaSeuflv CllJfv

A 1100 Ant tOU KElUcpOtx wbm- AI jJ505 ampit t6 EcWteplK6v toO KeAUlpoult wbm- I

a ACOOtpoundP1Kr UKtllt KEAUCPOUlt m C otQgepo Am-middot E cta8epo wbm- l

J nUKv6t11t pOIlt Am-t

1 ~vtact~ p8u)JatOt -ypal1l1fllt A I CUv6Pt11CIt Bessel J OUV6ptrICLlt Bessel K OuvCtPtIlOLlt Bessel r JlBtpOV J(UAIVOPUC(l)V CUVtEtIlY)1EVWV (oICti~) m t Xp6volt sec an pU~at (JUvQPCioemlt J o 8 lplOJla KUAI5plJ((l)v CUVtEta)I1fVwv (ywvia) r ad

JlQ-YVl1tlKTt 0IanEpat6Cllt 0 secm- l

~ Jla)VltlKTt OlunEpat6tlllt oepoc n socm- l

g ElSllCfI avt[CraCIt om p Ilhpov ICUAIVOP1K(l)V auVtElQ-YJl~voov (aKttlt) m ~ optcJla KUAIOPIK(l)V OJVtECQ-YlJivoov ()wv[a) rad BJ1 OlVapt11Ol~ Jo 5ui at (Koo5tJ(01[0ncl~ Fortran) BDJI CUgttlPt11Ol~ Jo ilui U1

BJ2 cmvQptl1Ol~ Jo OICt a BDJ2 OJVtlPtl1Ott J o Oltl a FTI TtuKv6r11t poft J 0t6 a FTI TtuICv6C11~ po1~ J lila t ~ r FT ~uKv6c11~ pO~~ J (~~[CWOLlt 2113)

~

Jlt-

SIUHU bullj- -- ~

01

5 He-rlilz 1 Erzeugung von Stato nl ren Magne tfeldern In elnem elcktrlsch lcllcnden MaterI aL ASE A Research 9 p 7 1966

I Cars law H Tuc()e) J Operatlonal Method s in APplied Ma shy 6 Paerson R Tbe FIeld Induced by E dd y - Current In a Scm-shythemati cs Dove r 1963 Intlnlte Solid ProceedJngs or tb e IRE p 88 January 1962

2 DerusPapin Kallmann COUlS de Ca lcul Operatlonnal EdlLion 7 Sabonnadere J Method es nUTTi tr lqu es d lllYerslon de la transshyAlbin Micbel 1963 fOITTlation de Laplace R evu e Genra l de I E lec tricite p 201

F6vrler 191)73 McLachlan N Bessel Funetlons (or Engineers Ox rord 196 1

8 K(ll~ E 1I1volln ampIVOpptUIUlTpoundOV ISle IUl)lv6pn6 JB)Ofllll )6YQl tt~ovshy4 Smlllhc N S tatic a nd Dy na mi C E lec lrlltily Me Graw-HiII 1939 VlltGlV peu~6t(j]v dlOtpL13n tilt dlOOlttOP[fI 1968

Transient eddy current distribution in a cylindrical shell due to a current impulse BV E Klezl

lummarv

in the present paper we are considering the transient eddy current distribution in a cylindrical shell due to a current impumiddotise in a conductor located on the axis of the cylindrical shell The maximum calcu lated trans ient current density lor a given amplitude depends only upon the duration 01 the impulse The time in which the value of the curren t density decreases to one hundredth of its value at a given

instant is independen t of the time of the impuJse

Finally the maximum calculated value is les8 than that of the current density which has been calculated for the s teady state or the same a mplitude and of sinusoidal shape

The dis tribution or the current density depends upon the resistivity of the cond ucting material of the shell and the magnetic permeability which is assumed to be constant

bull Mecbanlcal-Electrl cal E ngIn eer Doctors degree of the Technical UnIversity o r Athens Gr adlLa t e o f Ma 1bem a t ic6 of Un [yersll y o f Tbell Balonllii EngIneer at lbe Publi c E lec tricIty En Lerprise

I

~l6 IOUALO~ 1969

J

I

) J a U JO I MJ 0 ~ ItO

crTOIXiCOVTQ Kp6C tpla omrpopetllco pael TO) Ke)UIpOUt fltO~ np6i tfit petc OK(vac r = 10 em r = 15 em r = 20 em El~ to CX 7 napiOt(llQl 1 ~poundtaao~~ tfllt 1tuKvb111tOl poflc oul Illav PEUI-lQtro9110W 81apKela( 0005 sec Kat oui KUoqlOlt nilA1V alClrVO~ I em sv4 a[ tpEle )JpoundlQ6oMll avnato~xtCOvtQ np6c ttl abta ~a911 d)~ lCat TtpOTlYOU~v~

Etc t6 err 8 Q1tpoundIKovltetQ 1 )1Etal3oAn tfc ItUKVOtTltOC poflt fila ppoundu-Wtdl9TlcW olaplCdw 0001 sec Kat Sui dJulpoC oKttvoC lOcm At 600 KQjl1CUMrt aVnatOl1ttoVtUI ftp6r to Ma laquo1tshyv~ r = 100 em Kat r = 105 em E~ t6 ax 9 tl1t8LlCovttat(t1 1JpoundlapoAr TflC mlKVOtrftOt poflc Sui QUiplCpoundlav PBu)JQt(f)9iJCJWlt 0005 sac Kat oui d)ucpolt nlCTvolt 10 em Avl$ 01 OlIO lCa)11tUMrl avtunolxltovtal ItP~ to avrodpm PMT)

E~ lSlac fit avrottpoo Jtepllttroae~ 6 ()ttoAo)La~61 heveto 05ui ppoundi)1JCl AvtaOpoundrot I = lOOA Kal Kattl XPovLKf Pfl)JQta O5msee

H 1tQPOUOlQO~Vn ell tJiv JtQpQ)PQcpov 21 ~tQSolTt tll OLQVolll1 tbv oWOPP8UIl(ltWV ttPOEKUjEV AK t11I aVQ)uCucflt )ooampWt rfll OlClqlOPLKfj~ A~LOroOuo l 6ttoia nept)pacppoundL tflv rtUKv6rlrQ POfl1 Cl()v OwoppWllarCOV ~vC6t roO tl)w-yi)Jou 1C8shy)UqlOUt AutTt KaO taul1lV fl 5~Qvo~Tt Iflt 1CUKv6ll1COI pofjl t~QPrdCQl tK lll Evduewt lOI) peU1JCllol C1t 1tl1)It poundK tll dSlK11 6vnCJlaOeoolt roO U)KOO Col) K8AOiJOOt lCat AK tfl~ )JQ)VlTIKIt 81a1[EpaCot1lCOt QUroO OewpOu~eVl1lt Otagepdlt H )JpoundlQ~Afl tflt lhavo)Jft poundIvaI tlVolorOt tlt leuroCPQ)WV~Kf~ plC111 Col) xp6vou ICat Av6t Rap6-yoVtolt 6 6Tto10~ t~QPtdCal EK clt OlvaplilOampWt Bessel Jo AveaptfJCrot rfit IhapKdat rfjlt peu)Jaroo9Jicrampmt l llelOlOll r)lt 1tUKv6l1rot POfl1 ellt r6 lv tCaroot6v l1t tl)Jft nv 61[oiav Aa)JS6veL afir1 elt ~va roPIO~VOV Xp6vov tl1[6 rflt 6vtlp~eoot rOO cpatVOlJevou Ttpashy))JQto1[olpoundhaL Elt C6v aUr6v xp6vov 6 61[otolt ov-nCrmXEl 1[EplTtou poundit 01 sec OU10llt l XP1cl)Jonoi1oLt 111Kpotepru il lapshyKdat ppoundu)Jar09flc~ clTtMJ)t l1eLOOvpoundl nv )JEyLCTI1V AjJcpavlshyo)Jhrlv TtuKv6L11CQ PO)I 1ampV oLvoppeujJlhoov KUl lXl t6v xp6shyvov tlTtOOPpoundCeOOI Qor(l)v Au~avojJEvou 100 p66oolt tvC6t Cou ICSA6qlOUlt jJE100tal fl ml1CV6111t pOflt tv~ fl I(U)mUAl1 )Juashy

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5 He-rlilz 1 Erzeugung von Stato nl ren Magne tfeldern In elnem elcktrlsch lcllcnden MaterI aL ASE A Research 9 p 7 1966

I Cars law H Tuc()e) J Operatlonal Method s in APplied Ma shy 6 Paerson R Tbe FIeld Induced by E dd y - Current In a Scm-shythemati cs Dove r 1963 Intlnlte Solid ProceedJngs or tb e IRE p 88 January 1962

2 DerusPapin Kallmann COUlS de Ca lcul Operatlonnal EdlLion 7 Sabonnadere J Method es nUTTi tr lqu es d lllYerslon de la transshyAlbin Micbel 1963 fOITTlation de Laplace R evu e Genra l de I E lec tricite p 201

F6vrler 191)73 McLachlan N Bessel Funetlons (or Engineers Ox rord 196 1

8 K(ll~ E 1I1volln ampIVOpptUIUlTpoundOV ISle IUl)lv6pn6 JB)Ofllll )6YQl tt~ovshy4 Smlllhc N S tatic a nd Dy na mi C E lec lrlltily Me Graw-HiII 1939 VlltGlV peu~6t(j]v dlOtpL13n tilt dlOOlttOP[fI 1968

Transient eddy current distribution in a cylindrical shell due to a current impulse BV E Klezl

lummarv

in the present paper we are considering the transient eddy current distribution in a cylindrical shell due to a current impumiddotise in a conductor located on the axis of the cylindrical shell The maximum calcu lated trans ient current density lor a given amplitude depends only upon the duration 01 the impulse The time in which the value of the curren t density decreases to one hundredth of its value at a given

instant is independen t of the time of the impuJse

Finally the maximum calculated value is les8 than that of the current density which has been calculated for the s teady state or the same a mplitude and of sinusoidal shape

The dis tribution or the current density depends upon the resistivity of the cond ucting material of the shell and the magnetic permeability which is assumed to be constant

bull Mecbanlcal-Electrl cal E ngIn eer Doctors degree of the Technical UnIversity o r Athens Gr adlLa t e o f Ma 1bem a t ic6 of Un [yersll y o f Tbell Balonllii EngIneer at lbe Publi c E lec tricIty En Lerprise

01

5 He-rlilz 1 Erzeugung von Stato nl ren Magne tfeldern In elnem elcktrlsch lcllcnden MaterI aL ASE A Research 9 p 7 1966

I Cars law H Tuc()e) J Operatlonal Method s in APplied Ma shy 6 Paerson R Tbe FIeld Induced by E dd y - Current In a Scm-shythemati cs Dove r 1963 Intlnlte Solid ProceedJngs or tb e IRE p 88 January 1962

2 DerusPapin Kallmann COUlS de Ca lcul Operatlonnal EdlLion 7 Sabonnadere J Method es nUTTi tr lqu es d lllYerslon de la transshyAlbin Micbel 1963 fOITTlation de Laplace R evu e Genra l de I E lec tricite p 201

F6vrler 191)73 McLachlan N Bessel Funetlons (or Engineers Ox rord 196 1

8 K(ll~ E 1I1volln ampIVOpptUIUlTpoundOV ISle IUl)lv6pn6 JB)Ofllll )6YQl tt~ovshy4 Smlllhc N S tatic a nd Dy na mi C E lec lrlltily Me Graw-HiII 1939 VlltGlV peu~6t(j]v dlOtpL13n tilt dlOOlttOP[fI 1968

Transient eddy current distribution in a cylindrical shell due to a current impulse BV E Klezl

lummarv

in the present paper we are considering the transient eddy current distribution in a cylindrical shell due to a current impumiddotise in a conductor located on the axis of the cylindrical shell The maximum calcu lated trans ient current density lor a given amplitude depends only upon the duration 01 the impulse The time in which the value of the curren t density decreases to one hundredth of its value at a given

instant is independen t of the time of the impuJse

Finally the maximum calculated value is les8 than that of the current density which has been calculated for the s teady state or the same a mplitude and of sinusoidal shape

The dis tribution or the current density depends upon the resistivity of the cond ucting material of the shell and the magnetic permeability which is assumed to be constant

bull Mecbanlcal-Electrl cal E ngIn eer Doctors degree of the Technical UnIversity o r Athens Gr adlLa t e o f Ma 1bem a t ic6 of Un [yersll y o f Tbell Balonllii EngIneer at lbe Publi c E lec tricIty En Lerprise