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-~~~~~ wV AD—A 077 907 AIR FORCE GEOPHYSICS LAB HANSCOM AFB MA F/G 4/s
SPACECRAFT CHARGIN6 MODEL — TWO MAXWELLIAN APPROXIMATIOtI, (U)JUL 79 P TSIPOURAS • H B GARRETT
UNCLASSIFIED AFGL—T R—79—0153 NL I
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Spacecraft Charging Model— Two :~,
~~Maxwellian Approximation 1~
., ,. ~~~~~~
P. TSIPOURASH. 5. GARRETT, Capt, USAF
13 July 1979
App rov .d for public tub as.; d ist ribution unlimit.d 11
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SPACE PHYSICS DIVISION PROJECT 7661 A
AIR FORCE GEOPHYSICS LABORATORYHANSCOM AP5~ MASSACHUSETTS 01731
AIR FORCE SYSTEMS COMMAND, USAF
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1~V _ _ _ _ _ _ _ _ _ _
Qualified requestore may obtain add1tjon~ copies from the Defense V .i~~cumentaUon Center. All other. ehould apply to the NationalTechnic.1 Information Service,
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SEC uRITY C~. R S S OU , V R Y O N ) F V ~~~R .~~V WI • ~ ~~~~~~~~~~~~
REPORT DOCtJMENTAT(ON PAGE ~~EF(, coMFq ~Er~~ G FORM
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4 o I r I ..E ‘ Pd SObIIIl.) - 5 ‘‘ S ~~L P & N 7 A PtAIOO COVE RED
( SPACECRAFT CHARG ING MODEL — Scientific, interim.~~~~~~~~ TWO MAXWELLIA N APPROX IMATION , ~~~~ — ___________
~ r M N ~~ oq( REPORT NUMSE R
- ERP~~~. 667 ~~~~-
7. A UTN O R(. ) S C O N I A A C ~ U.? G R A N T I IUMBER. 0)
V p~ h’si po u ras jH. B. 1 Gar rett 4 Capt . USAF
• P E N . rORM~NG O R G A N IZ A T I O N NAME A N D ADDRESS - l o ~~~~uE,~T 0 U ~~~~0
- OW ‘:N17 N U M B E R S
Air Force Geophysics Laboratory (PHG) f i 2 lO l F JHanscom AFB . 7661)0803 ~~~~ ~~ I V
M assac hu setts 01731 ~~~~~~~~~ — -------- V
II~ CO NTRO LLING OFFICE NAME AND AD DRESS ~~ ~~~~~~~~~~~~~~~A ir Force Geop hysics Laboratory (PHG) ( I I 13 Ju~EZ~ 79~~ /Hanscom AFE .
— ‘s ~4 J y B E P rIR PAG ES
Massa chu setts 01731 28IA MONITORIN G A G E N C Y NAM E B AODR ES5(I I dIf I?r.,I I 1,0,, C0nI,OII.flA OtI i ~ .) IS SECURIT Y C L A S S . (of 101. •Pp0rI~
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Un classified11 O E C L A S S I F I C A T I O N D OW N G R A DI NG
SCHEDULE
IA OISTRI8UTIDN S T A T E M E N T (of 1111. R•000I)
Approved for public release; distribution unlimited.
Il. DIST R ISUT ION ST A T E M E N T (of 15 •b.tI.oI .fllA,.d In Blook 20. II dIfI.,nn I 1101,. R.pn.I)
~~1/I3. SIJPP LE MENTA RY NOTES
39 . KEY WORDS (CnnIfno. A~, 11,0.1?. .ld. If ,,.o. ....y W,d Id,.NIIfv by blook nombe.)
Spacec raft chargingGeosynchronous modelingCharge modeling
20 A R A CY (Cont?,~.. on ,.,..,.. old. II n.o....n aod Id.flhl?I ’ b~. bIo~ I, ,.oI,.bIl)
he ambient plasma environment at geosynchronous orbit is assumed to berepresented by a two-component Maxwell -Boltzmann particle distribution.Given this , the equations f or ambient electron and ion currents to the space-craft are easily integrated. Likewise, the secondary and backscattered cur-rents can be expressed as integrals. The potential at which the current sbalance gives the potential between the spacecraft and ambient plasma. Themodel Is compared with actual data from ATS-5 and is found to agree within
DD ~~~~~~~~~~ ~473 EDITION OF I NOV KS IS OBSOL ETE UnclassifiedSEC URITY C L A S S I F I C A Y I I . )N O~ T H I S P A G E (ISb.n Dot? Eflt.,.d)
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t ncla ss i lied /~t . ‘ N I T , Cs A S S I F I C A l ION OF Y H I S PA G t I t~I.., flSl~
30. Ah~ t ra ’t (Cont i~iued)
1 200 \ I V?’ r a range III (1 t I l —~~ 0, 000 V. ‘lilt’ listI d el 38 I’e~ ld I I v app it c ab t e t .t he s i t u p it’ I ’ T f \ I t I I ! f T ( f ( ’ ! f t ~~II I1 I I IdS’ l . 1 1 ( ; a r - t ’ e t t and I ) v I ’ u rv st ( 1 t I7~ I) and can be.~~I I t t f l :lt,’Il to aI S\’ gtven s a t c l l tt e . ~~Il1Ip ie al gISrIthIlIle t X IW t ’SSIII I IS are IISII
(leveltlped isIr t he bnck scat t e red and SI’ ’ I lola I v C Ur r e n t S IS 4 RSUCt k1I~ (II’
tS’ I1S l)t ’ I ’8t Ut’ (’ and 1) . l t t ’ j S t I I I St hit’tI 1)S(If l1 151 1 S I 4 ~1 S I fk ’ant dee I I I S I ’ I l l ( ‘ (Sil li lUtert i tus’ wt th l lu t .4 sIgnIficant 1,155 III II’ 1 S I ~~~I~~ V .
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F N T T B F * T )N OF I
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Preface I
This paper grew out of discussions wi th S. I . l)s’ Forest , E . C. Wh ipp le ,
• Rub in , and L. \V . Parke !. The d l ! a W I ’ r ’ E’ pro v ided h~’ 1( 5 !) (S . E. DeForest) .C. P . P ike provided t ’xt eus ly e vSwour agement .
• 1, ’ I
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_ _ _ _ _ _ _ — - - ‘ V I
_ _ _ _ _ _ _ _ _-- V -
Contents
1. INTRODUCTION 7
2 . GENERAL THEORY 8
3. ELECTRON AND ION INCIDENT CURHENT 10
4. SECONDARY EMISSION CURRENT 12
5. BACKSCATTERED ELECTRON CURRENT 18
6. TWO MAXWELLLAN MODEL 20
7. DATA ANALYSIS “2
8. STATISTICAL ANALYSIS 25
9. CONCLUSION 27
REFERENCES 28
Il lustr at ions
Ia. Num ber Flux of Electrons (SE) in Units of n/cm 2 -sec-sr as aFunction of Maxwell-Boltzmann Temperature (TE) forVarious ‘~alues of Satellite Potential (b). N E is assumed tob e l c m 11
5 _ -
S
pItIGWU~~ ~~~~~ ~iL.AL~~ -
I
I l l u s t r a t i o n s
Ii ’ . \ w~~i . - r I ] s~ of (.1 1 ) t i u t - ~ I l l fi 1 1 1 1 5 1 1 - 5 I ’ I S 1 I I U I I t f i - T I
I t “ l i x ’s I — J I l l l O l l I ‘ l (‘ ‘ I t I I I V t 1 1 1 V I T ’ l ~ (IT V IS IS-s( I f ~~.l T , 1 i It I I’ - ’ t e i i t t t l ( Q ) • ‘\ ] 5 5 • I S T l ! ’ I I’ I! t I l I’ t ’ 1 ~ ~~~~
1 11
2 . l’1 t of i t ’ I ’ . ’ s I V ! 1 t ~~ I I 1 I V ( I f I - h - I t ‘ ‘ U I T . l I lt U l ’ ! I I d as 5~~T T I I I I I V I I 5 Duet I l L I 1 1 t l ’ - f l I i t I I - r l ” I . - l l t ( V ) IS 11 ( U I I T I I tI I I ] I .1I I l 14
,3~ h I ll III I I I I I t a r ’ - L iec t - t i \ ( f l i I ’ I I lox 1) 111 ’ ~~~- II’ I l l
:i !‘ IIfi lI’l t 1, 1 , 1 ~~ A a~ H. i t I I . , ‘ . a \S , d l V r I x It
~-.‘, ‘ :. II - 1 j 1, ] \ ‘ . i - sus t I , ] f . ~~ i t O ,’ ( I
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4 . I i ( I~
t ] ( I I , , _ 1 t _ I 1 4 I V Ill I II’ t , t l S ] I I- t l ’ T I I - Ii IS S I’ 5 li -u’sI I , - - I I 11 fl hi I t t i lUll i - ~ ) i S 1 I I I I ’ I II ‘ I I - T I / I S
- . R I I I I . -~ ~~I n - ! I ’ \ I l ( s t ! I l \ / l l’ r l ’ 1u~ D i - ‘ I I ; V ,. , ] , I t V I i_
t I r\ :d I I I I’ IOn \ t i i ’ I t I ’ I’ I lux i ~~I I ‘ ( I I I’ 1 ] ] \ I
II ‘ , It f l I’ I - / I t ’ V i I’ 0 515 P t ( V It I I IS
h i t 15 o t Ir~ -.~~- ‘ . 1 ‘ I, - : ’ I- I I- , lIU t I I \ I 1 1 ’ i i -, ’r I lox l)ue to 11,~H, t ’ : i t ’ . ! . ’ , a ~ 2 J ] ) I. . :\ ‘ a t ’ 1 1 1t J V ’ ] I I ’ t ’ , , T \ l l a: } I I J i nx i t
t i ’ 1 ,5 \ ‘ I- ’ T.US l ’ f l I’ I ’ I f t I ’ (i’~ . 1 I V I I i - u s ‘ ‘ ( s -n t i~~ I~~
7 . I .~~ . 0 , l V I ’SUS I i - ’ I I ’ ! I’ t , ’ n t l l lS f ( I ’ ,‘\ 15 1 12 \ r S — l I ‘ I t ’
TI t ’ ’ ’ -~ ’ V-’, ’ ’ I - -. i I l i i _ i ’ ’ ’ — . t ’ Iii. - ,‘\ - I ’ i , - t I I , l l \ I I ’ I I t i i t i I l l T — SnnI t - —
C - i i t l ’ a ~~, I I i 1 ]l~~I & , l I It l , ’ I l S , . 1111] t i , - .‘\ - ‘ I - l ’ ,~~~, ’ I I I T t ’ I ‘,s~~’I t ’ i t l S
•4
Table
1. St l t l S t l Il :\ T I I l V S I S ut A i ’5— ~ null s 1’h- ’ l ’ I l u ] I S e I) . t t :~ 23
V V - — - —- V ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ t_ . _
~~~~~~~~~~~~~~~~~~~~~~~~ ~~- ‘-,- -
~~~~~~~~ ‘ V - V -‘
Spacec raft Charg ing Mode l—Two Maxwe llian A pprox imat on
I. I ‘~‘I RO1 )L ( : I I ( ) ‘I.
1 2 .In ( 2 1 5- c e t t 1 111 G a r r et t and Do Forest , it s as don s 1St ra te .1 that the plasma
It ~~I - s y n c h : 1 - IflV S o r b i t 5 5 - u -s t - r t , ’r representable I~v expans ions t n t e r nss of
\ t~~x - u e l l i an I s t i ’ i I ’ u t 1 - 1 5 . 151 J l i I tt ICUIi t t ’ , a ( 1 1 - 5 5 r ip t to n in t e rf l l S of t h e sum of t w o
~1 ax -s c h u m I’ o n ,b l I ,l ( nt IS I S 1 1 1 1 111 1 - - adoquat clv represent the plasma Sn about
35/ lo t - cen t ill t he S ’ I S I S s t u u I L l ’ c I . In G ar r e t t , a simp le spacecraf t charging code
l ’ass ~ I ,~r1 t 1~e’ .s 1’rk It W h ip p l e 4 :lf l ’I Do I i i a - s t w a s developed wh i c h made use of
t i c si r e te u : i r ( i c l ’ ne lsu r~~ t - u ~~:u t S r e t t s rne d l,\ t h e A I S — a geosynchronous s a t e l —
I I - in I h I I I l’ l,t~~ u a:1l~ t’ ~O o \‘ ‘ - I ~ (l keV . Vrl le m odel ~u 1teu’euI , however , from
being unable to t rent ac c u r a t ely ~$ a x w e I I ian components except in a n a r r f n’ range
ot 1 ’ , tmt nH and I l’ t I p e rat ur e s f i l l s ’ to the ns’et,~ss i t v of t a k i n g dssc re te energy steps
II p Uhl I ( . l t O It / 12 JnI~ 197th
1. Gar ret t , I I . B. ( 1 17 7 ) Modeimg of the Geosvnchr t ’nous Orb it Plasma Envi ro n—.“ t — l ’ ar l i , A 1”GI V - F l l — 7 7 — 0 2 8 8 , AD A05:3 164.
2. t ; a r t - I ’t t , H. II . and ] ) c I ’o r e s t , S . F, ( l979b) An ana lyt i ca l s imu la t ion of thei~i’ i svn ch l on Ilus plasma e nv ir o n m e n t , to appear in Planet. Spa~ e Sci.
: . Ga rr e t t , 11. Fl . (1978) Sp a c e cr a f t Po t en t i a l Calcula tIons — A Model, A F GL -T R - 7 8 - O l l ( i , A F Surveys irs Geop1~~~Tcs , No. ~387 , AD A060 151.
4. Wh ip~~le , F . C (1 l~~~~) hlst FqUIliI1NUIS’I ±~~~~~~~~i~V~~ j ’o t e n t i a l o f a f l o d in t he
I JIpe r A t m o s p here , N A I A N — t ~l 5 — 6 5 — 2 9 6 .
5. DeL rest , S. F . ( 11 1721 Spa i ct r a f t c h a r g i n g at svnch - oni ’us orbit , 3. Geo.~~~~~lies. 27 : 1I~,l.
7
.1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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I ‘‘‘. ‘ ‘~~‘ - - 1 1 1 1 1 - u I 1 t • ‘ i p I ’ t , I t ~~~~~~~ I 21 ) kl’\’ Is oh I l i - ru 1 1 / 1 1 1 1 1 . 1 1 ! 49 , S I l O ) 5111 11
St ’ I lS I t I _ ! l I _ % l’ u ’ ~ T I - I t ’ t , — , - I~~, ’ I 5 l 1 , l l h t n!I I i ’ V _ I , It i : - i ’ ch it h u t ‘ I i . ’ - r u i ’ ,
5 - i u u t ‘ 1 ‘ . - such lI’ I lfII ’ t u n 5 1 1 5 I I’ I I I ’ ? ’ \ - - l i i Due I I- I I I I I( ’It I O I n l I h i i t I I I I I s - I I l is’ IUl ’ , lt T —
a s th I I M:~’~-. s ( ’ I I i u t n I i - - : i- i t - n t 100 I I f ln ’ t n I l .
In ‘H- hi .1 i t i f 1 1 1 1 , r I ’p 1- I ’t s t st ill 1 I ’ S I V t i i . ’ t ’ f l u i , l l I , I t t n - I n I I ’ Y l~ h- - l I T - I III
,- \ s oat h 1. - r u t is l IT Ius ~~~l - . ] 1 110 n - n - , - t - - - r \ it poo l ‘,v s l I I - - , l t ’ y . - l
~~ u - t the ~cs ults n I l II T i r I ) I I I V \ 1 . t \ ,s r l l I a u Ir I T I T I t I V I I I I 1 0 0 1 1- l I T t , -n - l a t u t l > 11 111 4
t i - t e r u t u a l ~~. h i t ’ t issu i l ~ l ’ n i I n n ! l s i l l 01 511 ’ S Il u. I l - t i t u l T I t o tss - \ I , I\ , \ ~~0 ,,II flh lII ’i
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r’ rs~~lt s lil l u n i t . ’ VS t l t l Ilil l 1 • y t i O 11111 n t t l , 21 ))) \‘ / I t 1 1 1 1 1 t ’ i ’ ~~~l ’ 5 0 S i l lS ilinI • 0 , V~~~ l \
- V I ’ t ’ the ‘ 151 p t — : Ut) V to — 19, (1(1 / I V , it lal ( ‘ O I C I I e l I I 5 ut ppl It IllIl It \ - n t V n - - h - i
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t n n ! ’ p l a s t t u ~i t I ’ u l u I l k ’ r u I t u l t I - ~ l Och h a r i~~- t t ho u i l l _ i t - 1 ( 2 I 0 I ”t ,
2. ; E \ F R U. TIIFo R ~
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r o - t o r u t t al until ~- - s uu l tbr iumss IS o .tn -hC,t . In t h u s T o u I~ iS I ~ ill I- n ’iIs i hr n n 1 l \ the .1 —
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sI - I I T I I I I I X - \ ~‘ni l t t t ’II ,- h , ’ n ’t n i l cu i ’m - s ’nt due to
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c t t l ’ I’ , ’’lI I.~~ Ill . I -r Ii ~~~~ - . t l t t j i m l n t l l t I 1lI\ t i l l ‘V I I I C h s t l - - I i l l :
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II I 5 0 1 1 1 1 ’ , , I / i t lS~ S S I I S S L I l T S ( l l t , l ’ I ? - 1 1 I , P V 1: 11 , 11 1 t I t i l O i! li t’ StI! _
t O 1 I’ I I /1 , 1 1 1 .11 ‘ I ’ t , t N 15 m c I I I ’ - ! ‘ - n Its- ,i ‘ 1011 l us h i ’ ’ l Ilt ~~ 11 I t - n I loll t • - - I II
V n x i s , l l X III (I ‘1 t I - u ’ I n I l l ,
1 1 - n u ~~ F I J V I / u )
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\ t il ’ - - . \ i ln I I - t I~~- I I ’ . i - i - u ’ , ‘l it S l l I ’ I t I l t i lt I~~ h tt ’ l ’ I’ n 3 n Ii) i I I I is t o - l u i - t i d e- i t t - _ I l l ’ IS’ ’ ’ ’ , Ill is l10li’II l.ii ’ n:l T’ t i t , n ’l lit , 5~~~I n I n r O t / t \ p l n ’ . I ] S , i ! l l l ’ T— 11 1 1 • ‘
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II ’ I t ! .es s ’ ot t u ’ i t t - I l t l l a l W m l t I t T ’ n I X ’ t i l l S V I I ’ i l l t I l 5i~ t i - it I , ~_~ i is.1 ~~n I n II! lJ l t I l’ o \ i i t l i I t 1 - 0 1 ,~~~\ t In n . 5 1 1 ’ l i t t t m i c- - / l I , l l t l n ’ l I] l l ’ iy in t i l l u h I S t t i 5 ] h l t ’ t t l t i l l s
It 1011 l’ l ,- ,IkS 1 5 15 n il the -! , - t t i l , - 11 p ’ , - ut ’t -s III’ the ’ 5 t t l ’lliIc and I ts s t t , - . t t l u t u st
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1. , n n l ~~~!’t ’ tt ~ II. II , I O n I Di’ n O t ’ nt S . l - ~, ( l I I 7 t 1 .t l l’ l 1lt~ — \ ’ ) l \ I I l p IllI, - h I ’ l, ’n l l ’n nl m l’III\.‘ ha- t ~~ I I I s;I V I s ’ e ’ e r a t t I ’ t , t l I 101 ,tt ~ t ’n’5 \ I iS ’ I t l O t l n tl5 n l ’ i I t t .3 . I,l n l i n i t ’n s . ~~~~I I 23 ~~V h 1 i i 1 .
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I I . I~~t !I V I t V , i t \ tV , ] , t t e t l S III
F 1. i ’ I t ’ i D n ’ T I l I s t 0 l i ’ ,I ’ I l t ’I’ in C \
~ 50 ‘ ,‘Il ut 1- n t l i t in) (t n units ot ’ ,V\ ’ i
1 l’ill’l’~~V of l’lI’dt 1 0115 Ill C\
K 1. I~ 12 , \ 19 ’’ Hr ~ I I I t l n ’ f l l S5 ’c — S r .
I l u r - - t u p l u n - u t . S c ill ’ I s It i d t I l l ’ nlItnI- l’r ‘ lux lIt t In I ’ l l l l Ot I S t ’S ’T l tilsIliglI i l_ C r - s t c l
i t as ‘~~~~ ‘ cu i- r , -nt — t h e t u s - a i’e I’ l lt l I l lis I’ - . 12’ . $ilsn’ l i t , - units 0 n dlsllI ’al’ 13
ssi l l be ll1I’ , n l I O l l ’ l!l’II ill ~5 5 n ii,9 s~ t s in (he 0:115 l’i c\ ’ l O u Is - f l 111511 \‘ it It , 5I~~fl
It ‘ I l l ’ c l iarpc s i l l Il l l’\t ’ II,’O in l ’ u n ’ i t t ’q l I l t ln I Tl / . I I. and I~ l It ’ I si S l It I l l il I t I
I t l n l(IIIS’ K, t !ut ’ Bo lt /nlui:irl n ’ ‘ ‘5 ~it I t t t ,
10
L - - .~~ V , - -
~~~~~~~~~~
—
F I ‘ ‘ -, ~. ‘-~ ‘Ml’i R FL ‘
— c -I .
~V
—-
‘ - ‘1
— I ’
~~n - l O OI
,
~~ ‘~~~~
2 4 b 8 0 4 l b Id
1 i p t i i e I a . \ t l l l I l l ( ’ r l-’lux of EI, c t l n I t I S ( j~~~
) in I f l I t s n t T I c flh — 5e ( - — s r as a I-un - —lIon (~f Maxa- ,’ l l- l / l t , ’: :- , I l u rm I l ’ t : t t l I ’ n - , itu l - ,-
~“ l - ~ for \‘Z l l ’ l n n ( I S \‘ n lii ~ ’~ n t 5 1 1 1 1 1 0 1
l l , 1 , l l t i . il ) ç’l) . IS assunled io h1 ’ 1 i ’Ill ’
‘9 ’ t~ N- 51 95 I -
- -
- 4 - - r
1 n - I000n3—
— ‘
- 1 - - iC ,9~_~ V5~ i
-4- -4 5 8 Itt 2 4 tI IS 2011 Cke ~
Figur e lb . Number F lux of Ions (J 1~ in Uni t s of n cm~ — s e c — S r as a l”un c ti on ofM a x w e l l — I l - I t / r I t a r n u T e m p e r a t u r e (T~~ for Various \‘I l l l l s ’ s of Sate l l i te P o ten t i a lt ,~) . N1 is assumed to he I cns 3
11
- I - ~~— —-
~ -- -
-~~~~~~~~~
-‘I
1~iX t I i l I l I - 1 \ , for t I l l 10155 ( I i55i I l i IC(l ‘ ci i - i - ps’ I n o t
l , n t ’ Q . II X —0 , i i I l I I l ’ i’ IllI n
~ l K1N 1
V I1
- ( I - ~~
/ 7 1 , 1
1 - r 0 0, x 0~ im3li vlng:
.~
—t n
,1~ k 1 \~~I 1 C (7h)
‘.1 I i t ’ m ’
N - I l t I lt i l i l ’ r U’ ‘IIS it V Ill I ntiS Iti Ii - ( X II
T -‘ I fl t s ’ t i l p e t ’ a t i l Z ’ e in ‘ ‘V
K1 1. 2 - 3 i 7 ‘~ 10 or lfl n f c l l h
2- s t - I ~ 5 I .
d
F x p r ’ - s s i - - l h . s lU and / 7 ~ are 1li,tt 1-d in Figul’c 1. ~~s we shall see , tI i , -v i l l I I I
t l t l V I i n l i l ’flt ,Ii importance in IOI I I IV spacect’aft charping 1I IIllicIIt t lnf i S and cams Ill’
i’a~~iIv app lied Ill ‘a lculate t i ii c ur r e n t t I n t i 0 sate l l ite T Iu ic Ill t i ll’ l I t I ll l lC t l t environ—
It i l ’ f l t ‘i n ! ’ a nI:tstna l- I I n l s u s t i lbg III 1151- lIr I l Ol i e - nt t l 3 l I I l l C l I t S . A-S an I -x ll rnple, f o r the
,n5 1 lIf ~ / - , i in -\ I1 iX i’ .C i ij l i l l d is t r i bu t iu l l (Ii i ’ I c ( IYu l t ) S and a negative potential:
1/ ” ~ ‘P11 - t~~’ ~~ ‘I’’F
~ I: N1. (N I N I ~, ‘ N2 I-: . T2 N (- 1 (8)
‘5 u s’ I I -
N h l - nun lbe s ’ - h ’ l I t i ~t ’.- 1 1 - 0 1 - I t - 1 - t run consponerit 1
~‘F’ 1 F ‘ I ( ‘t l l }I l r O t S h I I for 1 1 I ’c I X I I I ( - ( Impone nt I
N 2 N nunibe r iIen~ it V in I r I - i l - u t lOIn comli ponemI t 2
T2 1- — I - t u s p s - ra t u re for ( ‘ l i l t ron clll l lpon(’nt 2
Similar S- q u Ilt m - -~~ s fo llow r nr conibinat ions nt , -1 , II I’ III ~ l1l’ r 51,1111 5 Ill’ Maxws- i l ian
components.
I. ~F ( ( I’ . I ) -~R ‘~ I’ \II~~ l( )\ Ct it RI - ‘I I
~~r - u - I I n d a r v emission is t he rosult cu e le( ’t i’ r lns beIng e jected from C O s a t e l l i t e -
V
S U rt l l - l due to impinging electrons and 11115 5 ( i l -n uiOcollII l I Ill S 11 I C III ni important) .
The seco ndary eulsiss ion cul’reflt is g Iv i l i by i I - c t l le ns be r , ,l~~~ and .i ,~ are in u n i t s
of n, cr11
12
:a: ~::~~~a. - - - — , ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- - V -- V~~~~~~~~~~~~ -~~~~
I
/•
~~~~ ‘Ii 1~~ F - I I 1 1 11
Ill , t t u , ’. i- , t l !,iI I H in l I n u X y i l I If al pI , \ t O i I V t I ill I l u t ’ eh’n t 1 - ‘Il - - I ’
5 1 1 19 ~.it _ l
- , - t l - ,~
- i m l 9 ‘ I’
-~ I V I II i’ - i I — I t ‘- t iOt
It ‘i -
55 1 ‘~~- :
~1 ~ ~l _ ii
Ii 0 i i ~ -~
I ’ i . \ 2 . H l ’ ’9. I
t i l l I ii’ t I l Imi It l I l’ r 9 , S I I I - t ’ l’l’li 3 I I n I I I C V I I II 1 l 9 i 1 1 1 ,‘ . It 5 ,10 l ’ I ’V n I~~~l ’fl t o II,-
ill n I 0 . C , i ,n ’ l , l ’ 1 , 1 1 1 It it l i Fin t I l n ’ l l I l n I , i t I O1I0 ’ t I n - Il s n c l i t l , ’ r t i n II 1114 li l l) %I ln ’ I t u I 1 t III
9111 011111’ O l ’ I l ’ I O i i i \\ 1 1010, ’ ,
I n Il I - I - n ’ n ’ t l ’ ~ ~l I l - I 9 . I 1 I - ,. - I t 1 I~~n 0 - I n I - I I :
- / I’ i .( l . ’l 1 1 1 1 ’ Ii’
51
. 1 ‘S I ’ ~~ 1 F ~~~~~~~~~~~ II
V I n i: ~- ‘ ‘1
C / C 1 1 , 1 9 1 1 I ’ i t
I ~
i l l~
t Ill ’ l i l n I l l I f l i n I l t I c1 I I1 i i , It I n I ’ ~~~~~~~~~~~~~~~ I l I I I SI i cu i l l s , I’ 111151 , 11, 101 ’S l ’i ’ . Ill -
t t ’ 9 l I I ~~t ’n l It I I t i l t l C l I c , I i I \ 111111 9 Ill, ’ ( IIIt II1 I 11 11 1 1 I C . I l I i n i I l lt i l i l i o l I1l I l I I I ’. l ’l i i ’
I 1 ’ - i i I lli 11 0 0 1 0 1 . I ’ l l I,’ ~~~~~ ~~~ n i t ’ ) , I , It Il ’ n l Iii 1 19 1 1 1 1 ’ I~ 9 III d i l ’, l l l l ’ nliii f t t u -
It n t O I l t i l l t . 1 1 1 1 0 all -Il Il ( I I , I I It I i \ , lii - \ ‘ - l i - 1 0 1 e ’\ lil t
(I . — l i i h ’ \ t
~ :t
-- - -- - - - - ~~~~~~~~~~~~~~~~ - - _ _ _- - ~~~~~~~‘ -~~~ -- -
~~~~~~~~--
~~ - ~~~~~~ - V-~~~~~~~~ ~~~~~
I
0~~’ -I A I OMI NI J M ’I
~t— m•ostjrp d55
fst$ d551 0~ O -
z
~~ 04 ’ -
ii‘1,2’~~l 0.~’ -it~
000 In 1 1 ~~~~~ Ni4
l0~’l 0 0’ l0~ lO~ Il~~
’ I n 5~
PRIMARY ENERG Y .11
i- li re 2 . I ‘lol III’ I lie l O I n , 1 1 1 1 1 ~t nI I i l ’n ’t 1 011 1 Ret iliii,’t I V II’ n~~~~ n 1 1 , 1 , 1 1 i t i I l ime I n
i i 1 , t i n l il fl,I 1I1I1 II1 ’ l i I i l , ’llt ( I l l . l is ut 1 11111 1 1 1 1 1 1 ,‘f I- ’ iit - i - ~’s
0 8 4 ,
0 7 4
063
0 32 -
0 2 1 -
0 I I ~ -
000l~ 2 4 6 8 lb 2 4 9 I~ 20T E (kaV l
l- ’ iptmi” :4 . IFt I i l l III 5,’n - l l u Il:tI’\ 1-11 , 1 01 111 NiI l i i I ’ l ’ l’ 1 ‘ I I I \l)tie I,~ I-II ,n-t 1 111 130111110 i’diiie~~l I.l~q:) I~ A ms ibce i i l I ’ i t ~n -
h Ill \iiillll,’i- 1 - I I I X i t t—~i i i ’1ac , ’ 5, ?
~~~ \‘ l’i’ t- i i l t f l’l’ I 1 1 3 1 1 ’l ’ llh i l i l’
~~~ ~, 1 f ist ’ V i 1 1 1 1 1 1 0 I’i’I t ” i i t i a Is
14
-- ~~~~~~--V
~~~ •~ l-: 1~~i-:’ ~ ~~ ‘ i-:~
( 12 )
st here
t- 0-0. 021451 ’
~( I ’i~
) < 0.114:1 - 0. H42 c N ‘l’~ - 20(1 c V ~ 0-
1 -0 . 0003’I’ . -
L 0. 143 s 0. 740 e 1 ‘I’~ . ‘ 200 - \ ‘ ~
0
.-\ l tht ’ugh s t - i ’ h ave mit , t ( I S C I I tlii~ s ’ x p ! ’ l ’ s s ic ln in t I l t ’ mns ,ds ’ l l~~t ’ 5 i ’ ml t t ’ l hel l - , the
90 111 Iii so l l iputa t 11111 tO i l s’ i r I n t O t h is la t te r t ’x prs ’s s Ioml shi i nis ld nutsv s’igh Iili\ I lIsS III
in -cu l ’ Ic\ A s , lu n .~ l - v s ’ i~~ Wi ’ 11051’ sill ig Ilt ict -ul icy in this stuck ’ , IVC hive in ,-s ’ s- r - 4case in tegrated 1 : 1 4 . (1 1) ~~~ t l i I lIc it Cl i .
‘I’liO t ’ X p S ’ e s s i n n l l l n n l the SeCor i I I i i v 1 551155 iIIli ( I f s ’ l l ’ l t l’l,fl5 X liii’ t n n h I l l S W I t S
t~iks’ri to Ill’:
K2 , — c I ( t - : v ’~ - 0 N -‘ LI
= ~ K 1 c1t - 0 13 ‘ h- I ( 1~~t
0 Q V ~~~Q
st l it ’ c e
K 1 0. O1III , K~ - )
~ 1060 , \~ :100 , - 700
‘rhi s is plotted in Iii~=um’ t’ 1 over II plot Ill ts1(E) for alumsli l luSIS taken ii’uI I l
Whi pple . As t h e dev ia t ion 011, 51’ 100 kt ’\’ is signi fC’ant , sre have hi iii it (- (I our
iiiitdel to ~0 keV (we ll above t lie L- s’ 9 i on of nat ui’all\ i 1C cur ring chai’gi 119 phl&’Sloii lt’Illi ),
$ ( 1 the dev ia t i l l l l IS not of 1 of l cel ’ n in our s ’ali’ulat 10155.
In s e r t i n g Eq. ( 1 :1) in to N u t . (9 ) ss s’ i’ i mi d , t o t ’ ç~ — - 0:
~~~ ~~ ,f 6 1( E)?~(I-: ) l- : dl-: —4-
~4 - e’~~
F1 •
[K 1 ~~
1- dE I K~ J . e~~ ~~~~~ N ill .:] (14 )
w her’e h i1
is t h e mass o f t he ions.
- V 15
0 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ —
07Cor is ni ~l ill
1.1 Ghos h and I’O,ave
01 ,~ 1~ I t t Sl Ot\ Gilosh and KhIl Id
~ A ats e i ~I 01
0 01 II I I I I L. 11 III I - L L n I n , Is I IIl’s l0~ ll/~ IO~
PRIMARY ENERGY (,Vt
I fl, I l l l ’ 4 . t ’ I -~ ~~ tIn’ l’~’ r ’ c ’1l t : ip t ~ i’ i FIt’ s t l ’ IlIiS lleturmieil utsSn ’,, n l l n l i i ’ i , s I~ti t ’ In , loll ItinIllllill’dilii’lIt (II
I) OS .1 I iun, t lOll Ill
I ‘ 15(0 91
I’t ’rl’sI t c l IL I ig t l t t ’ ~~1’ n , ~~ i ’ I l lt e5 ,l l ’ I l t I n l i S 011(1 :it’t I’l t~ n Ilt I l ’ i l l l lt l l j )ttl at ii lllS , St C 0 i ’ l O V t ’
at I lit’ I
- ( 9 4 1 1) , I~ _ t0 III) - I’~- 5 1 ‘ 1 ’ i 52 . ( I ’
i_~~
) s 3 . ~, (~
-
-1’ ,(t. I’i
+ 11+ \ ‘ )( I I I + I)) dl
I t - i l l ’ I’ S ’
51 RI . El . N 1 . (l’ h II) -
52 = N I . N I ~~
t I ’ I) I - 1
53 1~ I K ‘ N 1 ( 1) 1/ 2 ‘
16
t~~- --_
~.~~ r , , - ___~~~~~_,_~_
-- - -
• Eq. ( 1 1 iS intt ’grat t’d 1,ISiII9 tin’ ( ; u i u s s — I a C t I , i l C (iua(hi’atui ’(’ f( Il’nsulas. InI- itiu l ’ s’ :~ We h ays’ plotted ~‘ ~~
as ii fum ~ s ’ t i l mi I n t ’l’
I and o. Although Slot 05 StI l l ~lt’as ~~~~ we can again approx isri ate these gt ’aph i ‘~il (‘5 till S il l an analvt ic fo r I l l
Jsj (T r . o) J J(T 1, 9) - W(’ l’ 1, o) ( 1 ; )
w lu l’re:
0 ~s =- t I
W(’ l’ 1. 9) (4 . 78 - 0. l i: l3 ~~~~ I7,i\10~~
bo - (0 . ~3 3 .78 .
-(0. 72” l0~~ ‘ 0 . i)00 18 . 000 1 ~°)- i’
- 0 :
I
439 - ;
384 4”I0000~~~_~~~~~~~~
us ~~ 4u = - t~ o0V-I
I 65-- 4it ov
‘ t o n
0
000b 2 4 6 8 0 2 4 6 18 20T 1(kev)
I- ’igu m ’c 5. Ratio of Secondary IUect l’on Number l”lux Due to 1(111Romba rdnient (J5~ ) Is A tiihieni Ion Numbe r ’ F’lux at Ssi rfa ’e (~Vs ’rs us ‘rem ps’rature (T 1) f o r Va rious Pot emit m i s
Eq. (1 6) can gtve negat ive so lu es as it is ~nhv an approximation. These valuesshould be set equal to 0.
17
-
~~~~~
5, n~(:K~(:-vrrI:iu:I) F.l,IA ’TRI)\ C(IRIU NT
As illlpltesi in Its iiatIII ’, I hit ’ has - ksn ’;iI t,’i’ t’d cut’i’eilt is the t’ t ’sult t n f t}u’
11a5 ’kn-’ I- a it ’ ’ l I i i g 511’ I’ t ’ t l l ’ I l i I I li ,,i the iiin idt’nt pium ’t iclt ’s . It is , fo r out’ s - a lt ’ imi at ions,
only a stgnif icant fac t o i ’ for e lect i n ’ i l S . This’ bas ic ’ equ al h Ilt I s :
J 1151’ ~~~~
f 1 1 1 1 1 )3~~’ ’, ) ‘ ( 1~~ dE ( 17)
w hi’ re
10 i f ~ . 0x
if~~ .0
11(1-I ’ , 11) P~ r c ’elst age of e lect i-oils sc at t ered it t a g iv e n ene rg~- K ’ as ar,’s~~lI (If an iris’ ident elect r’cifl at ene i’gy N.
1. 1 ene rgy of b~~. ’ ksn ’alt ei’ed par t ic l es (11: 1 1-3
K = l’111 ’ l ’4V of incident pa rt IcC’s
l-’t ‘I low ing 5 I ’ c’ng iass , 14( E’ , 1-3 is usually given in the not-nsa ! ized form:
14 1K , 1- ’) — ( ‘J3 ( 18)
G is g iven as i f uns ’ t i t ’ n oi’ K / N for aluminum b~- :
G(E’/ I-:) (E ’/ E)(l - I /N) (III)
We obta i l l e lt 1151. (19) f rom an approximate fit to Stem’nglass7
and I)I ’l - ’ I’ i,’sl
(p m ’ iva t I ’ s ’iIIIIIilUtSin ’Ot i lI l l , se t ’ c~am’t ’ et t3
). Substituting 1111 0 Eq. (17) :
Foi’ tti -~~0:
145K ~~~ ~‘ l-~ (20a)
7 . Sterngiass , N .J . ( 1954) I3ackseatter ing of kilovolt electrons from solids,Ph ys. fles. i~1,:34~ .
18
- — -~~~~~~~~~~~~‘ - — -~~~~~~~~ - - — - - -
~~-- -
~~~~~~~~-
~~~~~~-~-- ~~TJ :J~
L - ,n r ,~ 0:
~~l1S l- t l ’ ( t ’~~ i 1) I _ ~~~~~~~~ L 3 ø . ( 3 i 2 Q I 1
3 .
‘C. -\ LiJ IV I ) I t\ (20b )
ii here : ‘ I
P1 -~~ NI
’I’~~’’ I -
~
I A -~- ‘l~I
h 1, —
T h e m t eg l ’ at t I n is o” fom’nied Cv the Gauss —I agus’r re quadr atu r’e form ula .
rhe i t - s u I t s , nllrl l s a l l . - t ’d t ’\ ~~~~~ I I). am’e plotted in l- ig um’e 0 , I lls’ detai led
n u m i i e r i c ’ a l il l t l ii ! ’iIi 1 1 5 ( 1 1 1 5 mi I- ’i gu re 6 can hs’ roughly t i l t e d by:‘I
lIS~~, I I . ) . J 1 1( o . ‘I’~, ) ( 2 1 )
V ss here
j_
-~
- o - ~ 0
I1S t~~ I - — ) — -I
~ (0. 25,1 - 0. 0027 0 c o ~ (0 . 01167 + 0. 657 e °~ 184~ ) .
L -(0 . 00017 * 0. 0098 l ’ °’ 2 119) I’~ ~ 0
A s befit re , the actual integral wa s used for the calculat Ion .
‘9
_ _ _ _ _ _ _ _ _ _ —
~~~~~~~~~~~~~~~~~~~~~~~~~
-- ~~ n, —- —
o ~‘2049
0 4 ’-
9 4 1
‘ 12 3111 -
-0 3 4
- -
:: ~~~~~~~~~~:b0v
t~~ - 0 V -
—‘—----—-‘--- - —
11 22 -‘----‘---—‘~~
--------- -------- —----- ----- ‘ V — -~~ - Ii0 2 4 b 8 tO 2 4 ‘9 s 21
9 1 ’ 6 l I i n I of t I , I V ~~~~~~ n I ’ t C t C V i I I’ - ‘ I n n I l \ c~ t , r t Iu~I)tis’ In’ I i I ’ n t u n l l ,, t l u l V I t r i : u l~~: u t i , t 1,~~- l t n ~\ n i b u t - ’ :t t I t ’t ’t I n ”I\ u m l - i s - r I III\ t I 51: 1 1 1 1 1 ’ ~,1 I’~
V t -I —‘ 5 . -’ I ,‘ l - i t s ’i’at ul’s ’ 1 1 1 1 - ‘
1 V~i rI~~- u s l’~ ‘t l ’t l t u i is
~ , l’V.o ‘1 ~\.Y.~~i t , % ~ \ MUlfi- I.
- \ = & I ISc ( i~~~en t in liii Ilit l O n i O n i I n n l I , i;~ Il l l iOn ! I 6 1 1 1 , - t I C l i I1 ,’ i n - t , ~~~’
V ~~~~
4 ’ l ’ n ’ S l ’ I lt l I t I- v t - i l - u n - c t h a t , it l ,-:t ~ t n l l the ( ‘ t I C 5 l n ’l I t t ~‘\ i n 113(1 SI ’\ ’ I t t ,
t ’ t I 5 l l ,t 4 l n 4 1 ( ’ , 1 , I t l n n l l (ii Cc ad equately V I ’ 4 l l c - ’ I i l i l i 1 ,t 1 ’I ‘ 5 , ’ ~ iI I \’ I ‘ 1 , i i
n n 1 ’ 0 ~0iICl l I~~ t n - r hn ’ i the n l n n t I 1115 I O n l in t l S . h \ 4 1 1 ’ I I t I I n I ’ SI ll S t i l l S ‘ n I I I
_ i i l ! I l I l i — i I i l l u I t , ’t\ 80 S 1 i n ’ l lII n I tlit ’ n u l O n S — \ l t i u n - n ~~I’ n I 1 ’ m- t C _ Il’ t n OIl l l t I , \ t n l l l I 1 1 O I I I I I l \4 1 5 1 ’ a 1- l ’ t t I S ’ f it , and III 0110111 III ~
l n ’ I n ’ il l oh thi s ’ C l t t’ t ’S Ii s l m I 4 i 1 - \ i: l \ ,s ‘ l i l n I l IS
n 4 i I : l t c ’ a t s t s ’ \ lu t xss ’ t l iami at 1iII- In \ l1I lusi 5~ Il\ 55 Ii V Ill Cn ’tOn I’lll t’ i it It iV I n ’ l Ip t I
4 ’ Iuls Ila OS it (‘al l CC n h I l , ’ n ’ I 1’, I 1 5 , - i t’i’s~ i1l t I~ l I s t ‘ill’ 11I1’ ll t , ’ l l t ~- ‘f th i n i t s t I - l i - l u —
I l n I ll i l l l c t l n n l m , I ’ i l I -S , I’s ’ t i r ’ h X S n S i I l l l l S is, I G a l ’ l’ t - l t I l I t t i l t ’ 1) ih i m l t l t l l ~~ si 0 3 ,- t i
F) m’ s lI’iIII ’ll ill 1’~~rI li lt ’ C X 4 1 , 1 1 1 1 , ’ t l 1~~ _ Iilld li t I n C l l \ n ’ S t l t - l n i l I V , l l_ lal’l~’, \\ 1111 1
i l in ’ t n ’ l S ill i l i l l I l l , our n i l : l l ’gil l g l l l n ’ n h ’ i 55 ,15 d n S l C S O S i I ’ C1’ n ’I’l O’O,’t ’i InC Ill I ’
\I u i \ I s , l I l u I tI l Is t j ’ihut n Il,-’ ,
20
~1ni~~~ , l~~——--V
, — ,\ - -‘
~~=~~~~- - - - -— ‘ ‘1u
________ — - - “
V ~~~~~~~ ~~~~~~~~~~~~~~~~
“5 - .
i n ~~, (1) i~s i t o ’ s :
1~ h~~’ NI l : , i’l 1- ’) • ~ \ l t:, I2 l’ 3~ — fl. i~~, N 11, I l l) ‘ .l
~1çs , \21 , 1 2 1))
\ l h , ‘ I’ l l) - .1 5I 1n , \ 2 h - , 1 1 1 : 1 ) 1J~ 1 0. N l l , I l l ) ‘ ,l~~~~Nn , \ 2 l , l’21 ) )
N I I ’ , I ’ l l ’ ) - •~ 1l5I’~~ ’ N I t -‘ I’ll - I ‘ J I , i I ~~
0 21)
NIl’ , 111 - I \ i I \- ’ ‘ l l i i in i l i i l l : l t” ’ I nt l ’ i l S lt \ 1111 ! t I ’i i l t S ’ t .I IIII l lor t ’Is ’ct ‘on1 , 1 l ’ I an t I , ’ t l t 1
NIl I’ll ~ i I \ .I l’ i i I n i I 1 1 1 1 1 i ’ l l’ I t l s l t \ 1111 1 t I - l l , i n ,- I u lt ur e t - r ( i l - c t u n - I l
N I L I I i \l t x - ns 1’ill,IIl t Il9- inl m - nIl 11511\ amId l n I 1 1 I I I l u l t t i I t ’ n h in ’ll• n I l l a ’II, ’III
N I l , 12 1 M Ix - s I - i l ill mu ir i i, 1 1 1 1 1 1 5 Ill amid t et a I ’ rat iii’ , ’ for ioncI ’ l i l 4 ’ I 11, 111 2
~ 1’ i ! l n i n t l Ot t ’ l , , t I -I l • ‘ t l l ’ t t t l l I5’ t ’U (1V I q. ( 1
.1 1 inc ident i n n n I I I I ’C ilt 4 IV e f l 1I\ I ‘~~ (~~)
- 5 t ’ s nll lnI.l I V t’l(’ s ’t l ’ n ’l i t ’ t l i ’m ’ , ’mlt 4 1 5 t h lns I- 5(. ( 11)~, t- _ -
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S i ’ w hic h i ~‘ u i i i c t ’ , n I l ’ 51 t 1 1 ’ t ’ l 1 ’5 ‘ahl be (‘Il l } l l n lVt ’d . In this study , ~ s t a s ~tead i lvII I’ l l-c ii5~ ’ Il ill I V IC1 I V S (n S t t ’ 1 ’ s Omit il Eq. (22 ) h lecall l i ’ m it ’g l it ive . A t t i lis Pt ’ it , theIlIt ,‘rv,il t ’t ’ , tn -ke ) t’d Cs this va lue 11111 this ’ p t ’ e c e d i m t g value wa s S l l t l l I i S ’ Id ’ d it ito llit ’I’
inter-vals and ths n Ih l ’ I I S ( ’ S S i te i ’Ott ’d (mit t ml a s’los(’ uIt”1I’ oXiIliuit iI’i1 t o , (‘h ’ O ss uis found,115 11 n t ’ u t Il u i ly , ’ i n i g t lit ’ h e I~i Ilts of 11(11’ nss’ del , one f i n a l point me I l l u i lus t n l Cs’ nlis —
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t I l l s t I n h I ‘ t n l l l i , 3 110 l ’ u i i t t t ’ t ’ ’ i t i l t - l I n , ( l l i h ll I ll ’ ~f 1 ( 1 1 1 ‘1 ~ng A 1) svhi t ’m i II 15 mit t I I’ ll - I n ;
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1)0 n t t ’ I l t l t . ’a tI lt ’ 115111 Iiv ~ t -thi t’ sit- , Ill t I l t ’ i l t . ’ t l . l t i l ill l l l h l t I C , l 5 , l Ilt ’ “ t O l l n l l l id l ’ l l , ’rIs dell. n ) , V 4 Ci n ’ ,t iin i Ills ’ 0,11 I I 1,111, -Il n ’ n I t ’ t t I n 1 1 1 1 1 15 11 l l O t t 1 2 1,5 i- , l i I t S t n i ,‘ i i t Ins t I t l e
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t s s n ’ — ’ S I u l \ I s t ’ l l i u i m i u u I ’ l l t ’ il \ I t t l , i t i l n l l and II 511114 1. ’ lll u u l t ’ rI,II 1 h Il l I l ;’l ll . iI i ’ll l~~’ t ’ 1 l l c t S I’1.1 1 11 C t n 1 ,1 ft 110t tOil I l l s Ill I.e Ii
C) ( ‘ ) ~ ( I l ~I( ) ” .
In t h e ’ 4’ l t ’n ’ lS i Ill g S, ’ n ’ i l , n l lS l i t ’ Ilu i v. ’ ,‘iit luit ’d a pl’t t t ’elhu I’e n Il’ I~uktng aMuuxis’ t ’Iliuiii d is t r it ’ i it I n Ib I 110’ , l ’ s’ t h O u ) l l I I lt t I l- , u i m lv mium uln’r of ‘si I\Is t ’II IIIIl t l i 5 l i i I I I I —
I i l ,~ i5) . t l ln i n n ’t i ilhlt im ig I li t ’ Pt’ lt ’IiI iuil l l u f i e i - t ’mi , ’ t ’ Int’l ss ’et ’n I I sIi~it 1c tiv t ’nI s~its ’ l l i ts ’ Sill ’ Iuuc ~’amid t l it ’ i l l i I b I ’ lht t ’ T i \ ’ l s’ t ’ m imn t ’t l I , I 1llr i’ t ’st i II 5 I InI l n ’ :i I t ’ l i i i u i ( ’n ’ti 1 ,105 ( l i t - I 11111 Iv I lit ’.t,ti in tt n i t ’rI’ t ’r I’.’tit .‘t ’mi t his’ n lIISt ’I’Vt ’hI Ol in 1 )‘ t ’ C h l l n ’ t s ’ll 4, -I out ials) n I h ’ t I , ‘00 \‘ . l’liisIS I n I I ’ cI,i i l1il i l,’b i is-i t li tI lt ’ “ t ’X . l n ’l ’ n ’ ;t ls ’u lu t t O h m ) ims it ig t l it ’ tIt ’t~t i l e ’t I l iSt l ’ i l t t i t l I l i l
h int - I 11 111 n Il’ I a I i t ’ll ” 1, - i ’ Iv I i in ’lI u u m l C ‘ I ’ l l ’ n I t ~ ~ 7 (1() V W It S l ’ t ’ Ii l~~I’t t ’n l t u b I li:tt1 , 1 1 1 t ’ t t t ’t Il or f l it’ ( ‘111 , 1, ’ .- s t i l m i a l t ’ of ~ - l’
~. l. mi 1.1 1 (10.1 ) ‘1 1: ! 000 V , . ‘\ lIlt ’
r ,utl, t n t t , t n C i l i u ’s l I t I Ii,’ l ’e’ i Il ’ s~5t ’ t l t at i s l t i of I lit ’ n I l at rihut it ’ l l iuni ’t i~ ’ss and n’s i i ’ i t ’i)Il’, i lu i m ict ’ nh i . ’ u u S t ’S f I n n l l l C a r i e lt II I t i l ls 1tuu P s~ m ’ t~~n 1 1h1- i ’ t ’t I I- I uul , ‘ Ii ,; I i’,’sid IS ill
I , h i i i t ’ t ’ b l l t ’l i ) i’~’iI Ii t ’ \ 4 ’ t ’ n ’ ) I l I m IllS ,
t i l l ’ 41 1 155 t ’i (I f hilt ’ l t ’ n ’ lh lh inlt l , ’S hit ’ t ’St ’l)f ,hil i t t t i l l S 4111101’ , I h n b I S t ’V I ’ I I S miot t he(55 hirh (Si l l Il ,’ ilIll’ 1 1 1 5 . 1 1 l’i Iiiliiilt t I l t ’ 101 111, 1 i S I j I S n ’ l I 55 t ’nI Ill ( u t I ’ l - t ’ t t ”~
tail Ill f l i t ’ pn ’t o - m i l l h l l t S n l f I l C i l i - Il l , ’ au t’If hci s ’Il t , ui~i uulv t i n ’ t ’ X h i i ’ u ’ t ; S l n l l I t I ll’ t lte’ pt ltemil ~~~I l l s I S t i l n i l ’ l i t Ui l ’ n~~~. ( I’) , t ’H , ( II) , ( (11 ) , ui l inl ( I t ) , Mj i lti 1nlt’ ‘ S 1 1 l \ I 5 .’ u 1 1 , l m l
11 , 1 II I t ’ l l, I I , it . , Is’ it it iii , ,-\ , ( 4 , utt id l’tL’ , I,’ , t’ , ( t h l ’ l l l\ t C S ’ n i l n ’ t l , II t I I 1-~~lh i t t l n l u l l )1 , 1 1 1 , i t i n t I I S V I I I i l t o l m t l u l s ( 11 1 1 1 1 . (t ’n l l t t ’ n l ( t i I) , I’ , I) n ’t l i i t ’ I i\ \ In ’ V 1 4 4 t ’ l i m ’ i l l
I I - ‘I h ’ t ’ n I l I l I ’S i l l l I l t ’ ~ n I ui r — l’ t ’m ’ l’ t - SI 1 1 . 11 I’ ll ’ l I e) 01115 \V n lr Iss Iu l l ,
I I , — ) 1 1 1 1 1 1 1 I n _ I l , t O I l hi ’ 1 5 ( 5 1 1 5 h m 1 n s , I I i t l l_ l t h t ~ II l b ’ ’ I 1 l4 III, - t t ’ n l i I . i l 11015 ii) a ‘~ t i t ig ht I n n l I5 I l l - I
- - — I l l - Ill , 1 h i t ,‘ t l I I I n ’ 1 111 1 Stl t I Ill , 1 , 1 1 1 ) 1 u i l II II II lii ‘ , i l l n , , il~~’ l l t ‘ i h I l I l i I t ’ , t n Ii 1111
iilt I ’ n I u t l , ’ l \ I I ’ I t 51111 11 1’ ’ l i l t ’ l l I l ’ l h It n l t ’ i I i h it ,,1 n.)t , t n t I I Oft I . ‘ p t , ’ , ’ ) l t l l t ’ I I I 1:111; .
Re ferences
I. ; I ll ’ ’ ) 11. Ii , I I 1l~~~\ “\ I l ’Ill ’ i i l h1 ; - ‘I lIi. I 1 2 ’, - - ,’V l i n l h i n .li n’ i I, i ( H’It I ’ l l - . , - I , ~~~0n ’ li—
0 1 1 1 11 — P o n t I \I:i;i _ I ll lC’ 1414 V \ ) ) ,.\ll l - i l l- I ,
I, ( n : t ’ I l ’ t t , II . Ii , I l l - i I1 n I ’ i , ’ ’ t 0 I- . (1~~ OII~l A l 1 1 1 : 1 1 5 1 11511 t i l b l l l i I . I t 11 ’II l ’t l t l , V
l11 ’n I 5 5 I h c t~~~~~t l 0 . ‘ I , l l ~n t b :l t ’ i l V i l n ’ f l h l l ( ’ l l t , I n ’ ,t pl ’ ; l l’ il l l’ Iaun ,’ l . O l t l t C n ’ ‘I
4 . ( ; , I I - t - t ’ l t , 11 , 14 , ( I ! t ’ iit ~‘j’ ,I. I’I’ i 1 I t t t ’ o t n ’ t It LlI ( III’ I i I ; It l n - I b s — . \ ‘ S 1 n ’ n I ~ ’1 A l 112 -
I ’ I 4 - 7 l 4 - 1 1 1 1 ’ S , :\ i ’ . , l l ’V I ’ \ ’ In l ; t - . -4 t v - ~~u I 4 , ‘S n . IIL , \ l~ ‘(111,11 1 ‘ 1 .
4 , \ \ t i it~4 l1 ’ , 1’ . t - I t~~ h i 1 ~ flit’ ) n l l l l) it I i ’ l i h l l l l l l’ , t l it ’ l’n ’lI ’ I I t 11t1 n ’l a ho nK i i t l i.’I ‘~
‘t ’ A t I ll, IS ‘h - I t \ ,‘\b , -\ ‘ S - I - I - ‘ ‘- I’ I - 1 11 1
t s I , i~1 , I- - , ( 1 1 1 7 : ’ ) 1- .I l ; l . t ’ n l a l t t hllui h ’l l li l u t V , i l lcIl l l ’il nOlS - l I d , ,1 , i , I ’ h I t ’ i l \ ’ .
lIt ’s , - ‘ :11 . 11 .
I ; , i n , l 1 I I ’ll , I I, 11 . :uuil I ) t ’ l o - I~t ’sI , i-~. 1’ , ~~ I 1 :11 11 1 411111 ’ V O l 5 1 1 1 1 ’ ‘t l. I t n ’I ’ll - n ’t I’ ll t’Ill\
‘ V n i l 1 4 4 ’ I t n l’I l ; l t t ‘n l t l ’ l i l lz i l h I l, , , , n S \ l l c I l I n , i l h , l I S n Il I’ll , .1 , ( 1 2 ’n ’ t l I l \ ~ , Ut
l i- I :‘~l. 4 —2 ) 1 1414 . —
7. 1—~t l ’ l ’ m t 4 I 1 t 5 S , 1- ..) . ( I l 1 ,V t ’t I iu in _ lc sI u i t I t ~ I~ i I 1~I II ( s h l n ’ i n I l t ’ l t ’ l ’ I I I O i l , l I , ,I i I 4 - h I l l — ,PI1\ a , l i , ’s. O ’ :- i’I I ,
14 , ( : t 1 1 1 1 1 , 11, 14 , , l(I,iI’i~i, - ‘5 , I , , z,u, l t ’ ,t ,t ’ I ’ . I’ , ~~~~ n 1 ) t ’ l t ’ n i l n I 11 111 ~~l i j ’ l l I t ’ b l l It
I’ ’ ) l’i lt o h ) -s it I It’ ‘10 t i n ’ hl’ n llln ‘115 5 l l I~ lI , 1 , - I I t , ’ .) l’s- 1~ , 1 -‘ I 5011i11’l I~ 1 . 1
In P s - n, ’ ,’ ,’ - 1 1 1 1 4 1 5 112 t i l t ’ 01 1 1 1 1 1’ ” I t ’ I ll ’ st ‘O i l I’ I t ’ n i i t ’ l i ,hi iS ‘Un n l l IS -12 1h 1 t l ,
I
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