An Introduction to Explosive Magnetic Flux Compression Generators

8/3/2019 An Introduction to Explosive Magnetic Flux Compression Generators

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LA-5890-MS4(3!6,6

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. .AUC-34Reporting Diite: February 1975Issued: March 1975

An Introduction to ExplosiveMagnetic Flux Compression Generators

byC. M. FowlerR. S. CairdW. B. Garn

ei DO NOT CIRCUIATE

PERMANENTREQUIREDBY(D ____.10s a lamossc ient i f ic labora t ory

of t he Universi t y of Cal i forn iaLOS ALAMOS, NEW MEXICO 87544

/ \An Affirmative Action/Equal Opportunity Employer

RETENTfONCONTRACT

UNITED STATESENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

CONTRACT W-740 S-ENG. 36


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Work pa r t ia lly su ppor ted by Air Force Weapon s Labora tory, Defen seAd va nced Res ea rch Pr oject s Agen cy, U.S . Air Force Foreign Tech n ologyDivis ion , a nd U.S . Ar my Ma ter iel Com ma nd , MICOM.

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ABSTRACT . . . . . . . . . . . . .

1 . INTRODUCTION . . . . . . .

CONTENTS. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

IL E XPLOS IVE S MAGNETIC FLUX-COMPRE SS IONGENERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.B.

c.

_,

E.

Elemen ta ry Gen era tor Th eory . . . . . . . . . . . . . . . . . . . . .Types Of Gen era tors . . . . . . . . . . . . . . . . . . . . . . . . . . .1 . Sp ira l or Helica l Gen era tors . . . . . . . . . . . . . . . . . . . .2 . Pla te Gen era tors . . . . . . . . . . . . . . . . . . . . . . . . . . .3 . Str ip Gen era tors . . . . . . . . . . . . . . . . . . . . . . . . . .4 . Cylin dr ica l Implos ion Sys tem s . . . . . . . . . . . . . . . . . . .5 . Coaxia l or Cylin d r ica l Gen era tors . . . . . . . . . . . . . . . . .6 . Sph er ica l Gen era tors . . . . . . . . . . . . . . . . . . . . . . . .In it ia l En ergy Sou rces . . . . . . . . . . . . . . . . . . . . . . . . . .1 . Pr ima ry En ergy Sou rces .. . . . . . . . . . . . . . . . . . . . .

a . Direct Feed . . . . . . . . . . . . . . . . . . . . . . . . . .b . In direct or In du ct ive Feed .. . . . . . . . . . . . . . . . . .

(1 ) Elim in a t ion of Per tu rba t ion s . . . . . . . . . . . . . . .(2 ) Redu ct ion in Size of In it ia l En ergy Su pply . . . . . . . .(3 ) Overcom ing Sou rce In du ctan ces . . . . . . . . . . . . .(4 ) Redu ct ion of Magn et ic Forces . . . . . . . . . . . . . .

2 . Gen era tors a s In termedia te En ergy Boos ters . . . . . . . . . . .a . En ergy Boos t in g . . . . . . . . . . . . . . . . . . . . . . . .b . Force Redu ct ion . . . . . . . . . . . . . . . . . . . . . . . .

Techn ica l Aspects of Gen era tor Tech nology . . . . . . . . . . . . . .1 . Switch in g an d Pu lse Sh apin g.. . . . . . . . . . . . . . . . . . .2 . Use of Tra n s formers . . . . . . . . . . . . . . . . . . . . . . . .3 . Gen era tor Lim ita t ion s . . . . . . . . . . . . . . . . . . . . . .\a . Flu x Losses . . . . . . . . . . . . . . . . . . . . . . . . . . .

b . High Magnet ic Field Effects . . . . . . . . . . . . . . . . . .c. In tern a l Voltage Lim ita tion s . . . . . . . . . . . . . . . . .

En ergizin g th rou gh Tran s form ers . . . . . . . . . . . . . . . . . . .

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1244678101111111112121314151617171818202224252729

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AN INTRODUCTION TO EXPLOSIVE MAGNETIC FLUX COMPRESSION GENERATORSby

C. M. Fowler , R. S. Ca ird an d W. B. Ga rn

ABSTRACTVa r iou s types of exp los ive flu x compres s ion gen era tors a re illu s t ra ted

an d th eir rela t ive advan tages a re compa red . Exper im en ts a re des cr ib ed inwh ich en ergy was su pp lied by th es e gen era tors . Th e exper im en ts weres elected to sh ow both vers a t ility an d lim ita t ion s of th e devices . Generatorp r in cip les a re der ived from lu mped pa ram eter circu it th eory.

I. INTRODUCTIONExplos ives flu x compres s ion devices h ave

been d is cu s s ed frequ en t ly in th e litera tu re in recen tyea rs . However , for th e mos t pa r t , a va ila b let rea tmen ts of th e su b ject h ave been specia lized .

Th is repor t gives a ra th er th orou gh back -grou n d cover in g mos t a spects of exp los ives flu xcompres s ion tech n ology, bu t n ot a t a very deta iledlevel. In s tead , th e text h a s been developed moretowa rds u nifyin g th e su b ject . Va r iou s app lica tion sa re m en t ion ed, bu t th e em ph a s is h a s been on thos ein wh ich th e Los Alam os Scien tific Labora tory h a sbeen in volved . Som e coh eren ce h a s been given toth e report by con s ider in g in la ter s ect ion s a specificexample, th a t of u s in g su ch a device to su pp ly ala rge amou n t of en ergy to a s izeab le in du ctan ceload. It is s h ewn th a t m an y a spects of th e tech n ol -ogy mu s t be con s idered before a ten ta t ive solu t ionto th e prob lem is ob ta in ed . Th e d is cu s s ion isla rgely des cr ip t ive, a n d th rou gh ou t , circu it th eorya n a lys is h a s been employed . Wh en more deta ileda n a lys is is requ ired , s u ch a s a d is cu s s ion of m ag-n et ic field d iffu s ion , oth er referen ces ma y becon su lted .> 2

IL EXPLOSIVES MAGNETIC FLUX-COMPRES-S ION GENERATORSTh e gen era l p r in cip les of exp los ives m ag-

n etic flu x-compress ion devices h ave been rea son -a bly well docu men ted . 3 -7 In gen era l, ch em ica lexp los ives a re u s ed to compres s an in itia l m agn et icflu x by d r ivin g pa r t , or a ll, of a con du ctin g su r fa cewh ich con ta in s th e flu x. Work don e by th e con du c -tors m ovin g aga in s t th e m agn et ic fields resu lt s inan in crea s e in th e elect romagn et ic en ergy. Th eadd it ion a l en ergy comes or igin a lly from th e ch em -ica l en ergy s tored in th e exp los ives , a pa r t ofwh ich is t ra n sm it ted to th e movin g con du ctors .Th ese devices a re n orm a lly ca lled flu x-compres -s ion gen era tors or , more s im ply, gen era tors . Th eexp los ively dr iven con du ctors a re frequ en t ly ca lleda rma tu res , a n d occa s ion a lly, n on dr iven elem en tsof th e gen era tors a re ca lled s ta tors .

Elemen ta ry gen era tor th eory is p res en tedin Sec. II. A, d ifferen t cla ss es of gen era tors a redes cr ibed in Sec. II. B, an d th e m ean s of s u pp lyin gin it ia l gen era tor en ergy a re d is cu s s ed in Sec. II. C.More tech n ica l a spects of gen era tor tech n ology a ret rea ted in Sec. II. D, wh ich a ls o in clu des a d is cu s -s ion of opera tin g lim ita tion s . A specific example,

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th a t of deliver in g 109 J to a n in du ct ive loa d of 10 vH,s h ews h ow lim ita t ion s a ffect th e des ign of a gen er -a tor sys tem . Attemp ts to en ergize th e loa d byd irect gen era tor feed wou ld be thwa rted by th edevelopm en t of exces s ive in tern a l gen era tor volt -ages . Ca lcu la t ion s bas ed u pon idea lized s ys tem sa re given in Sec. II. E an d in d ica te th a t th e diffi-cu lt ies can be resolved by tra n s form er -cou p lin g th eloa d to a gen era tor-d r iven p r im a ry coil.A. Elem en ta ry Gen era tor Th eory

Figu re 1 s h ews th e ba s ic componen ts of acla s s of gen era tors of th e h elica l or s p ir a l type. Atth e lower r igh t is a fixed extern a l loa d coil. ofin du ctan ce Ll, wh ich is to be en ergized by th egen era tor . Th e gen era tor its elf con s is ts of th eextern a l h elica l win d in g. t oget h er with th e explo-s ive-loa ded m eta l cylin der , or a rma tu re. Initialflu x is su pp lied to th e gen era tor a n d s er ies load

Leads from Hellcat sectioncap bank./ \

\ -wL Det on a t or Load coil 1

Fig. 1 . Sp ir a l gen era tor , before exp los ivein it ia t ion .

Armoture 71. 1-mn=_,

Fig. 2 . Th e gen era tor of Fig. 1 a t a la te s ta gea ft er explos ive det on at ion .

coil from a capa citor ba nk . It ca n be seen th a t th ea rm a tu re its elf s erves a s pa r t of th e condu ct in gcircu it . When th e exp los ive is deton a ted , th ea rm a tu re expan ds , r esu lt in g in a con ica l meta lf ren t movin g with exp los ive deton a t ion velocity.Th e deton a t ion is so t im ed th a t th is con ica l fron tsh or ts ou t th e gen era tor in pu t a t or n ea r pea kcu r ren t or , equ iva len t ly, pea k flu x in th e gen era -tor . Th is a lso effect ively is ola tes th e ca pa citorba n k from th e s ys tem . After closu re of th ecu r ren t in pu t . th e con ica l f ren t proceeds down th ea rm a tu re, con tact in g th e h elica l tu rn s in a more orles s wip in g fa sh ion . Figu re 2 gives a view of th egen era tor fa ir ly la te in th e deton a t ion s ta ge. Th ein du ct a n te of th e gen era tor is rou gh ly proport ion a lto th e s qu a re of th e n umber of tu rn s in th e h elix,an d in vers ely proport ion a l to th e rem a in in g len gthover wh ich th e tu rn s a re spaced. Th e gen era torin du ctan ce LG thu s va r ies more or les s con t in u -ou s ly with t im e from its in it ia l va lu e Lo to zeroa ft er a rm a tu re motion h as ceas ed .

If th e cu rren t den s it ies developed in th egen era tor do not get la rge en ou gh to d is tor t th esys tem , th e gen era tor in du cta n ce ca n be given a s afu n ct ion of th e tim e. Un der th is cond it ion , th egen era tor cir cu it can be d rawn s ch ema tica lly a ssh own in Fig. 3 . Here th e gen era tor is sh own as ava r ia b le in du cta n ce LG(t). a n d th e extern a l load tobe en ergized is L1 . Allowan ce for sou rce or was tein du ctan ce (from va riou s extern a l lea ds to th e loa d,res idu a l gen era tor in du cta n ce, etc. ) is in d ica tedby l., an d cir cu it res is t an ce is sh own a s R. Th eequ at ion govern in g th e perform an ce e of th is circu itis th en :

dz [( LG+IO+L1) I]+ IR=OI(0)= IO. (1 )

11 0 9 0 11L~(t) L,

Fig. 3. Sch ema tic of gen era tor cir cu it . Th e loa dcoil L1 is in ser ies with th e gen era tor .

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Tim e is measu red from th e in s tan t th a t th e a rma -tu re sh u ts off th e cu r ren t in pu t , a t wh ich time th ecu rren t is I o an d th e in it ia l gen era tor in du ctan ceis LG(0), den oted by Lo below.

If th e circu it were perfect ly con du ctin g, R =O, th e well-kn own electrodynm ic res u lt is r ecov-ered th a t flu x LI is con served in a perfect ly con -d u ct in g cir cu it . Un der th is con dit ion , th e con s er-va t ion of flu x leads to th e resu lt :

1=

1/ 2

LO+40+L1LG+!O+L IO1

(2)

Th e in du ctive en ergy in th e cir cu it , E =(LG + 20 + L1)12 , ca n be rela ted to th e in it ia l

cir cu it in du ctive en ergy, E = 1/ 2 (LO+ J O+L1)2 0XI , a s follows :o (Lo+&o+L1E. )G + .&O + L1 O (3)

Under bu rn ou t con dit ion s , LG = O, th e fin a lcu rren t an d circu it en ergy become:

1=

E.

LO+2+L o 1110 + L1 o

Lo+ l.+ L140 + L1 Eo .

(4)

(5)

Th e res is ta n ce R in a n a ctu a l cir cu it isu s u a lly rela ted to th e gen era tor act ion in a complexway. Among th e s ign ifica n t fa ctors a ffect in g th eres is tan ce a re ch an ges in con du ctor sk in depth ,t empera tu re, an d pa th len gth a s gen era tor act ionproceeds . For illu s t ra t ive pu rposes , h owever , wecon s ider th e ca se wh ere R is con s tan t . If, fu r th er ,th e in du ctan ces in th e gen era tor cir cu it a re fu n ction son ly of th e t ime, th e solu t ion of Eq. (1) is

L (0) [1I(t)= 10% J Rexp - T o LT(Y) y (6)

wh ere we h ave abb revia ted th e tota l cir cu it in du c -ta .n ce LG +- lo + L1 by LT.

Th e in du ctive en ergy E becomes

:0)XP[-2!*1 7 )(t ) = Eo~We con s ider th e ca se wh ere both th e loadin du ctan ce L an d th e los s in du cta n ce to a re con -1s tan ts a n d we employ th e followin gff>rm for th e gen era tor in du ctan ce:

specialized

(8)

Th is in du ctan ce form approxim a tes th a t for th ep la te gen era tor d is cu s sed in Sec. IL B with in it ia lin du cta n ce Lo an d bu rn ou t t ime T. Equ ation s (6 )an d (7 ) th en redu ce to th e followin g:

[ 1~_~7LT(0) LoI(t ) = 10 ~ T~-+[1T(0 ) LoE(t ) = E. ~ T

(9)

(lo)

At bu rn ou t , t = r , th e cu rren t an d en ergya re a t a maximum . Th e en ergy is d is t r ibu tedbetween th e two in du cta n ces .LO and L1 in propor-t ion to th eir in du ct an tes . Th e maximum cu rren tan d en ergy in to th e load L th erefore become1

(11)

1El(T) = E. ~-10

~_~TLO+ LO+L1 Lo

AO+L (12)1

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It is clea r from th ese equ a t ion s th a t th equ an t ity Rr / L. mu s t be les s th an 1 for cu rren tamplifica t ion , an d les s th a n O. 5 for en ergy mu lt i-p lica t ion . As a s pecific example, con s ider a gen -era tor h a vin g th e form ind ica ted by Eq. (8 ), witha n in it ia l in du ctan ce of 1 p H an d a bu rn ou t t im e of10 u s powerin g a load of 10 nH. As sum e a sou rceor los s in du ctan ce of 2 nH, a res is tan ce of 10 maand an in it ia l cu rren t of 5 x 105 A. Th e in it ia len ergy in th e circu it becomes :

E. = 1/ 2 102 (Lo+ io+L1)

. 1/ 2 (5 x 105 )2 X[l. 012 x 10-6 ]= 126.5 kJ .

From Eqs . (11 ) a nd (12 ) th e cu r ren t an den ergy mu lt ip lica t ion s a t bu rn ou t become:

0.91(7)/10 = (- ) = (84.5 )09= 54; I = 27 MA,

o :.::; (-)08=:35=2.2;1(r)/ E -El = 3 .7 MJ .

It is clea r th a t good gen era tor pra ct ice ca llsfor a m in imum of circu it res is tan ce an d sou rceinductance. If th e res is ta n ce were n egligib le, th ecu rren t m u lt ip lica t ion wou ld be 84 .5 an d th e en ergym ult ip lica tion 70.5 . If th e sou rce in du cta n ce werea lso n egligib le, both cu rren t an d en ergy mu lt ip li-ca t ion s wou ld be 101 .

W bile th e cond it ion for cu rren t mu lt ip lica -t ion , Rr / L. < 1, wa s der ived for a s pecific gen er-a tor form , a rela ted type of res tr ict ion app liesmore gen era lly. Th is may be seen by expan d in gEq. (1 ) :

Th e la s t fou r term s , in compa rison with th e cir -cu it sketch of Fig. 3 , ca n be seen to represen tvoltage d rops a cros s th e load in du cta n ce, th eres is tan ce, th e sou rce in du ctan ce, an d th e res i-du a l in du cta n ce in th e gen era tor . Th e firs t termis th e poten t ia l acros s th e movin g a rm a tu re and ,in fact , is th e s ou rce voltage for th e res t of th ecircu it . Th e term I dLG / dt [ is som ewh a t a n a lo-gou s to a res is ta n ce an d is sometimes referred toas su ch . For th e s im ple gen era tor form u s edabove, th e ra t io RT/ Lo is , in fact , R/ I dLG/ dt [ .III gen era l, for cu rren t mu lt ip lica t ion th e circu itres is tan ce mu s t be les s th an some weigh ted va lu eof I dLG / dt I for a gen era tor with a rb it r a ry t imedependence.

It is a lso clea r from Eq. (13 ) th a t th egen era tor a rma tu re poten t ia l I(dLG / d t)mu st exceedth e voltage d rop acros s th e res is tan ce IR, or th ein it ia l cu rren t mu s t decrea se with t ime.

For th e gen era tor example given ea r lier ,th e a rma tu re or d r ive voltage becomes a t

dLG I Lo=-=-27x106 ~A=ldt r 10-5

bu r nou t :

. - 2 .7 IVlv. (14 )

Th is is a very la rge in tern a l volta ge for agen era tor to su s ta in , an d mos t gen era tors cann otdo SO. Man ageab ility of in tern a l voltages is agen era tor con s tra in t wh ich will be d iscu ssedlater .B. Types of Gen era tors

Almos t an y n umber of gen era tor types ca nbe con ceived bu t very few tu rn ou t to be pract i-cable. Th e most u sefu l gen era tor types will bedescr ibed below, togeth er with some of th eirvar iants .

1 . Sp ira l or Helica l Gen era tors . Asch ema tic d rawin g of a gen era tor of th is cla s s issh own in Fig. 1 , a n d its opera t ion is descr ibed inSec. 11. A. Th ese gen era tor s a re ch a racter ized by


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very la rge in it ia l in du ctan ces owin g to th e mu lt ip letu rn win d in gs of th e sp ira l. Th e in du ctan ce L of ah elix of n tu rn s an d rad iu s R over a length u isgiven approxim ately by:

n2R2L = 3 .95 ~+oo9R #H (MKS) (15a )

n2R2L = 0 .1 ~+o.9R pH (R, w, in ch es). (15b)

Th es e two formu la s will be u s ed frequ en t lyin th is repor t a nd a d is cu s s ion of th eir lim its willb e h elp fu l. Gen era l a pp licab ility of th e form u la isgiven by Terman . 8 Th e squ a re of th e rad iu s in th en um era tor a r ises from th e a rea in s ide th e circu la rwin d in gs over wh ich flu x is measu red . For sp ira lgen era tors , th is term is rep laced by th e d ifferen cebetween th e squ a res of th e ra d ii of th e h elix an dth e a rm a tu re, s in ce flu x is la rgely exclu ded fromth e a rea occu p ied by th e a rma tu re. In ca s es wh ereth e flu x-con ta in in g area is not circu la r , a n ade-qu a te approximat ion can frequ en t ly be ob ta in ed by

2u s in g th is a rea d ivided by ~ in p la ce of R . Th erad ia l term in th e den om in a tor is an edge effectcor rect ion term wh ich makes a llowan ce for th efin ite len gth of th e solen oid. For sp ira l gen era -tors th e edge effect cor rect ion term shou ld a ccou n ton ly for th e fin ite th ickn ess of th e an n u la r spa cebetween helix an d a rma tu re in s tead of th e en tirea rea en clos ed by th e h elix. Ha lf of th e an n u la rra d ia l s epa ra t ion serves bet ter for th e edge cor -rection here. St rict ly speakin g, th e formu la isapp licab le on ly wh en th e cu r ren t den s ity is u n iform .Th is does not lead to appreciab le er ror form ult ip le -tu rn coils . For wide con du ctors , a s ins in gle-tu rn coils wh ere th e wid th is compa rableto th e coil d iameter, th e cu r ren ts a re more con -cen t ra ted n ea r th e en ds of th e condu ctors . Fo rth ese ca ses , in du ctan ces ca lcu la ted from th e for -mu la s may be too la rge by 1O-2OYO.

As a specific example, a gen era tor within it ia l a rma tu re rad iu s of O. 1 m, an d sp ira l

section of 20 tu rn s , ra d iu s O. 2 m, an d len gthO. 5 m h a s an in du ctan ce of 87 KH, accord in g toEq. (15a ). Th is la rge in du ctan ce is to be con -tra s ted with th e ca lcu la ted in du ctan ce of O. 2 2 IJ Hfor a s in gle-tu rn solen oida l gen era tor of th e samedimensions. Th e O. 2 2-pH va lu e is more typ ica l ofth os e for th e oth er gen era tor cla ss es con s ideredlater .

In pr in cip le, Eqs . (4 ) an d (5 ) in d ica te th a ten ormou s cu rren t an d en ergy mu ltip lica t ion s a reposs ib le in low in du ctan ce loads . In pra ctice, an umber of fa ctors s everely lim it s p ira l gen era torperforman ce. In tern a l gen era tor voltages a remore lim ited becau se of th e pos s ib ility of b reak-down between tu rn a of th e h elix. Gen era lly speak-ing, s u ch gen era tors opera te over fa irly lon gt imes , a n d u n der th ese con d ition s maxim um cu r-ren t den s it ies a re lim ited to va lu es of order 1 MAper cen timeter of con du ctin g pa th . Th u s , if th egenera tor is to deliver a cu r ren t of 20 MA, th etu rn s n ear th e gen era tor ou tpu t s h ou ld be of order20 cm wide. Oth er lim ita t ion s a r is e from th eten den cy of th ese gen era tors to pocket flu x if th etu rn s a re spa ced too clos ely. Pocketin g occu rswh en th e expan d ing cone of th e a rma tu re shortsou t pa r t of a tu rn before completely wip in g ou t apreced ing tu rn . Good sp ira l gen era tor des ignth erefore ca lls for rela t ively widely spa ced tu rn s ,wide ou tpu t tu rn s , a nd clos e mach in ing toleran ceson both th e a rma tu re an d th e h elica l s ection .

Th e rela t ively lon g gen era t ion time forth is cla s s of gen era tors lim its th eir u s e in manyapplications. Never th eles s , th ey h ave been u sed

9 , 10su ccess fu lly as power sou rces for O-p in ch es11an d pla sma gu n s , a lt bou gh both app lica t ion s

requ ired th a t th e p la sma devices be switch ed in toth e circu it a t a rela t ively la te time in th e gen er -a tion p er iod . Th e t ime sca le of opera tion of th esegen era tors a lso su gges ta th eir u s e a s powersou rces for certa in la s er devices an d for ch a rgin gwa ter capa citors wh en por ta b ility is a fa ctor.

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Mos t of ou r own gen era tor app lica t ion s forth e n ear fu tu re ca ll for m u ch fa s ter gen era tors .Th e sp ira l gen era tor is expected to be in va lu ab le a san in termed ia te en ergy boos ter--th a t is , it willam plify th e en ergy from th e in it ia l sou rce to su pp lyth e s ta r t in g en ergy for th e fin a l, or ou tpu t , gen er -ator.

2 . Pla te Gen er at or s. Th e c ro ss -s e ct ion -a l view of a p la te gen era tor is sh own sch ema t ica llyin Fig. 4 . Sh own a t th e r igh t is a solen oida l loadcoil con n ected to th e gen era tor by a tra n sm is s ionline. Exp los ive b locks a re p la ced u pon th e u pperan d lower p la tes of th e gen era tor, a s sh own . Ini-t ia l flu x is su pp lied to th e gen era tor by a capacitorbank th rou gh th e sma ll, open s lot s h own a t th eu pper left s ide of th e gen era tor . Cu rren t flowth rou gh th e gen era tor con du ctors is in d ica ted bya r rows , an d th e field developed in th e gen era torcavity by th e cu rren t is in d ica ted by cross es .

Th e exp los ive b locks a re deton a ted s imu lta n -eou s ly over th eir ou ter s u r fa ces a t su ch a t ime th a tth e in pu t cu r ren t s lot is closed a t, or n ea r , peakin pu t cu r ren t. Th is opera tion s im ulta neou slyelim in a tes th e capacitor ban k from fu r th er in ter -a ction with th e sys tem an d traps th e in it ia l flu x ina completely en closed meta l s ys tem . Th e pos itionof th e driver p la tes a t a la ter t im e is shown byda sh ed lin es , ea ch p la te m ovin g wit h velocity V.

/

)A~/////////////xplosive block.. . / //// -1 + \- $ + ;== ~=

t__.= = ~===:=== +

//////////////

Fig. 4 .

6

Pla te gen era tor sch em at ic. A la ter gen er-a t ion s ta ge, a fter exp los ive in it ia t ion , iss h ewn by th e n ew pos it ion of th e h or izon ta lp la tes in d ica ted by da sh ed lin es .

Th e flu x-compres s ion process of th e gen era tor ist hen evid en t.

Th e wid th of th e gen era tor , perpen d icu la rto th e p lan e of th e figu re, is den oted by w an d th elen gth , a s s h ewn on Fig. 4 , by .c. Wh en th e topand bot tom pla tes a re s epa ra ted by a d is ta n ce xth e gen era tor in du ctan ce is given by Eq. (16).

L =% = 1.257 ~ wH(MKS). (16)

If th e cros s -s ection a l a rea lx is wr itten a s T timesan effective rad iu s squ a red , th e in du ctan ce form u labecom es iden t ica l to th a t of Eq. (15a ) for a one-tu rn solen oid with n o edge cor rection .

The exp los ively driven p la tes gen era llya ccelera te somewh a t in th eir ea r ly s ta ges of mo-tion , bu t gradu a lly approa ch a m aximum velocitywh ich is govern ed by th e p la te an d exp los ive typesa n d t h ic kn es s es . After th is s ta ge is reach ed , ~is th en given by~=-p: . 2V. (17)

Th is approxima te con s tan cy of ~ form s th e ba s is ofth e s ta temen t th a t th e gen era tor in du ctan ce formu laof Eq. (8 ) approxima tes th a t for a p la te gen era tor.

Th e ra tio of th e gen era tor len gth to it swid th l/ u en ters Eqs . (16) an d (17) an d is u su a llyrefer red to a s th e number of squ a res in th e gen er -a tor. Th u s th e in du ctan ce of su ch a gen era tor is1 .257 pH per meter of p la te s epa ra t ion for ea chsqu a re, or 1 .257 nH for ea ch m illim eter of p la tes epa ra tion per squ are. In it ia l p la te s ep ara tion sfor su ch gen era tors s eldom exceed O. 1 m , an din it ia l in du ctan ces a re th erefore in th e few-ten th sm icroh en ry ran ge, depen d in g u pon th e n umber ofsqu a res . For rea son ab le cu rren t an d en ergy am -p lifica t ion , load in du ctan ces mu s t th erefore belim ited to a m axim um of a few ten s of n an oh en rys .In th is con n ect ion it m igh t be rema rked th a t th ein du ctan ce of th e t ra n sm iss ion lin e (Fig. 4 ) wh ichconn ects th e gen era tor to th e load , an d is a sou rce


10/34

or loss term , is a lso given by Eq. (16). Even fort ra n sm is s ion lin e p la te s epa ra tion s of on ly a m illim -eter , th e los s in du ctan ce exceeds 1 nH per squ a re.Su ch t ran sm iss ion lin es sh ou ld be kep t a s sh or t a n dwide a s pos s ib le an d s epa ra ted by th e sm a lles t d is -ta n ce compa t ib le with volta ge s ta n doff.

Th e ma jor advan tages of p la te gen era torsin clu de rela t ive s im plicity of con s tru ct ion , en or-mou s cu r ren t -ca r ryin g capacity wh ich is con trolledby th eir wid th s , a n d th e sh or t t im e sca le overwh ich th ey may be opera ted . Developm en t of n ewdeton a tion sys tem s n ow a llows in it ia tion of la rgea rea s of exp los ives with h igh s im u lta n eity. Th isadvan ce h a s proba b ly open ed u p n ew a rea s for gen -er at or a pp lica tion s .

3 . S tr ip Gen er at or s. Th e cros s s ectionof a s t r ip gen era tor is s h ewn sch ema tica lly in Fig.5 . In it ia l flu x is in trodu ced in to th e sys temwh ich con s is t s of th e gen era tor an d th e load coil.Th e d irection of cu r ren t flow is s h ewn by a r rowsan d th e magn et ic fields by cros ses . Deton a t ion ofth e exp los ive is tim ed to sh or t th e cu r ren t in pu t s lota t peak cu r ren t , or flu x, in th e sys tem . As deto-n a t ion proceeds down th e exp los ive s t rip , th e topp la te of th e gen era tor is d riven downwa rd , a s p ic-tu red by dotted lin es for on e t im e s tage of th edetonation. Th e flu x-compres s ion proces s isevident.

Fig. 5 ,Lood coil

Str ip gen era tor s ch ema t ic. Deton a t ionproceeds down th e exp los ive s t r ip an d ala ter gen era t ion s ta ge is in d ica ted by th en ew pos it ion of th e top con du ctor sh own byd as hed lin es .

Th e in du ctan ce of th e gen era tor a t a n ys tage of deton a tion is a ga in given approxima te elyEq. (15a ), wh ere th e term w is th e wid th of th egen era tor perpen d icu la r to th e figu re an d th eeffect ive rad iu s is th a t of a circle wh ose a rea

by

equ a ls th e rem a in in g gen era tor cros s s ect ion . Ini-t ia l in du ctan ces of su ch gen era tors s eldom exceeda few ten th s of a m icroh en ry. Gen era tors of th istype a re th e lea s t expen s ive to con s t ru ct. Th eycan a ls o be con s t ru cted to h ave la rge cu r ren t-ca ryin g capacity by m akin g th e wid th s su ita b lylarge. Con sequ en tly, th ey h ave been u sed exten -s ively for gen era t in g h igh magn et ic fields in la rgevolu mes (typ ica lly in th e low megagau s s ran ge).Th ey can a ls o be u s ed with advan tage to make in i-t ia l s tu d ies for p rogram s th a t requ ire n ew gen era -t or t ech n iq u es .

Th e mos t common va r ia n t of th is cla s s ofgen era tors h a s exp los ive s tr ips on both u pper an dlower p la tes . In th is ca se, th e m eta l con tou r iaa ltered in su ch a fa sh ion th a t th e d r iver p la tesform , in cros s s ect ion , th e equ a l a rm s of an is os -celes t ria n gle. In an oth er va r ia n t of th is gen era tortype, Bic h en kov 12 cla im s th a t 15% of th e in it ia lexp los ive en ergy was con ver ted to m agn et ic en ergy.Th is is th e la rges t s u ch con vers ion efficien cyrepor ted to da te.

4 . Cylin dr ica l Im plos ion Sys tem s .Severa l views of a cylin d r ica l im plos ion sys tema re sh own sch em a t ica lly in Fig. 6 . Two of th esketch es sh ow th e sys tem before deton a t ion . Th ein it ia l a s sem bly con s ia ts of a th in -wa lled cylin dercen tered with in an exp los ive r in g ch a rge to wh ichis a t ta ch ed a r in g of h igh qu a lity deton a tors . Th eth in -wa lled m eta l cylin der , u su a lly ca lled a lin er ,p la ys th e role of th e gen era tor a rm a tu re. An in i-t ia l flu x is in du ced with in th e lin er , in m os t ca s esby pa s s in g cu r ren t th rou gh a coil pa ir extern a l toth e sys tem . (See s.ko Sec. II. C. lb . ) Deton a tionof th e ch a rge is t im ed to correspon d to peak flu x inth e lin er . Th e th ird sketch sh ows th e pos it ion ofth e lin er a t a la ter s ta ge in th e im plos ion .

7


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6:+,:===_etonatorring \ \t h en r ec ove re d. Typ ica l in it ia l lin er in du cta ncesa re u su a lly on ly a few ten s of n a noh en rys s in cemos t lin er r a d ii an d len gth s a re on ly a few cen t i-meter s .

Th is cla s s of gen era tors is of h is tor ica lin teres t beca u se it wa s th e fir s t type d iscu s s ed inth e op en litera tu re. 3 Magn et ic fields in exces s of15 MG, th e la rges t ever a ch ieved terres t r ia lly,h ave been produ ced in some sys tem s . Su ch field scon ta in th e m os t con cen tra ted electrom agn et icen ergy den s ity ever p rodu ced over a n exper im en ta lW[ner 0r0ver5eegion --a lmos t a m ega jou le per cu b ic cen t im eterOwin g to th e ra p id ra t e a t wh ich a rea is

f (3) d!) decrea s ed du rin g th e la t ter s ta ges of imp los ion ,field r is es common ly ach ieve va lu es in exces s of15 MG/ / .rs .. Th e ra te of field in crea se is on e meas -u re of th e speed of gen era tor opera t ion . In th is\ / sen se, cylin d r ica l imp los ion sys tem s a re fa s terFig. 6 . Views of a cylin dr ica l im plos ion sys tem .

Th e u pper an d lower left figu res sh ow th esys tem before im plos ion . Cylindricalim plos ion is ach ieved by s im ulta neou slyin it ia t in g th e row of h igh qu ality det . on -tors mou n ted on th e r in g c ba rge. Th elower r igh t figu re sh ows a view of th elin er a t a la ter s ta ge of th e imp los ion .

In sofa r a s th e lin er m ay be ass um ed to beperfect condu ctor , flu x with in it is con served ac-cord in g to bas ic electromagn et ic th eory. Th efollowin g rela tion th en obta in s:

. .

a

BOR04 = BR. (18)

We can obta in th e s ame rela t ion from en gin eer in gcir cu it th eory a s follows : In th e absen ce of en dcor rect ion s , th e in du cta n ce of th e cylin der is givenapp roxima tely by Eq. (15 ) for a s in gle -tu rn s ole-n oid wh ere th e term rAJs th e len gth of th e lin er .Con serva t ion of flu x LI th en shows th a t th e lin ercu rren ts va ry in vers ely a s R2. Sin ce th e m agn et icfield is a lso p roport ion a l to th e cu rren t , Eq. (18 ) is

th an oth er gen era tors by an order of m agn itu de ormore. Ra tes of cu rren t in crea s e a re a lso u s ed a tt im es to cla s s ify gen era tor s peeds . However ,th is ra te is n ot in tr in s ic to a gen era tor cla s s s in cecu rren t -ca rryin g capacity ca n u s u a lly be a lter edby va ryin g th e wid th of th e gen era tor con du ctorswith ou t a pprecia bly ch an gin g th e gen era t ion t imescale.

Cylin d r ica l imp los ion s ys tem s a re expen -s ive. Grea t ca re m u s t be exercised to ma in ta ina s symmetr ic a n im plos ion as POSS ib le. Lin erdimen s ion s m u s t be h eld to very close tolera n cesan d on ly th e h igh es t qu a lity exp los ive sys tem s canb e t ole ra te d. On ly ra rely is th e region of h igh es tfield s (a sma ll region n ea r th e cen ter of th e lin er )su ita b le for exper imen ta l u se. However , th ereh ave been recen t im pres s ive a dvan ces in th e u seof tra n s formers in h igh field en vironmen ts . Th u s ,th ese sys tem s in combin a t ion with a cen tra lly lo-ca ted tran s former ca nn ot be ru led ou t a s powersou rces for some h igh speed app lica t ion s .

5 . Coaxia l or Cylin dr ica l Gen era tors .Th e u pper sketch of Fig. 7 s h ows a coaxia l


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rTo cap bank Annulor load coil Q ~+

T Ring of detonators

Fig. 7 . Coaxia l or cylin d r ica l gen era tors . Th eu pper figu re s h ews bas ic compon en ts ,con s is t in g of a n in n er , explos ive loadeda rm a tu re an d a cylin dr ica l ou ter s ta tor .A la ter gen era t ion s tage, a fter explos ivein it ia t ion , is in dica ted by th e con ica la rma tu re fron t movin g with deton a tionvelocity a n d sh own by dash ed lin es . Ava rian t of th is con s tru ct ion with extern a la rma tu re an d in tern a l s ta t or is s h ewn inth e lower figu re.

gen era tor an d loa d coil. Gen era tors of th is typea re u pon occa s ion a ls o ca lled cylin dr ica l gen era tors .Th e bas ic gen era tor compon en ts in clu de th e s ta tor ,or ou ter cylin der , an d th e a rma tu re, th e explos ive-loaded in n er cylin der . Th e load coil p ictu red isa n n u la r or dou gh n u t -sh aped . In it ia l cu rren t issu pplied by a capacitor ban k th rou gh th e an n u la rin pu t s lot a t th e left . Arrows sh ow th a t th e cu rren tflows a lon g th e ou ts ide cylin der , th rou gh th e loadcoil, an d back th rou gh th e a rm a tu re. Magneticfield lin es B, in d ica ted by circles an d cros ses , a recir cu la r or tan gen tia l. Th ey en cir cle th e a rma -tu re an d a re res t r icted es s en tia lly to th e an n u la rspace between th e a ta tor an d a rma tu re an d to th eloa d coil.

Deton a tion of th e a rm a tu re explos ive isa ga in t imed to close th e in pu t cu r ren t s lot a t su chtime th a t maximum cu rren t or flu x is in th esys tem . As deton a tion proceeds , th e a rm a tu reexpan ds in a con ica l fron t wh ich moves with deto-n a t ion velocity. Aga in , th e mann er in wh ich flu xis compres sed is clea r .

Th e lower sketch of Fig. 7 sh ows th e mos tcommon va rian t of th is cla s s of gen era tors . Hereth e cen tra l cylin der p lays th e role of s ta tor , wh ileth e ou ter cylin der becomes th e a rm a tu re. Th eexplos ive, in th e form of a h ollow cylin der , isdeton a ted by a rin g of deton a tors , s h ewn a t th eleft of th e figu re. Th e con ica l fron t of th e a rm a -tu re a t on e in s tan t of deton a tion is sh own by dottedlines.

Th e in du ctan ce of a coaxia l gen era tor oflen gth .4 a n d with ou ter an d in n er ra d ii (s t a tor an da rm a tu re for th e u pper sketch of Fig. 7) R2 an d RIis given by Eqs . (19):

L = # log R2/ R1 (19a)

L = 0.2 log R2/ R1 vH/ m . (19b)

Th e above in du ctan ce formu la s a pp ly on ly to a SYS -tern wh ere th e two cylin ders a re of equ a l len gth an dth e en d con du ctors a re perpen dicu la r to th e cylin -ders . Correct ion s mu s t be made for va r iou s con i-cal en d con du ctors a r is in g from th e a rma tu reexpan s ion , a s well a s those bu ilt in to th e sys temin it ia lly (Fig. 7 ). In it ia l in du ctan ces of coa xia lgen era tor s a re a lso sma ll, s eldom exceedin g a fewten th s of a m icroh en ry. As an example, from Eq.(19b) a cylin dr ica l gen era tor of 1 . 5-m len gth , withs ta tor rad iu s of 30 cm and a rm a tu re ra d iu s of 10cm, h a s an in it ia l in du ctan ce LG(0) = (1 . 5)(0 . 2)x log (30/10) = 0.33 PH.

Th is cla s s of gen era tors is ch a racter ized byh igh cu rren t -ca rryin g ca pab ility a n d ru ggedn es s .Sin ce cu rren t flows a lon g the cylin d r ica l axes , th e

9


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min imum wid th ava ila b le for ca r ryin g cu r ren t is th ecircum feren ce of th e in n er cylin der . In th e aboveexample th e a rm atu re, with a rad iu s of 10 cm , h a sa wid th of abou t 63 cm ava ila b le for th e cu r ren t.Su ch a gen era tor cou ld ca r ry ~bou t lIJ O MA for am icros econd or two.

Th e ru gged n a tu re of th e gen era tor can beseen from / Yig. 7. As men t ion ed ea r lier , exp los iveen ergy is con verted to magn et ic en ergy by forcib lymovin g th e gen era tor a rma tu re aga in s t magn et icfields t ra pped in th e gen era tor an d load circu it .The genera tor effectiven ess th erefore improves asth e magn et ic fields in crea se. Th e magn et ic fields ,in tu rn , exert p res su re on th e con du ct in g elemen tsof th e gen era tor . In th e cas e of th e cylin dr ica lgen era tor , th e pres su res tend to compres s th eim er cylin der an d expand th e ou ter on e. Becau s eboth con du ctors form complete clos ed su rfa ces ,th ey can su s ta in mu ch grea ter magn et ic p res su res .Th e sph erica l gen era tor d is cu s s ed below, a s wellas th e cylin dr ica l implos ion sys tem an d, with someres erva tion s , th e p la te gen era tor d is cu ss ed ea r lier .a re a lso ru gged . Th is is in con tras t to sp ira l a n ds t rip gen era tors wh ich a re of flim s ier con s t ru ctionan d a re often lim ited in performance by m agn eticforces.

6 . Sph er ica l Gen era tors . The sketch ofa sph er ica l gen era tor is s hown in Fig. 8, togeth erwith an an n u la r or dou gh n u t-s h aped load coil. Thegen era tor con s is ts of s ectors of two sph eres join edtogeth er with con ica l con du ct in g glide p lan es . In i-t ia l flu x is developed in th e sys tem th rou gh th e in pu tcu r ren t leads conn ected a cross th e circu la r open in gbetween th e in n er spher ica l s ector an d th e left con i-ca l s ection . Th e in n er sph erica l sector is d r ivenby th e exp los ive device (sh own cros s -h a tch ed) an dp lays th e role of th e a rma tu re. Th e ou ter s ph er ica ls ector is th e s ta tor . Th e exp los ive device is deto-n a ted a t s u ch a time th a t th e expan d in g a rm a tu resh orts ou t th e cu r ren t in pu t open in g a t peak in pu tcur ren t . Direct ion s of cu rren t flow a re in d ica tedby a r rows adja cen t to th e con du ctors . The

Curren tInput

Fig. 8 . Sph er ica l gen era tor sch ema tic. Th e in n ersph er ica l s ector is d riven ou twa rd by th ecen t ra l exp los ive an d s erves a s th e a rma -tu re. The extern a l s ph ere is th e s ta torand th e an n u la r r in g conn ect ed to th issph ere is th e load coil. A la ter gen era -t ion s tage, a fter exp los ion , is s h own byth e n ew pos it ion of th e a rma tu re in d ica tedby da sh ed lin es .

m agn etic field lin es a re circu la r or ta n gen t ia l a n da re loca ted symmetr ica lly a rou n d th e gen era toraxis . Th eir direction s in to an d ou t of th e d iame -t ra l sect ion sh own in th e figu re a re in dica ted bycross es an d dots , respectively. The pos ition ofth e a rm a tu re pa r t way th rou gh gen era tor act ion isin d ica ted by th e da sh ed circu la r a rcs . The flu x-compress ion process is aga in eviden t.

Th e in du ctan ce of th e gen era tor depen dsu pon th e d ifferen ce of th e two sph erica l ra d ii a n du pon th e cone ha lf-a n gle. Den otin g th e s ta tor an darma tu re ra d ii by R ~ and R ~, respectively, a n d th econ e h a lf-a n gle by 8 , th e in du ctan cebecomes:

L = (P/ ~) (R2-R1) 10g (cot ~)

expression

(20a)

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L = 0.4 ( R2 -R1) log (cot ;), PH (MKS) (20b)

As a specific example, wh en th e cone h a lf-a n gle isO. 1 ra ci an d th e s ta tor an d a rm a tu re ra d ii d iffer by1 m th e in du ctan ce of th e gen era tor is 1 .2 KH,

In common with th e coaxia l gen era tors d is -cu s sed ea r lier , th is gen era tor a ls o h a s en ormou scu r ren t - cd r ryin g capab ility an d h a s a p a r t icu la r lyr u gged con s tr u ct ion . Th e sph er ica l s h ape of th ea rm a tu re makes it a tt ra ct ive for u s e with n u clea rdevices , a n d a lso ea s es th e prob lem of con s tru ct in ga su ita b le deb ris con ta inmen t vess el if s u ch isrequired.c. In it ia l E ner gy Sources

As n oted in Eq. (5 ), th e en ergy ou tpu t of agen era tor is p roport ion a l to th e in it ia l en ergy E oin t he gen er ator . For th is rea son it is u su a lly ad -van tageou s to load gen era tors in it ia lly with th ela rges t amou n t of en ergy pos s ib le. Gen era tors a reflu x-compress ion devices an d a lm os t an y sou rceth a t can fu rn is h th e in it ia l en ergy in m agn et ic formis a poten t ia l s ou rce for th e in itia l gen era tor en ergy.Gen era tors a ls o work more efficien t ly aga in s t la rgemagn et ic fields an d it is u su a lly advan tageou s toh ave th e in it ia l magn etic en ergy a ls o a t rea son ab lyh igh fie ld s .

Pr im a ry en ergy sou rces a re d is cu s s ed inSec. II. C. 1 . Th e d is cu s s ion is res t r icted to capa -citor ban ks , in du ct ive s tores , a n d ba ttery ban ks ,a lth ou gh for some low-en ergy devices oth er sou rces ,s u ch a s fer roelectr ic an d fer rom agn etic m a ter ia ls ,h a ve a p p lic a tio n . Gen era tors a s in term ed ia te en er -gy boos tin g sou rces a re t rea ted in Sec. H. C. 2 .

1. Pr im ary En ergy Sou rces . In it ia len ergy can be su pp lied to gen era tors eith er bypa s s in g cu r ren ts th rou gh th em directly, th erebycrea tin g th e in it ia l magn et ic fields , or by gen era -t in g th e fields in an extern a l coil wh ich su r rou n dst h e gen er a tor . Capacitor ban ks a re u s ed a lm os texclu s ively a s d irect field en ergy sou rces , wh ere-a s extern a l s ou rce coils m ay a lso be su percon du ct -in g or b a tt er y- pow er ed .

a . Direct Feed . Previou s illu st r a-tion s (Figs . 2 , 4 , 5 ,a n d 7) sh ow leads from capa -citor ban ks to th e gen era tors . Th e cu r ren t d is -ch a rge th rou gh th e circu it u pon switch in g in th ecapacitor ban k follows th e cla s s ica l s in u soida l d is -ch a rge repres en ted by Eqs . (21):

f rEOCI=VO ~ Sin u t = LT SinmtTE _l- ~ CV02Oc

a? dLOI = Lo 2Eoc/ LTOGL

E=~OEoc.OG T

(21a)

(21b)

(21C)

(2 ld )

(21e)

Here, C is th e capacita n ce of th e ban k , V. it sc b a rgin g volta ge, LT th e tota l in du ctan ce of th ecircuit .

Th e per iod of th e d is ch a rge is given by Eq.(21b ) an d maximum cu rren t occu rs a t th e qu a r terper iod . As des cr ibed ea r lier , gen era tor deton a tionsys tem s a re t im ed to clos e off th e cu r ren t in pu t su p-p ly a t , or n ea r, peak cu r ren t an d Eqs . (21d) an d(2 le) th en give th e in it ia l flu x an d en ergy of th egenerator. After th is tim e th e capacitor ban k isou t of th e circu it a n d Eqs . (21 ) no lon ger app ly.

Th e pres en ce of res is ta n ce in th e circu itn eces s ita tes some modifica t ion s in Eqs . (21). Us u -a lly th e effects a re rela t ively sm a ll. Cu rren ts a ren orma lly redu ced by 10-1570 an d in it ia l gen era toren ergies by 20-30Y0 . However , in ca s es wh ere th egen era tor in du ctan ce is sm a ll it is im pera t ive tokeep th e was te in du ctan ce term s sm a ll, a s s eenfrom Eq. (21e), oth erwis e mu ch of th e in it ia l en er -gy ava ila b le from th e capacitor ban k will en d u p ins ou rce in du ct an ces .


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Capacitor ban ks th a t s td re en ergy in excessof 100 kJ a re n ow rela t ively common . Generallyspeakin g, in s ta lla t ion an d ma in ten ance cos ts go u pa s th e inh eren t d isch a rge time of th e ban k is de-creased. Th e in h eren t d is ch a rge tim e of a ban k ofgiven en ergy is redu ced a s th e capacita n ce is de-crea sed (wh ich th erefore requ ires a h igh er ban kvolta ge), an d a ls o as th e los s indu ctan ce term s a rereduced. Su ch cos ts for fa s t ban ks can exceed byan order of m agn itu de those for a s lower ban k of th esa me en ergy. With in ra th er wide lim its gen era toropera tion is rela t ively in depen den t of th e tim e re-qu ired to su pp ly th e in it ia l en ergy. Th u s rela t ivelyS1OW ban ks of modes t volta ge are effective a s in itia len ergy sou rces --a con s iderab le advan tage from anecon om ic viewp oin t.

b . In d irect or In du ctive Feed. Gen er-a tors a re in it ia lly en ergized in du ctively wh en th efollowin g d ifficu lt ies a re experien ced :

(1 ) Pertu rba t ion s th a t a r is e from exp los iveclosu re of th e cu rren t in pu t open in gs n ecess a ry ford irect cu rren t feed a re exces s ive,

(2 ) In itia l capa cit ive s torage is too h eavy orbulky,

(3 ) In it ia l gen era tor in du ctan ce is so lowth a t th e sou rce in du ctan ce in th e capacitor circu its tores too mu ch of th e ava ila b le en ergy,

(4 ) Forces on th e gen era tor or load a re toogrea t with d irect feed .

(1 ) Elim in ation of Per tu rb ation s.An a s sembled cylin dr ica l im plos ion sys tem an dsome of it s compon en ts a re s h ewn in Fig. 9. Theth in -wa lled cylin der , or lin er , is of s ta in less s teelwith a th in in n er cla dd in g of copper. A capacitorban k in trodu ces flu x in to th e lin er by en ergizin g th ecoil pa ir s tra dd lin g th e exp los ive r in g c ba rge. Thedeton a tors h ave n ot yet been mou n t ed on th e ch a rge.Th e absen ce of an in pu t lin er s lot p reclu des per tu r -ba t ion s du r in g exp los ive compress ion an d th e sys temPerform s qu ite rep rodu cib ly. The en ergizin g coilsa re su fficien t ly s tu rdy th a t in it ia l magn etic fields oforder 25 kG can be in du ced with in th e lin er.

. .. .-. ..

\

- ;. -W-d. , . . ... ,>.,: t.-.b- -:... t~. .-. . .,... r., ,. u ---------------- . . . . .

Fig. 9 . Ph otograph of cylin dr ica l flu x- compres -s ion sys tem componen ts . Th e a s sembledsys tem is sh own a t th e top. In d ividu a lcompon en ts sh own in clu de a coil pa ir a n dth e th in -wa lled cylin dr ica l lin er . Ther in g of deton a tors h a s n ot yet beena t ta ch ed to th e ch a rge shown in th e a ss em -b led s ys tem .

Compres s ion fields of a rou n d 4 MG are obta in ed byimplos ion . At tempts to pu t more en ergy in th es ecoils resu lt in des t ru ction of th e coils by magnet icforces. When th e en ergizin g coils a re wou n d ofh eavy weld in g cab le th ey can su s ta in som ewh a th igh er cu rren ts before des tru ct ion an d in it ia l m ag-n etic fields of 30-35 kG can be in du ced in th e lin er .Compress ion fields of 5 -6 MG can th en be ob ta in ed .Effor ts to ob ta in s till la rger in it ia l fields by mean sof coil pa ir s h ave led to oth er magnet ic force effectswh ich per tu rb th e sys tem . High er in it ia l fields ,su ch as th ose requ ired to produ ce compres s ionfields of 10 MG or more, a re n ow u su a lly produ cedin a s in gle coil wh ich su r rou n ds both th e lin er an dth e exp los ive sys tem .

Th e a rma tu re, or lin er, is made of s ta in -les s s teel becau s e it s res is t ivity is rela t ively h igh ,bein g some 30 t imes th a t of copper . If th e lin erwere per fectly condu ctin g th en n o in it ia l flu x cou ldbe in du ced with in it . With lin er th ickn es ses oforder 1 -2 mm an d d iameters of order 10 cm , typi-Cd of th e sys tem s u sed h ere, capa citor ban k-coilp a ir r is et im e$ of 150-200 ps a re su fficien tly lon g

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for a dequ a te flu x pen etra t ion th rou gh th e lin er . Onth e oth er h and, th e implos ion time sca le is moreth an an order of magn itu de fa s ter . Rela t ively goodflu x trapp in g th en resu lts du rin g imp los ion becau sein su fficien t t im e is ava ila ble for a ppreciab le flu xdiffu sion ou t of th e lin er.

In some of th e ea r lier cylin dr ica l imp los ionsys tems t~ lin ers were s lot ted so th a t th ey cou ldbe en ergized direct ly by a capacitor bank . Th elin ers cou ld th en be made of bet ter condu ctors , su cha s a lu m in um or copper . Sys tems u s in g th eselin ers cou ld produ ce compress ion fields u p to 2 or3 MG in a fa ir ly reprodu cib le mann er , bu t th eperforman ce became more erra t ic a s th e in it ia lfields were in crea sed to va lu es n eces sa ry for pro-du ct ion of h igh er compres s ion fields . Th e originof th e erra t ic beh avior was traced to imp los ion per-tu rba t ion s ca u sed by th e lin er s lot.

(2) Redu ct ion in Size of In itia lEn ergy Su pply. Except in g wa ter capacitor , wh ichh ave a s torage lifetim e of on ly a few m icroseconds ,ca pacitors a re rela t ively bu lky as en ergy s tores .Typ ica l h igh -en ergy den s ity capacitors s tore en ergya t a few ten th s of a jou le per cu b ic cen t imeter an dabou t 150 J / kg , wh ereas wa ter ca pacitors can s torea jou le per cu bic cen t imeter for a sh or t time. Onth e oth er h and, a magn etic s tora ge u n it with a fieldof abou t 30 kG h as a s torage en ergy den s ity of 3 .5J / cm3, a n order of magn itu de grea ter th an th e cor-respondin g u nit for h igh - en ergy den s it y capacitors .Sim ila r ga in s can be obta in ed with in du ct ive s toresfor th e en ergy s torage den s ity per u n it mass .

In a recen t tes t ser ies , gen era tor-poweredpla sma gu n s were rocket -lau n ch ed to a ltitu des of200 km. 13 Upon fir in g, th e pla sma gu n s disc ba rgedsome 300 kJ of neon pla sma in to th e ionosph ere.Th e tota l rocket pa yload wa s abou t 500 kg, of wh ich230 kg wa s a llowed for th e gen era tor power su pply.Th is mass lim it was met , a s were a n umber ofadd it ion al geom etr ic an d con stru ct ion al con stra in ts .Su ch pla sma gu n s a re norma lly powered by capaci-tor ban ks , bu t th a t wa s clea r ly imposs ib le in th is

ca se s in ce th e ban k and its a s socia ted circu it rywou ld h ave requ ired a mass of some 8000 kg. ofth e tota l power s u pply mass , 140 kg were requ iredfor th e in it ia l en ergy sou rce, a sma ll 16-kJ capa -citor bank made of h igh -en ergy den s ity capa citors .

Some con s idera tion h as been given recen tlyto a s im ila r exper imen t in wh ich comparab le massan d s ize res tr iction s were placed u pon th e powersu pp ly bu t where p la sma en ergies of a few mega -jou les were requ ired . Resu lts of ea r ly ca lcu la tion sru led ou t a capa citor bank as th e in it ia l en ergys tore becau se of th e exces s ive mass and volumerequired. On th e oth er h and, in du ct ive en ergys torage appea red qu ite fea s ib le. An extern a l sole-n oida l coil wou nd a rou nd th e gen era tor wou ld been ergized, th u s s u pplyin g th e in it ia l magn etic en er-gy to th e gen era tor. Two types of in du ct ive s toress eem ed fea sib le: a h igh pu rity, cryogen ica llycooled a lumin um coil, powered in fligh t by a ba t-tery bank; an d a su percon du ct in g coil en ergizedbefore lau n ch . Pa r t ly becau se of s ch edu lin g prob -lem s , it was decided to res tr ict fu rth er in ves t iga -t ion s to th e su percondu ct in g coil en ergy s tore. Asma ll exper imen ta l effor t was u n der taken to tes tu se of th is type of s torage for gen era tor a pp lica -tions. At firs t glan ce it m igh t appea r u nn eces sa ryto tes t su ch a sys tem . However, th ere were somequ es t ion s rela ted to th e mu tu a l cou plin g of th e ex-tern a l s tora ge coil to th e gen era tor du r in g th eexplos ive gen era t ion s tage. From th e s tan dpoin tof su pplyin g th e in it ia l en ergy to th e gen era tor ,t igh t cou p lin g of th e s torage coil an d gen era tor isdes irable. However , idea lized ca lcu la t ion s a lsos h ow th a t u n les s th is cou p lin g is redu ced n ea r gen -era tor bu rn ou t mu ch of th e en ergy gen era ted willretu rn to th e en ergizin g cell.

Figu re 10 shows th e va r iou s gen era tor com -pon en ts u sed in th e su percon du ct in g s tora ge tes ts er ies . Th e s pira l s ect ion of a sma ll h elica l gen er-a tor is sh own in th e cen ter . In pu t lea ds from acapa citor bank , when u sed, a re a t th e top, an d anin tegra l coaxia l load coil exten din g beyond th e

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-,

..

Fig. 10 . Sma ll-sca le gen era tor u s ed in flu x in pu ttes ts . Th e sp ira l sect ion with in tegra lcoaxia l load is s h ewn in th e cen ter. Th eth in -wa lled a lum in um a rma tu re, loadedwith ca s t cyclotol explos ive, is s h own a tth e righ t. In it ia l flu x is in trodu ced in toth e genera tor in s evera l ways : by capa -citor ban k d irect feed th rou gh cablesbolted to th e holes sh own in both sp ira la nd a rma tu re in pu ts ; by in du ct ive feedth rou gh th e capacitor bank powered coils hown a t th e left , in to wh ich th e gen er -a tor fit s ; a nd by a s teady field produ cedby a su percondu ctin g coil s hown in Fig.. .11 .

gen era tor win d in g is s een a t th e bottom of th is sec -tion . Th e gen era tor a rma tu re, made of a lum in uman d loaded wit h cyclotol, is s h ewn a t th e r igh t.Severa l iden t ica l gen era tors of th is type were firedwith va r iou s sou rces of in pu t en ergy, in clu d in gd irect feed with a capacitor ban k , in du ctive feedth rou gh an overwou n d coil powered by a capacitorbank (a s sh own at th e left in Fig. 10), a n d fin a lly,in direct feed from a su percon du ctin g coil a s shownin Fig. 11 . The genera tor , wh ose ou ter d iameter

Fig. 11. Su percon du ctin g coil u s ed a s sou rce ofin it ia l gen era tor flu x. On ly pa rt of th ecoaxia l load sect ion of th e gen era torshown in Fig. 10 is vis ib le, projectin gbelow th e su percon du ctin g coil s ys tem .

wa s on ly abou t 11 cm , is ju s t vis ib le in Fig. 11project in g from th e bot tom of th e h elium dewa rwh ich hou ses th e su percon du ctin g Nb-Ti coil.

In a ll th e tes ts an effort wa s made to su pp lyabou t th e same in pu t flu x to th e gen era tor . R e la -t ive genera tor performan ce for th e va r iou s tes tswa s gau ged by th e ra tio of maximum ou tpu t cu r -ren t in to th e coaxia l load coil a t gen era tor bu rn ou tto th e in it ia l flu x su pp lied to th e gen era tor.

Th e tes t resu lts were qu ite sa t is fa ctory.Th e bes t resu lt s were obta in ed with su percon du ct -in g en ergy s torage and th e wors t with direct feed.The ra tio of maximum gen era ted cu rren t to in it ia lflu x for th e su percon du ct in g feed tes t wa s some 15~0grea ter th an th a t for th e d irect feed tes t .

(3 ) Overcom in g Sou rce In du ctan ces ,Magn etic fields p rodu ced by d irect cu r ren t feed a re

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u su a lly clos ely con fin ed to th e cu r ren t ca r ryin g ele-men ts , in clu din g th os e of th e gen era tor . In t hiss en s e su ch feed is efficien t. Th is m ay be compa redto in d irect feed s itu a t ion s , su ch a s sh own in Fig. 9for th e cylin dr ica l implos ion sys tem feed wh ereextern a l coil pa ir s a re u s ed . Here, th e bu lk of th emagn et ic en ergy is loca ted ben ea th th e coils an d n otwith in th e lin er . In oth er words , th e cou p lin g is}qu it e poor . In d irect feed becomes more efficien tth an d irect feed wh en th e sou rce in du ctan ce in th ed irect feed a r ran gemen t gr ea t ly exceeds th e in du c -ta n ce of th e gen era tor . Su ch a ca s e is illu s t ra teds ch ema t ica lly in Fig. 12 .

As p ictu red , th e en ergizin g circu it con s is t sof a 100-kJ capacitor ban k with a circu it sou rcein du ctan ce of O. 1 IJ H. Th e low in du ctan ce of th es in gle-tu rn solen oida l load coil, 4 .2 nH (a s ca lcu -la ted from Eq. (15 a )), m akes it u n fea s ib le to en er -gize it d irect ly beca u s e of th e la rge sou rce in du c-tan ce. As s een from Eq. (21e) on ly abou t 47 . of th ein it ia l ban k en ergy EOC gets in to th e load coil. ASca lcu la ted from Eq. (21 a ) th e peak cu r ren t th rou ghth e circu it is IPK = [2 x 1 05 / (0 . 1 00 0+O. 0 04 2)1 0-~1 2= 1 .39 MA or 2 .28 MA/ m over th e 61-cm coil len gth .Magn et ic fields in lon g solen oids a re given by B = IJ J ,

(b) q1---1 .Fig. 12 . Flu x in ject ion in to a s in gle-tu rn solen oid

by d irect feed (a ) an d by in du ct ive feed(b ). Th e s in gle-tu rn solen oid h a s arad iu s of 2 .54 cm , an d len gth 61 cm .Th e mu lt ip le-tu rn solen oid h a s a rad iu sof 3 .05 cm an d 61 tu rn s a re equ a llyspa ced over a len gth of 61 cm .

wh ere J is in am peres per m eter. For th is ca s eth e peak field becomes BPEAK = 2 .86 W/ m2 or 28 .6kG. Th e s ame an a lys is for ca s e (b ) of Fig. 12 ,wh ere th e coil in du ctan ce is 22 .1 uH, gives IPK. [2xlo5 / (o. 1 +22 .1 )1 O-Y2 = 95 M. Howevers in ce th ere is 1 tu rn / cm , th e lin ea r cu r ren t den -s ity becom es 9 .5 MA/ m an d th e solen oids field a tpeak becomes BP:*K = 11 .9 W/ m2 of 119 kG.

Th is example pres en ts a ra th er extrem ecompa r is on becau s e sou rce in du ctan ces can u su a llybe made con s iderab ly sm a ller th an O. 1 KH an d th ecou p lin g of th e s in gle-tu rn solen oid to th e m u lt ip le-tu rn solen oid is som eth a t bet ter th an can u s u a llybe rea lized . Never th eless man y ca ses a r is e inwh ich it is more profita b le to en ergize in du ctively.

(4 ) Redu ct ion of Magn et icForces. Magn etic fields exer t forces on cu r ren t -ca r ryin g con du ctors an d can be qu ite trou b lesome,n ot on ly on u n su ppor ted con du ctors du r in g th e exp lo-s ive or gen era tion s ta ge of a gen era tor bu t a lsodu r in g th e time in wh ich th e in it ia l en ergy is in t ro-du ced in to th e gen era tor. Th ese m agn et ic volum eforces can be con ven ien tly t rea ted a s pres su res onth e con du ctin g su rfa ces given by Eqs . (22):

2P = ~ (CGS)

2P = ~ (MKS).

(22a)

(22b)

Figu re 13 illu s t ra tes both d irect a n d in du ct ive feedof th e p la te gen era tor wh ose len gth is 1, in it ia lh eigh t Xo, an d wid th u (perpen d icu la r to th e figu re).In th e d irect feed ca s e th e magn et ic field is es s en -t ia lly con fin ed to th e in ter ior of th e gen era tor an da ll gen era tor faces a re su b jected to magn et ic p res -s u res wh ich ten d to force th e p la tes ou twa rd . Inca s e (b ), th e fields on both s ides of th e gen era torfa ces a re equ a l. Alt bou gh th ere a re n et compres -s ive s t res s es on th e gen era tor p la tes , th ere a re n on et forces on th e p la tes ; con s equ en t ly th ere is n oten den cy for th e gen era tor to expan d .

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As an example, if th e p la te a rea .1 den s ity is 1.S=0

B=o /(a) Direct feed (b) Inductive feedFig. 13 . Magn et ic field s p rodu ced in an d ad ja cen t

f!o a recta n gu la r cros s -sect ion coil byd irect cu rren t feed (a ) a n d by in du ct ivefeed (b ).

We can es t im a te th e degree of motion of th etop an d bot tom p la tes for th e d irect feed ca se a sfollows . Let th e a rea l den s ity of th e pla tes be mgrams per squ a re cen t im eter , an d su ppose a peakmagn et ic field BM is bu ilt u p in th e gen era tor intota l t im e T. Th e field depen den ce on t im e isa s sum ed to be of th e form

B(t) = BM (;)n . (23)

Wh en n = 112 , th e field bu ildu p approxim a testh e s in u soida l t im e va r ia t ion ob ta in ed by capa citorba nk feed , wh ile n = 2 correspon ds more closely tofield bu ildu ps ob ta in ed from explos ives gen era tor s .Th e pres su re on a u n it a r ea of th e p la te is given byEq. (22a ) a n d th e equ a t ion of motion of th e pla tebecomes

m j/

Th e

B2. 8r u g (+)2.

p la te d isp lacem en t Ax a t t im e t becomes

2M t(2n + 2)Ax==.

T2n (2n + l)(2n +2)

an d th e d isp lacem en t a t B , t = T, becom esM.

BM(Ax)T = ~ T(2n + 1) (2n + 2)

(24)

(25)

(26)

gin / cm (somewh a t more th an 1 mm th ick for cop-per ) a n d a peak field of 100 kG is obta in ed in 50 u sfrom a capa citor d isch a rge, th e p la te is d isp la cedabou t 1 .7 mm when th e field rea ch es 100 kG.

Su ch a d isp la cem en t is in tolera b le for mos tsys t ems . III th e ca se of th e p la te gen era tor , a dd i-t ion a l exp los ive m as s res ts on top of th e u pper p la tea n d th is in crea ses th e effect ive m as s by perh aps a norder of m agn itu de. Even so, th e resu lt in g d is -p lacem en t of O. 17 mm is s t ill s er iou s for someappl icat ions . It is clea r from Eq. (26 ) th a t th ed isp lacem en t is les s ser iou s if th e t im e T can bereduced. For example, of two capa citor ban ks ofequ a l en ergy bu t d ifferen t ca pa cita n ces , th e on e ofsm a ller ca pacitan ce wou ld deliver its en ergy to th ecoil in a s h or ter t im e an d th ere wou ld be les s p la t edisplacement .

Anoth er way of com ba t t in g th e d is p la cemen tp rob lem is to s a cr ifice s ome in it ia l flu x in th e gen -era tor by fir in g it before pea k field is r ea ch ed .Th u s from Eq. (23 ) when n = 1/ 2, 90% of th e max-im um flu x is reach ed wh en t = O. 81 T. Su bs t itu t ionof th is t im e in Eq. (25 ) s h ows th a t th e d isp lacem en ta t th a t t im e is on ly a bou t O. 9 mm in s tea d of th e1 .7 mm ob ta in ed a t pea k flu x. Th e sma ll s a cr ificein flu x is u s u a lly worth a ccep t in g to rea lize th es ign ifica n t decrea s e in gen era tor compon en t dis -placement s .

2 . Gen era tors a s In term ed ia t e En ergyBoos ters . Gen era tors a re fr equ en t ly u s ed a s in ter -media te en ergy boos ters (Fig. 14).

A B c DFig. 14. Circu it s ch ema tic of a sys tem th a t

em ploys a s er ies boos ter gen era tor B.Th is gen era tor boos ts th e in it ia l en ergys tored in th e ca pa citor ba nk A to ah igh er va lu e wh ich th en s erves a s th ein it ia l en ergy for th e ou tpu t gen era tor C,wh ich fin a lly en ergizes loa d D.

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Gen era lly speak ing, th e type of ou tpu t gen er -a tor C requ ired is determ in ed by th e ch a ra cter is t icsof th e load D to be en ergized . Two s itu a t ion s a r is efrequ en t ly in wh ich it is n ot fea s ib le to power th em a jor ou tpu t gen era tor d irectly from th e pr im a ryen ergy sou rce A. Firs t , th e pr im a ry en ergy sou rcemay s tore les s en ergy th an requ ired to en ergize th eou tpu t gen era tor . Secon d, th e magn et ic fore es gen -era ted du r in g in it ia l en ergy bu ildu p in th e ou tpu tgen era tor by d irect feed may be too d is ru p t ive. Thefollowin g examples illu s t ra te th es e poin ts .

a . En erg y Boo s tin g . Figu re 15 sh owsa sh ot a ss embly on th e fir in g table. Th e as s emblyin clu des an en ergy boos t in g gen era tor. Th e su bs e-qu en t shot wa s on e of th e prelim in a ry tes ts lead in gto th e developmen t of th e power su pp ly u s ed in th erocket -lau nch ed p la sm a gu n experimen ts m en tion edea r lier , in wh ich th e pr ima ry en ergy sou rce was a16-kJ capacitor ban k . Th e ver tica l coaxia l loadcoil, s h own a t th e righ t , h ad an in du ctan ce abou tequ a l to th a t of th e average p la sma gu n in du ctan ce(wh ich a ctu ally va r ied with time du rin g d is ch a rge).The cab les com ing from th e top of th e load coilwere conn ected to field mea su r in g probes .

Th e ou tpu t , or ma jor, gen era tor conn ectedto th e load coil is s hown in th e cen ter . It is a

Fig. 15 . Shot setu p with a s eries boos ter gen era tor .

rela tively low in du ctan ce sp ira l gen era tor capab leof ca r ryin g s evera l megamperes an d su pp lyin gs evera l h u n dred k ilojou les in to th e p la sm a gu n load ,p rovided in itia l in pu t en ergies of 60-75 kJ a reava ila b le. Sin ce on ly 16 kJ were a va ila b le in th ecapacitor ban k , th e sp ira l gen era tor s h ewn a t th eleft (pos it ion ed h or izon ta lly) wa s des ign ed to boos tth e en ergy to abou t 75 kJ a s in it ia l en ergy for th em ajor gen er ator . Th e m a jor gen era tor wa s a ls o asp ira l gen era tor with low in it ia l in du ctan ce an drela t ively h igh cu rren t -ca r ryin g capacity. Leadsfrom th e in it ia l capa citor ban k en ergy sou rce en terth e boos t er gen era tor from th e left . Th e ou tpu t ofth e boos ter gen era tor is con nected to th e in pu t ofth e ma jor genera tor by coaxia l cab les . Th e ma jorgenera tor wa s n ot deton a ted u n t il boos ter gen era torburnou t . Du r in g th e boos ter gen era t in g s ta ge, th ema jor genera tor fu n ction ed a s a load coil.

In th e a r ran gemen ts s h ewn in Fig. 15 an din Fig. 16 , wh ich is d is cu s s ed la ter , th e boos tergen era tors a re ser ies -con n ected to th e ou tpu t gen -era tor. It is a ls o poss ible to en ergize ou tpu t gen -era tors in du ct ively by mean s of boos ter gen era tors ,a lth ou gh it wa s not p ra ct icab le for th e rocket -la u nch ed power sou rce.

b. Force Redu ct ion . Equ a t ion (26)gives an approxima te expres s ion for gen era torcompon en t d is p la cem en t wh en a peak magnet icfield BM is rea ch ed in a time T.

Th e d isp la cem en t depen ds s t ron gly on th etime h is tory of th e field r is e to peak . Equ a t ion(26) wa s derived u n der th e a ssumption th a t th e mag-n et ic field in crea s ed to peak accord in g to Eq. (23),wh ere th e s in u soida l field r is e p rodu ced by

l?ig. 16. Two-s ta ge s t r ip -p la te gen era tor .

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ca pa citor ban ks wa s a pp roxima ted by u s in g n = 1/ 2in th e equ a t ion . On th e oth er h an d, th e field bu ild -u p from man y exp los ive gen era tor sou rces is fa ir lywell a pproxim a ted with a va lu e of n = 2 . Accord in gto Eq. (26 ), th e componen t dis placem en t su fferedfrom capa citor ba nk en ergiza t ion wou ld be fivet imes a s grea t a s th a t ob ta in ed from gen era tor en er-giza t ion to, th e sam e field BM in t ime T.

Th e above d is cu s s ion is on ly qu a lita t ive, bu tth e pr in cip le in volved is qu ite r ea l a n d in m anycases m in im iza t ion of componen t disp lacem en ts iscru cia l. Figu re 16 is a ph otogra ph of a two-s ta gegen era tor s ys tem illu s tr a t in g th is p r in ciple. Th es ys tem con s is ts of two ser ies s t r ip gen era tor boos -ters , th e tr ia n gu la r ch ann eled section s , a n ou tpu tpla te gen era tor an d a load coil. Th e cylin d r ica lloa d coil an d p la te gen era tor ca vity a re formedfrom th e la rge cen tr s3 bra s s wedge. Th e s t r ipgen era tor explos ive (n ot sh own ) con s is ts of s t r ipsof sh eet explos ives p laced in th e fou r ch an n els ofth e t r ia n gu la r sect ion s . Th e p la te gen era tor exp lo-s ive s ys tem con s is ts of a sepa ra te p iece of HE,togeth er with a p la n e wave len s . Th ey a re p la cedu pon th e ch an n eled fla t s ect ion over th e tr ia n gu la rwedge cu t ou t of th e bra s s block. Th e sequ en ce ofopera t ion s is a s follows : In it ia l en ergy is su pp liedto th e en t ire a s semb ly from a capacitor ban kth rou gh th e in pu t s lot a t th e top . At peak flu x, th es b eet explos ives a re deton a ted a t th e fa r en ds of th et r ia n gu la r s t r ip gen era tor s . After closu re of th ein pu t cu rr en t s lot , deton a t ion p roceeds an d flu x ispu s h ed in to th e p la te gen era tor a n d loa d cavit ies .Th e pla te gen era tor explos ive is deton a ted a t s u cht im e th a t th e top pla te s ta r ts compres s in g th e flu xin th e wedge-sh a ped cavity u pon bu rn ou t of th es tr ip gen er at or s.

Th is sys tem wa s fir s t developed to produ ceh igh m agn et ic field s in th e loa d coil. In it ia l field sp rodu ced by th e capa citor ban k were a bou t 75 kG,th e m axim um va lu e th e sys tem cou ld with s ta n dwith ou t exces s ive s t ru ctu ra l d is tor t ion from mag-n et ic for ces . Th e s tr ip gen era tor a ct ion in crea s ed

th is field to abou t 375 kG a s th e s t a r t in g field forth e p la te gen era tor s ta ge. Aga in , field s h igh erth an th is va lu e p rodu ced too mu ch d isp lacemen t ofth e top pla te. Fin a l field s of a rou n d 2 MG werep rodu ced in th e loa d coil a t p la te gen era tor bu rn -ou t .

A n umber of in ves t iga tors h ave u s ed s p ira lgen era tors a s boos ters for coaxia l gen era tors , a n dSakh a rov et a l. 5 h a ve developed a sys tem in wh icha sp ir a l gen era tor is u s ed a s a boos ter for a cylin -d r ica l flu x-compres s ion sys tem .D. Tech n ica l Aspects of Gen era tor Tech n ology

Switch in g an d pu ls e s h ap in g gen era tor ou t-pu ts in d irect loa d - feed s itu a t ion s a re discu s s edb riefly in Sec. II. D. 1 . Use of tra n s former cou p lin gto exten d th e ra n ge of im pedan ces ca pab le of bein gen ergized by a gen era tor is t rea ted in Sec. H. D. 2 .Va riou s gen era tor lim ita t ion s a re dis cu s s ed inSec. II. D. 3 , an d it is sh own th a t h igh -en ergyd irect feed of la rge in du ct ive s tora ge u n its by agen era tor is n ot fea s ib le. Sect ion II. D. 4 p resen tsidea lized ca lcu la t ion s wh ich sh ow th a t su ch in du c-t ive s tora ge u n its ca n be en ergized th rou gh tra n s -form er cou plin g.

1 . Switch in g an d Pu ls e Sh ap in g. It wa smen tion ed ea r lier th a t , s u b ject to con d it ion s dea l-in g wit h th e n a tu re of th e s in gle ou tpu t pu lse, gen -era tor ou tpu t s can often be h an d led in ways cu s to-m a rily u sed with m ore con ven t ion a l electr ica lsources .

Th e ou tpu t of a s p ira l gen era tor u s ed in th eO-p in ch exper imen ts of Refs . 9 a nd 10 was sh a rp -en ed by mean s of a n on lin ea r fu s in g elem en t s oth a t an in it ia l h igh -voltage sp ike cou ld be p laceda rou n d th e 6 -p in ch coil. Th e exper im en ta l s etu pu s ed is sh own sch em a tica lly in Fig. 17. Th e gen -era tor bu rn ou t t im e wa s abou t 40 ps . Becau s e ofits rela t ively s h or t len gth , th e O-pin ch p la smacou ld be s u b jected to m agn et ic compres s ion foron ly a few m icros econ ds . To m ake th e pla sm acon du ct in g, an d th erefore magn et ica lly compres -s ib le, it wa s a ls o n eces s a ry to pu t a h igh -volta ge

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qI f0 I

Fig. 17 . ~en era tor A,.

with n on lin ea r fu se elemen tB. Th e fu s e is so des ign ed th a t th e d ie-lect r ic in su la tor D breaks down acros sth e spa rk gap C a t a pres cribed volta gean d t im e du r in g th e gen era t ion s ta ge,th u s switch in g loa d E in to th e sys tem .

pu ls e a rou n d th e O-p in ch coil before su b ject in g it toth e m agn et ic compres s ion field . Th is wa s a ccom -p lis h ed by th e combin a tion of pu ls e sh a p in g an dswitch in g in d ica ted by elemen ts B, C, an d D. E le-men t C was a sp a rk ga p switch s et to b reak down a ta specified volta ge, determ in ed by th e pretes tedbreakdown s t ren gth of th e d ielect ric in su la tor D.Elem en t B wa s a ca refu lly con s tru cted res is tivefu s e des ign ed with low in it ia l res is ta n ce an d con -s tru cted in su ch a m an n er th a t it vapor ized (th u sleavin g th e circu it ) n ot on ly a t th e volta ge n eces s a ryto break down th e spa rk gap , bu t a ls o a t an appro-p r ia te p res elected t im e du rin g en ergy gen era t ion .Owin g to th e n on lin ea r ch a ra cter of th e fu s e, th egen era tor ou tpu t pu ls e wa s con s id era b ly sh a rpen edbu t a t a s ign ifican t cos t in en ergy.

Th e rocket -la u nch ed p la sm a gu n exper im en tsfu rn is h examples of a ct ive switch in g, an d a ls o dem -on s t ra te th a t h igt ily complex gen era tor sys tem s canbe m ade to work reprodu cib ly. Th e s ch ema t ic ofth e sys tem actu a lly u s ed is sh own in Fig. 18 . Th ein it ia l en ergy sou rce wa s a sm a ll 16-kJ capacitorban k . A boos ter gen era tor in crea s ed th is en ergyto a va lu e su ita b le for th e in it ia l en ergy of th e lowerin du cta nce ou tpu t gen era tor . Th e p la sm a gu n wasswitch ed in to th e circu it ra th er la te in th e ou tpu tgen era tion s ta ge. Before th is t im e th e gen era torcircu it wa s completed by a ba lla s t load coil s h ownin th e figu re. All switch in g was a ccomplis h ed by

%ot;k ~ Sooster r - out Dut

Bollast Iood k

Fig. 18 . Sch ema t ic of rocket-born e gen era tor -powered p la sm a gu n sys tem . Deton a -tors were fired s equ en t ia lly to a ctu a teth e p la sm a gu n n eon va lve (l), switchin th e capacitor ban k (2), in it ia te th eboos ter (3 ) an d ou tpu t gen era tors (4 ),a n d to switch in th e p la sm a gu n (5).

de tona to rs . Th e n eon p la sma gu n was pu ls e -loaded .Th e fir s t deton a tor fired a ctu a ted a m ech an ism torelea s e n eon to th e p la sma gu n . Switch 2 comectedth e capacitor ba n k to th e two gen era tors an d ba lla s tload. Th e th ird deton a tor fired th e boos ter gen er -a tor wh ich th en in crea s ed th e en ergy flow in to th eo u tp u t ge ne ra t or . Th e deton a tors for th e ou tpu tgen era tor were th en in it ia ted . Fin a lly, a t th ea ppropr ia te t im e, switch 5 was fired an d th e p la sm agu n was cou p led in to th e circu it .

Th e sh ot a s s embly of Fig. 15 sh ows th e twogen era tors u s ed in th ese exper im en ts , togeth erwith a s im u la ted p la sm a gu n load coil. Th e p la sm agu n is is ola ted from th e ou tpu t gen era tor by a det -on a tor a ct iva ted switch , clea r ly vis ib le. Th e det -on a tors a re obs cu red . Th e ver tica l circu la r r in gju s t in fron t of an d to th e left of th e coaxia l loa dcoil s erves a s th e ba lla s t load coil. It is con n ectedto th e pa ra llel tra n sm is s ion lin e ju s t a h ead of th edeton ator switch p la tes .

Th e fin a l pa ckagin g of th e va r iou s compo-n en ts in to th e rocket p ayload was la r gely th e re-s pon s ib ility of San d ia Labora tor ies . Fin a l tes ts ofth e pa yload before a ctu a l la u n ch were ca r r ied ou ton th e fir in g tab le, a s were a ll th e preced in g de-velopm en t sh ots lea d in g to th e fin a l des ign . Figu r e

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19 shows th e sh ot s etu p for one of th ese tes ts . Thepayload was in verted to make it ea s ier to d iagn oseth e n eon p lasma . (Th e p lasm a gu n was mou n ted inth e aft s ect ion of th e payload . ) In th is tes t , a ll oper -a tion s were ca r ried ou t by telemetry comman d. Acomplete a s sembly, in clu d in g both payload an drocket, is sh own mou n ted on th e lau n ch er in Fig.20. Th ree experimen ts were ca rr ied ou t an d a llwere su ccess fu l. Deta ils of th e gen era tor develop-men t p rogram , from con cep tion to lau n ch , m ay befou n d in Ref. 13.

2 . Use of Tran s formers . In th e gen -era tor exam ples con s idered so fa r , th e loads to been ergized h ave been fed d irectly by th e gen era tors .Fu r th er , th ey h ave been es s en tia lly low in du ctan ce

Fig. 20. Complete a s sem bly oa th e lau n ch pad ,sh owin g th e rocket an d payload wh ichh ou ses a gen era tor -powered p la sm a gu n .

loads. Circu it res is ta n ces , a lth ou gh br iefly d is -cu s s ed , h ave been t rea ted a s u n avoidab le los ste rms . Th e reason for u s in g low in du ctan ce loadsfollows from Eq. (5 ), wh ich sh ows th a t load en ergymu lt ip lica t ion va r ies in vers ely with th e load in du c -tance.

Gen era tor cu r ren ts a re a tten u a ted whenres is tan ce is in th e circu it , a s s h ewn gen era lly byEq. (6 ) an d by Eq. (9 ) wh en th e gen era tor in du c-ta n ce h as th e form of Eq. (8 ). Th e en ergy absorbedby th e res is ta n t e R a t genera tor bu rn ou t can beca lcu la ted for th is cas e from Eq. (9 ):

ER(r ) = ~712 Rdto

Fig. 19 . A gen era tor-powered rocket -born ep la sm a gu n tes t sh ot on th e fir in g table.As ide from th e compon en ts in d ica teds ch em a tica lly in Fig. 18 , th e payloadhou sed an on -boa rd capacitor ban kc ba rgin g su pp ly, deton a tor t im in g an dfir in g u n its , telem etry comman dreceivers an d t ran sm itters to telem etervar iou s d ia gn os t ic s ign atu res .

Here E. is th e in it ia l in du ctive en ergy in th e cir -cu it , 1 / 2 102( LO+ 2.+ L1). In th e presen t con text,

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ER(r) is an expres s ion for en ergy los t to th e res is -tan ce, bu t th ere a re s itu a t ion s wh ere it wou ld bedes irab le to en ergize res is tive loads su ch as la sercavities. In th is ca se, la rge mu lt ip lica t ion s wou ldbe des irab le. Un for tu n a tely, th e maximum res is -tive en ergy ga in occu rs u nder th e following con -ditions:

Rr/ Lo = 0.5 (28a)

ER(r)M.X =E olog[(Lo+L1 + Ao)/ (L1 +~o)]. (28b)

Th e loga r ithm ic dependen ce on the in du cta nce ra tioso res tr icts en ergy ga in s in to a res is tan ce load th a tth ere a re very few cases where it is favora ble todirect ly en ergize a res is tan ce by a gen era tor .

Th ese examples h ave led to th e ra th er wide-sprea d m iscon cept ion th a t explos ive gen era tors a resu ita ble on ly for powerin g low in du ctan ce loads .Th is is t ru e for th e d irect feed applica t ion s discu s -sed so fa r . However , wh en tran s formers a re u sedto cou ple to low in du cta n ce loads , in to wh ich gen er -a tors opera te more efficien t ly, it becomes poss ib leto en ergize a wide ran ge of impedan ces with gen er-ators . Th ese impedan ces can in clu de res is tiveloads as well a s loa ds with in du ctan ces fa r grea terth an th e in du ctan ce of th e gen era tor its elf. Figu re21 sh ows sch ema tica lly a gen era tor sys tem withtran s former cou p lin g to an in du ctan ce load L3 WhiC his to be en ergized.

Th e p rimary circu it con s is ts of th e gen er -a tor , a sou rce in du ctan ce, a n d p rima ry loa d coil1 Th e secon da ry circu it con s is ts of th e load L3to be en ergized and a tran s former coil of in du ctan ceL2 . Th e mu tu a l in du ctan ce between L1 and L2 isdenoted by M. Switch in g is provided in th e secon -da ry circu it a t a rb it ra ry time T.

For demon s tra tion pu rposes th e circu its a rea ssu med to be n on res is t ive. In th is ca se, flu x iscon served in both circu its . Pr ior to switch in g inth e second circu it , cu rren t 11 flows on ly in th e

L3Fig. 21 . Sch ema tic of cir cu it th a t s h ows h ow a

gen era tor is u s ed to power a loa d L3th rou gh tran s former cou p lin g to th epr im ary gen era tor load coil L1.

p r imary, an d th e in it ia l flu x in th e seconda ry cir -cu it is ob ta in ed on ly in du ct ively. If th e gen era torin du ctan ce is denoted by Lo a t switch t ime (n owtaken a s t = O) t h e circu it equ a t ion s (from flu x con -serva t ion ) redu ce to:

(LG(t) + jo+ L1)I1 + M12 = (Lo+ 20+ L1)10 (29a)

MI1 + (L2 + L3)12 = MI o

22M k LlL2

(29b)

(29c)

Equ at ion s (29a ) an d (29b ) can be solved a lgeb ra i-ca lly for th e cu rren ts . At gen era tor bu rn ou t ,t = r an d LG(~) = O, th e secon da ry cu rren t 12becomes:

- MLOIOBu rn ou t : 12 = (L2+ L3)(L1+ l.) - M2 (30)

Genera lly s peak in g, th e cou plin g coefficien t k ofEq. (29c) is made as la rge as poss ib le. For agiven cou plin g coefficien t , th ere is a n opt imumva lu e of L2 to get maximum secon da ry cu rren t an dth u s en ergy in to L3. From Eq. (30 ) th is va lu e isfou n d to be:

For 12 (MAX): L2 = 3 .l-kz L,

(31)


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Under th is con dition th e cu r ren t and en ergya t bu rn ou t becom e:

2 1 / 2k

[lLo

12 = - ~ 10 L3(IO+L1)(20+L1- k2L1) 1 (32a)LL 212

k2 10 03=r (l.+ L1)(~o+ L1 - k2LJ

:


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.

.- . . . . . .-. -~ .-- ,- _=-__-... . --+. .,.- -.:L .-

. - .-. . .- . _ ._ .-,.,. ~. ... ,--- ----- ---.._

~- .- .

A,, . . . .. -_

a ..-*e..- .

-+=a, . . . . . _. .. . . . .. ,______ _Q

- . ..,. :. -- - -1.. ..-. ___

Fig. 22 . Views of a dou b le-en ded s in gle-s ta ge s t r ip gen era tor in va r iou s s ta ges of a ss embly. Th e lowerr igh t view s h ews th e completed gen era tor with exp los ive an d s econ da ry coil in p la ce ready fortesting.

Fig. 23 .. Secon da ry coil for dou b le-en ded , s in gle-s ta ge s tr ip gen era tor . No. 17 en a rn el-coa ted copper wire is wou n d on a poly-eth ylen e form a t abou t 2 tu rn s / cm .

-WmY-x-rf.;: 2X3

,.. ..-2 J ,s, ;, - .,.,.,. , ,, . .. f,,..,.,.. . . . . . . . _ ..,,. -- !-2 !---- +.1 ,: .. ,-. > ,: .,,-. .1.--WY%MY=

+Fig. 24 . Secon da ry coil of th e type s h ewn in Fig.

23 recovered a fter fir in g an d section edto sh ow th e win d in g pen et ra tion in to th epolyeth ylen e coil form . Th e win d in gsh ave pen etra ted over 9 mm in to th e core.

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Th ese advan tages do exis t . Among th em isth e capab ility of p rodu cin g enorm ou s en ergy bu rs tsin t ime sca les n ot n orm a lly ava ila b le oth erwise.Fu r th er , u n like capacitor or in du ct ive s torageu n its , gen era tor des ign s can be read ily modified toa llow th em to meet ch an gin g load requ iremen ts .Aga in , u n like capacitor d isch a rges , gen era tor ou t -pu t volta ges and cu r ren ts h ave la rge tim e region swh ere th ey a re approxima tely in ph a se. For someapp lica tion s th is can be a decis ive advan tage. Oth eradvan tages a r is e from th eir extremely h igh ra tioof en ergy ou tpu t to weigh t an d volume.

Idea lly, th e type of gen era tor requ ired isgovern ed s tron gly by th e type of load to be en er -gized . If th e cu rren ts requ ired a re n ot excess ivean d th e time sca le of th e experimen t is not tooshort , s p ira l gen era tors a re probab ly bes t becau s eof th eir in heren tly la rge en ergy m ult ip lica tion . co -axia l, s t r ip , a n d sph erica l gen era tors a re wells u ited to power loads wh ere la rge cu rren ts a rerequ ired bu t wh ere th e experimen ta l t im e sca le isnot too short . Pla te genera tors a re capab le ofca r ryin g very la rge cu rren ts an d can opera te onsu bs tan t ia lly fas ter t im e sca les . Cylin drica l flu x-compress ion sys tem s a re u s ed when very in ten s emagnet ic fields a re requ ired . If th ey can be u sedto dr ive tra n s formers , th ey h ave th e capab ility ofpowerin g extern a l loads on s t ill sh orter t im e sca les .

Econ om ic fa ctors a ls o p lay a role in gen er-a tor s election . St r ip gen era tors a re rela t ively in -expen s ive becau s e th e fabrica t ion of both th e m eta lcompon en ts an d th e exp los ive sys tem a re s imple.Pla te gen era tors and cylin dr ica l implos ion sys tem srequ ire expen s ive exp los ive in itia tion s ys t ems , bu tth e res t of th e exp los ive sys tem an d th e meta l fa b r i-ca tion a re rela t ively s im ple. The h elica l sect ion ofa sp ira l gen era tor is expen s ive to fabr ica te bu t th eexp los ive sys tem is s im ple.

A n umber of oth er tech n ica l factors mu s ta ls o be con sidered . Th es e in clu de: m in im izin gsou rce or loss in du ctan ce term s ; m in im izin g u n -wan ted mot ion of sys tem compon en ts by m agn etic

forces , both du r in g in t rodu ct ion of th e in it ia l en ergyan d du r in g th e en ergy gen era tion s ta ge; m in im izin gor elim in a tin g meta llic jets wh ich a re often formeda t con tacts between meta l s t ru ctu res in rela t ivemotion ; keep in g flu x los ses to a m in im um du r in g th egen era t ion s ta ge; an d preven tin g in tern a l volta gebreakdown in side th e gen era tor .

Wh ile th ese fa ctors a re im por ta n t in an ygen era tor app lica t ion , th ree of th em a re of specia ls ign ifican ce in th e pres en t s tu dy in th a t th ey re-s t r ict th e cla s ses of gen era tors th a t can be u s ed .Th es e fa ctors dea l with flu x los ses , h igh magn et icfield effects , a nd in tern a l voltage breakdown , an da re t rea ted in th e followin g section s .

a . Flu x Losses . Flu x los ses a reea s ily u nders tood for some mechan ism s . Pocket-in g of flu x by a ltern a te con du ctin g pa th s a r is in gfrom in tern a l b reakdown s or prem a tu re closu re ofpa r t of th e flu x-compres s ion region a re examples .Res is ta n ces in th e circu it cau s e some flu x loss byredu cin g th e magn itu de of cu rren t gen era ted . Un-recoverab le flu x is a ls o tra pped in th e con du ctin glayers of th e gen era tor componen ts .

A rea son ab ly good accou n tin g of th ese los s escan be made for mos t gen era tors , p rovided th ecu r ren t den s ity does n ot grea t ly exceed 1 MA/ cm .Helica l gen era tors u su ally a re an om alou s ly los sy,even wh en th ey a re th ou gh t to be free of flu x pocket -in g. When th eoret ica l p redict ion s a re forced to fitexperimen ta l da ta by ad ju s tmen t of th e gen era torres is ta n ce, th e res is ta n ces so ca lcu la ted a reu su a lly fa r h igh er th an can be accou n ted for. Weth in k pa r t of th is d ifficu lty can be t raced to a rm a -tu re performan ce. A compa rison of th e arm atu rerequ irem en ts for a sp ira l a n d coaxia l gen era tor canbe made by compa r in g th e u pper sketch es of Figs .2 an d 7 . Th e arm atu re dyn am ics in both cas es issimilar . In both cas es gen era tor cu r ren ts a reca r r ied axia lly by th e a rma tu re. However , in th esp ira l con figu ra t ion s th e in it ia l flu x is given ess en -t ia lly by axia l fields a r is in g from th e h elica l cu r -ren ts , a s opposed to th e flu x in th e coaxia l

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gen era tor wh ich a r is es from pu rely ta n gen tia l orcircu la r m agn et ic fields . Flu x compress ion in th esp ira l gen era tor th erefore requ ires gen era t ion ofcircu la r eddy cu r ren ts a rou n d th e a rma tu re form agn et ic field bu ild u p with in th e spa ce between th es p ira l a n d h elix. O ne e xp la n a tion thatwou ld a ccou n tfor th e rela t ively la rge los s es in sp ira l gen era torsis a s follows : If th e a rm a tu re were to su ffer axia lcra ck in g or oth er s ign ifican t axia l s t ra in s , th es em igh t lead to an oma lou s ly h igh res is ta n ce for th etan gen t ia l eddy cu r ren ts , bu t wou ld h ave on ly m in orin flu en ce on th e res is ta n ce to axia l cu r ren t flow.

In gen era l, it h a s become cu s toma ry toch a ra cter ize h elica l gen era tor perform an ce by afigu re of m er it , 6 wh ich accou n ts for a ll flu x loss esin an approxima te

An Introduction to Explosive Magnetic Flux Compression Generators

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