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D E S I G N A N D T E S T I N G O F A 2 5 -S T A G E E L E C T R O M A G N E T I C C O I L G U NW. R . Cravey , G . L . Devl in , E . L . Loree , S . T . S t rohl , and C . M. Young

T e t r a C o r p o r a t i o nA l b u q u e r q u e , N M 8 7 1 0 9

Abs t r a c tTet ra has recent ly des igned and fabr i ca ted a 25-s t age pro to type e lec t romagne t i c co i l gun . To da te , f ive s t ageshave been succes s fu l ly t e s t ed . In i t i a l re su l t s t rack ve ry we l l w i th predic ted va lues . Each coi l i s s equent i a l lyf i re d a s t h e p r o j e c t il e m o v e s d o w n t h e b o r e. A h y b r i d c o n t r o l s y s t e m i s u s e d t o m e a s u r e t h e v e l o c i t y o f t h epro jec t i l e a s i t en te rs each co i l and ca lcu la tes the t ime- to- f i r ing . Compute r predic t ions based on th i s mode lindica te ve loc i t i e s grea te r than 3000 rn / s can be achieved . Current ly , the sys tem has been t e s t ed wi th 10 kJde l ive red to each co i l. Sol id d ie l ec t r ic swi tches a re used to t rans fe r the energy f rom each ca pac i tor to the co i l s .P e r f o r m a n c e o f t h e c o il g u n , c o m p u t e r m o d e l i n g , a n d l a b o r a t o r y r e s u lt s a r e d is c u s se d .

In t roduc t i onT h e P h a l a n x a n t i m i s s il e a n d t h e V u l c a n a n t i a ir c r a ft w e a p o n s s y s t e m s a r e s u c c e ss f u l e x a m p l e s o f h i g h r e p e t i ti o n r a t e ,l o w p r o je c t il e m a s s c h e m i c a l b a s e d w e a p o n s s y s t em s . E l e c tr o m a g n e t i c b a s e d w e a p o n s a r e c a p a b l e o f a c h i e v i n g h i g h e rpro jec t il e ve loc it i e s than chemica l based weapons . Hig her pro jec t i l e ve loc i t ie s mean h igher pro jec t i l e energ ies fo r thes a m e p r o j e c t il e m a s s .E l e c t r o m a g n e t i c g u n s h a v e b e e n s tu d i e d fo r m a n y y e a r s b y m a n y d i f f e re n t o r g a n i z a ti o n . T h e r e h a v e b e e n t w o p r i m a r yt e c h n o l o g i e s w h i c h h a v e b e e n f o c u s e d u p o n : r a i l g u n s a n d e l e c t r o m a g n e t i c c o i l g u n s . R a i l g u n s h a v e d e m o n s t r a t e dimpres s ive pe r form ance , b u t they have been l imi ted by ba r re l wear due to brush contac t s . Coi l guns , on the o th e r hand,do not have the l imi ta t ions of ba r re l wear ye t have ran in to obs tac les a s soc ia ted wi th a rm ature hea t ing a nd c ru shing . Toda te , mul t i s t age co i l guns have l aunched pro jec t i l e s to ve loc i t i e s not exceeding 1000 m/s .T e t r a h a s d e v e l o p e d a n o p t i m i z a t i o n m e t h o d f o r t h e d e s i g n o f c o il g u n s w h i c h i n c r e as e s t h e e f f ic i e n c y o f th e s y s t e ma n d r e d u c e s t h e a m o u n t o f s t o re d e n e r g y r e q u i r e d . A f t e r v a l i d a ti o n o f c o m p u t e r m o d e l s u s i n g T e t r a ' s c o il g u n ,pro jec t ions have been m ade wh ich show a ve loc i ty of grea te r than 3000 rn /s can be achieved us ing inform at ion l ea rnedd u r i n g t h e d e v e l o p m e n t o f t h e o p t im i z i n g m e t h o d . A p h o t o g r a p h o f T e t r a 's c o il g u n i s i l lu s t r at e d i n F i g u r e 1 .

F igure 1 . 25-S tage e l ec t romagne t i c co i l gun .

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DesignO p t i m i z a t i o n m e t h o dO p t i m i z a t i o n o f t h e c o i l g u n i s r e q u i r e d t o i n c r e a s e t h e e f f i c i e n c y o f t h e s y s t e m a n d t o r e d u c e t h e a m o u n t o f s t o r e de n e r g y r e q u i r e d f o r e a c h s h o t . B o t h o f t h e s e i te m s h a v e a s i g n i f ic a n t i m p a c t o n t h e c o s t a nd s i z e o f t h e c o i l g u n s y s t e m .W e h a v e i n v e s t i g a t e d o p t i m i z a t i o n o f c o i l g u n s u s in g t h e c a l c u l us o f v a r i a ti o n s . T h i s p r o c e s s l e a d s t o s o m e i n t e r e s t i n gc o n c l u s i o n s c o n c e r n i n g th e d i r e c ti o n s t h a t d e s i g n s s h o u l d g o . W e h a v e f o u n d a n u m b e r o f c a s e s w h i c h c a n b e s o l v e da n a l y t i c a ll y . A n e x a m p l e i s t h e c a s e o f o p t i m i z i n g th e s y s t e m f o r l o w e s t re s i s ti v e lo s s e s in t h e p ro j e c t i l e . W e c a n w r i t ethe acce le r a t ion , a , o f a p ro jec t i le in a co i l gun as :

1 1 2 8 M 2a 2 m L , d ~ (1 )

whe re m i s the p ro jec t i le mass , Lp i s the se l f induc t ance o f the p ro jec t i le , I d i s the d r ive c u r r en t , and the las t t e rm i s theg r a d i e n t o f t h e s q u a re d m u t u a l i n d u c t a n c e . A n i n t e r e s t i n g o b s e r v a t i o n i s t h a t t h r e e d i f f e r e n t c o m p o n e n t s c o n t r i b u t e t othe acce le r a t ion o f the p ro jec t i le . One con t r ibu t ion i s the p ro jec t i le it s e l f th rough i t s ma ss and se l f induc tanc e . An o the rc o n t r i b u t i o n i s t h e d r i v e c u rr e n t . T h e t h i r d c o n t r i b u ti o n i s t h e g e o m e t r y o f t h e c o i l / p ro j e c t i l e s y s t e m , t h e m u t u a li n d u c t a n c e o r m o r e a c c u r a t e ly t h e g r a d i e n t o f th e m u t u a l i n d u c t a n c e ( s qu a r e d) . W h e n o p t i m i z i n g t h e s y s t e m l o s s e s, o n erecogn izes tha t the un recoverab le lo sses such as ohm ic hea t ing a r e p ropOr t iona l to the d r ive cu r r en t . I n equa t io n 1 , f o ra g i v e n l e v e l o f f o rc e , d r i v e c u r r e n t r e q u i r e m e n t s c a n b e r e d u c e d b y d e c r e a s i n g t h e i n d u c t a n c e o f t h e p r o j e c t i l e a n d / o ri n c r e a s i n g t h e g r a d i e n t o f t h e m u t u a l i n d u c t a n c e . T h e e n e r g y l o s t d u e t o o h m i c h e a t i n g o f t h e p r o j e c t i l e i s g i v e n b y :

E p r o je c ~ o - - f I p 2 R p d t ( 2 )

w h e r e Ip i s t h e p r o j e c t i l e c u r r e n t a n d R p i s t h e r e s i s ta n c e o f t h e p r o j e c ti l e , t a k e n t o b e a c o n s t a n t i n t hi s e x a m p l e . T h ep r o j e c t i l e c u r r e n t c a n b e w r i t t e n a s :

~ - - 1 ~ ~ (3 )

I t shou ld be no ted tha t cons tan t acce le r a t ion guaran tees the lowes t peak acce le r a t ion fo rces on the p ro jec t i le by the meanv a l u e t h e o r e m . T a k i n g t h e a c c e l e r a t i o n a s a c o n s t a n t , e q u a t i o n 2 c a n b e re w r i t t e n a s :

2 m a 2 R p t n 2E~Y~at" - - Lp f d M 2 a t (4 )

d t

w h e r e a o i s t h e c o n s t a n t a c c e l e r a t i o n , a n d t is t i m e . N o t e t h a t b y l e t t i n g M 2 = e Q , w h e r e Q i s a d u m m y f u n c t i o n a l , t h ee q u a t i o n i s e a s i e r t o w o r k w i t h . B y u s i n g t h e c a l c u l u s o f v a r i a t i o n s , o n e c a n d e t e r m i n e t h a t t h e f u n c t i o n a l f o r m o f t h em u t u a l i n d u c t a n c e w h i c h m i n i m i z e s e q u a t i on 4 i s :

2M 2(x) - M o 2 e - h x ' ( 5 )

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where h is a posi t ive constant for the family of minimal funct ional forms. The min imu m pro ject i le resis t ive loss en ergycan now be wri t ten as:

116 m Rp V/ l ,~ (6 )E~J"cat" = 9 Lp h

w h ere Vf s the final veloci ty, 1 is the length o f the acce lerat ion s tage.The importance of this process is that , by the use of the calculus of variat ions, losses can be reduced by shaping thecoupl ing between coi l and project i le and by shaping the drive current. The resul t ing funct ional form s are not ent irelyintui tive. Add it ional opt imiza t ion have been perform ed and wil l be presented in a future paper.C o m p u t e r mode lAlthough our original intent was to design and bui ld a ful ly opt imized coi l gun, budgetary constraints cause d us insteadto build a coi l gun based upon exis t ing capaci tors and ut il ize lessons learned fro m the opt im izat ion s tudy. To this end,we d evelop ed a computer code to model and pred ic t the performance o f a mul t i s tage co i l gun . In i ti a l ly , the codepredicted the coupl ing between projecti le, and then predicted project i le motion. This was used to opt im ize the systemgiven the avai lable capacitors . Once the system was buil t, the coupl ing was measured and input into the code. The c odewas then used to opt imize the t iming. The co de has a real is tic ci rcui t mod el and calculates the couple d electrokinet icsystem of equat ions. Losse s are accumulated and temp erature depend ent resis tance and specific heats are ut i lized.S y s t e mThe coi l gun consis t of twenty five individual s tages. A single s tage c onsis ts of a series cap aci tor C o, s tarter switch S o,and coi l L o. A second sw itch, S~ is placed across the capaci tor C O o cro wba r vo l tage reversals . The RL C circui t that isformed is underdam ped and t r ies to reverse the vol tage across the capaci tor C o. Switch, S~ is f i red w hen the vo l tage o nC O pp roaches 50 0 V and protects the capacitor from vol tage reversals. A typ ical current w ave form rings up to 100 kAin 25 us and then decays exponent ial ly to zero in 250 Its .A project i le is place in the breach end of the gun. T he fi rs t coi l is f i red and the project i le is forced d ow n the b arrel . Asthe project i le move toward the second coi l i t crosses a laser beam which sends a s ignal to the t iming and controlhardware. T he t iming and control system measures the veloci ty of the project i le and calculates the ne cessary delay andfires the next s tage and the projecti le is accelerated again. The process cont inues throug h al l twe nty five s tages with theproject i le increasing in veloci ty through each s tage.High Cu rren t Dens i ty Coi l sHigh cu rrent densi ty coi l construct ion was used to yield improve d coupl ingbetween coi l and project i le. A cross-sect ional view of a coi l is i l lustratedin Fig ure 2 . The co i l s were cons t ructed us ing compacted rec tangular l it zwire to achieve m axim um packing a nd lowest resis t ive losses . The l i tz wirewas w rapped w i th KA PTO N insu la t ion for vo l t age ho ld-off p ro tec tionbetween turns. KE VL AR fiber was used to provide a mechan ical restraintdur ing energ iz ing of the co i l s . KEVLAR f iber was used because of i t sunique high tensile s t rength capabi l it ies . Once the coi ls were assem bled,they were placed in a vacuum chamber and immersed in epoxy and pot ted.After the epoxy was cured, the coi ls were sent out for f inal machining ofthe bosses and fiber opt ic pi lot holes . G-10 end plates were used in theconstruct ion of the coi ls . The coi l assemblies were axial ly pre-loaded to 8ks i by compress ing the co i l s t ack (barre l) to reduce m ovem ent o f the co i l

. ~ O~perLugnam~ a r V ~

. . . . ~ . . . . . .. . . H e d a r F a ~l Z, l a r w ' ~ p e d L t z

I I I W H

G 1 0 R a I ~Figu re 2. High current densi ty coi l .

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wind ings during launch. Once the coi ls are in place a com posi te f ly-way tube is inserted into the s tack. The flywa ytube was cons t ructed of a wov en f iberg lass mat imp regnated wi th a h igh t empera ture cure epo xy res in .Labo ratory measureme nts were made of the coupl ing betwee n a project i le and the coi l using a high frequen cy bridge.These resu l t s were compared wi th computer model s genera ted us ing Nagaoka 's ' s and Lyle ' s methods . Excel l en tagreem ent was achieved between the computer m odel and laboratory measurements . A c urve fi t of the spacial dependen tcoupl ing prof i l e was crea ted fo r use in the computer m odel .

Sol id Dielectric SwitchesSol id dielectric switches where selected for the coi l gun for their high current carrying capabi l i t ies and low cost . Theswi tches were no t the f i r s t cho ice due to the t ime for tu rn-around dur ing each sho t , however , due to budgetaryconstraints they were just i f ied for a proof-of-prin ciple demo nstrat ion. S ol id dielectric switches o f this type have beendem onstr ated in other appl icat ions with great success (Ref. 1). The opera t ion of the switch is s t raightforwa rd, aninsulating material, in our case K AP TO N is placed between two sacrif icial plates , one plate is bored to hold a e xplodingbr idge wi re (EBW), and the o ther i s machined wi th a kn i fe edge . Once the s t age capaci to r i s charged , a capaci to rdischarge uni t is discharge into the EBW, the wire explodes, blast ing the KAPTON into the knife edge where i t i s cutand a plasma is forme d betw een the two switch plates . Since switch j i t ter was a ma jor concern fo r t iming of the coi lgun, w e me asure d the j i tter of the switch at 500 vol ts and fou nd i t to be less than 600 ns.There are two C DU s for each s tage capaci tor, one for the s tarter switch and a second one for the c row bar switch. W henthe CDU s are f i red, they float to the charge vol tage of the capaci tor bank. We de signed a capaci tor discharge uni t w hichwas bat tery powered and fiber opt ical ly t r iggered to completely isolate the uni ts form the control system and ground.

Timing and Cont ro l Sys temThe t iming and control system incorporates f iber opt ic sensors for project i le locat ion and veloci ty measurements . In asequent ial ly f i red coi l gun, s tage t iming is cri t ical for maximum efficiency. A programmable control ler was designedto analyze the opt ical s ignal and via least squares approximation based on analyt ical data, predict real t ime opt imumtriggering for each s tage. Instantaneous veloci ty measurements are processed and then s tored so tha t project i le velo ci typrofi les can be later recal led and analyzed for each shot .

TestingTest ing of the coi l gun was conducted into a s teel project i le t rap. The t rap was fi l led with cot ton rags, corrugatedcardboard, and sand part i t ioned into three separate chambers . A TD S540 digi t izing osci lloscope wa s used for captu ringal l shot data. A 486/66 PC was used to program the t iming and control and reduce shot data.Diagnos t i csSevera l d iagnos t i cs were used for gun t es t ing . The detec tor s ignal coming f rom the l aser d iagnos t i cs was used tomeasu re p ro jec t il e ve loci ty . The pro jec t i le c rosses a beam upo n ex i t ing each co i l . The t ime the beam i s b locked wasmeasured and used with the project i le length to yield the exi t veloci ty for each s tage. A separate laser system wasincorporated at the end of the barrel. The system was mad e up o f three sol id s tate laser diodes and three detectors . T helaser detector pairs were spaced 10 cm apart. By measuring the t ime between the bea m crossings for al l three beam s andaverag ing an accura te m easurem ent o f the ex i t ve locity was ob ta ined .Rogowski co i l s were des igned and bu i l t fo r measur ing the curren t th rough each co i l . The Rogowski s ignal s wereintegrated and scaled to yield the current discharged through e ach coi l . The R ogo wsk i s ignals were used to determ inei f a p ref ire o r p re-crow bar occurred dur ing the sho t. A m ul t ip lexer box w as cons t ructed which a l lowed the record ingof 64 channels of data on a s ingle 4 channel digi t izer.

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Performance Resu l t sA maximum of f ive s tages have been tested to date. The resul ts from these tes ts yielded a veloci ty of greater than 200m/s. The resul t from the laboratory t racked except ional ly wel l with computer project ions. Several charge vol tages(energy levels) have been tested and compared to computer project ions as well . Once the com puter mo del was val idatedwi th the l abora tory resu l ts , p ro jec t ions were m ade wi th capaci to rs which more c lose ly match des ign requ i rements .Several tests were conducted for various s tage numbers and charge vol tages. Single s tage 10 kV shots w ere tes ted fi rs t .A veloci ty of approximately 150 m/s was achieved with a s ingle s tage. A three s tage shot was taken with a chargevol tage of 8 kV w hich resul ted in a f inal veloci ty of greater than 150 m/s . Final ly f ive s tage shots we re take n at 6 .5 kVcharge vol tage on ea ch capaci tor. A resul t ing veloci ty of 200 m/s w as obtained. As the numbe r of s tages were increased,the charge vol tage was lowered to increase the l i fet ime of the coi ls .A plot of the veloci ty for each s tage as measured in the laboratory compared with model predict ions is i l lustrated inFigure 4 .The excel l en t agreement be tween the model p red ic t ions and the l abora tory resu l t s bu i ld a h igh l evel o fconfidence in the computer predict ions for addi t ional s tages.

50 0 L I I i

4 0 0J 1 0 k V 2 0 6 u f

/ J ~ 1 " ~ 8kV , 206uf -~ o 200 / ~ ~

1 0 0 ~ 5 kV , 2 0 6 uf _

0 I I I1 2 3 4 5Stage Number

Figure 4~ Com par i son o f model and l abora tory m easurements fo rvarious numbers of s tages and energies .

Project ionsProject ions were m ade on the final veloci ty that can be obtained from al l 25 s tages. The projec t ions yield a veloci tyof greater than 9 00 m/s at a charge vol tage of 10 kV. An addi t ional 100 m/s can be add ed i f the project i le is ini tial lycooled with l iquid ni t rogen. As has been mentioned due to budgetary constraints , we had to design the systemaround ex i s t ing capaci to rs which grea t ly reduced the energy t rans fer e f f ic iency of the sys tem.

Com puter m odel s w ere genera ted fo r var ious capacito r va lues and energy l evel s fo r a th i r ty s t age gun and the f ina lveloci ty wa s recorded. Veloci t ies in excess of 3000 rn/s can be obtained with the correct capaci tors m atche d to thesys tem. A p lo t o f the ve locity per formance for many of the conf igura tions modeled i s i llus tra ted in Fig ure 5 . Th i sresul ts confirms that the value of capaci tors used on the present system are to high and most of the energy isdiss ipated in the coi l after the project ile has left the usable f ield. One ca se which yields a high ve loci ty for amin im um amou nt o f energy occurs when a 34 kV, 52 I t s capaci to r is used for each s t age.

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C o n c l u s i o nTet ra has deve lope d a opt imiza t ion metho d for the des ign of e l ec t rom agne t i c co i l guns . The op t imiza t ion inc reases thee f f i c i e n c y o f t h e s y s t e m a n d r e d u c e s t h e a m o u n t o f s t o r e d e n e r g y r e q u i r e d . T o d a t e T e t r a h a s d e m o n s t r a t e d 2 0 0 m / sv e l o c i t y w i t h f i v e s t a g es . T e t r a c o i l g u n m o d e l s h o w s e x c e l l e n t a g r e e m e n t w i t h l a b o r a to r y r e s u l t s g i v i n g a h i g h l e v e lof conf idence in compute r pro jec t ion of an opt imized sys tem. A ve loc i ty of grea te r than 3000 m/s can be achieved f roma 3 0 s t a g e c o i l g u n w i t h t h e p r o p e r c a p a c i t o r m a t c h i n g .

t -LU" oo

0O

6 0 0 0 0 . . . . = . . . . I . . . . I . . . . a . . . . I . . . . I . . . . I . . . .

5 0 0 0 0

4 0 0 0 0

30000

2 0 0 0 0

1 0 0 0 0

uv w ~

A

D ~

0R

F G. . . . I . . . . I , , , , I , , , , I . . . . I . . . . I . . . . I , , , ,

5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 0 3 0 0 0 3 5 0 0 4 0 0 0Projectile Velocity

^ 2 0 6 u f , 1 2 k V , 2 0 Cs 2 0 6 u f , 1 0 k V , - 1 5 0 Cc 2 0 6 u f , 1 0 k V , 2 0 Co 2 0 6 u f , 1 0 k V , - 1 0 0 Cs 2 0 6 u f , 1 0 k V , 2 0 CF 206 u f, 5 kV , 20 CG 2 0 6 u f, 5 k V , - 1 5 0 C" 2 4 u f , 6 0 k V , - 2 0 0 C

2 7 u f , 44 kV , 20 CJ 27 u f , 44 kV , 20 CK 24 u f , 60 kV , 0 CL 5 2 u f , 3 0 k V , 2 0 Ca 2 4 u f , 6 0 k V , - 8 0 CN 2 4 u f , 3 0 k V , - 1 5 0 Co 2 4 u f , 3 6 k V , - 1 5 0 CP 2 4 u f , 5 0 k V , - 1 5 0 Co 2 0 6 u f , 1 8 k V , - 1 5 0 CR 2 0 6 u f, 1 2 k V , - 1 5 0 Cs 5 2 u f , 4 4 kV , 2 0 Cr 52 u f , 44 kV , -20 Cu 5 2 u f, 3 4 k V , 2 0 C ( 5 0 m / s g a s i n j e c t)v 52 u f , 34 kV , 20 Cw 3 2 u f, 4 4 k V , - 2 0 Cx 5 2 u f , 3 4 k V , - 1 5 0 C

F i g u r e 5 . Com pute r pro jec t ions for va r ious capac i tor and energy conf igura t ions . The v e r t i ca l ax i s is the s toredenerg y pe r s t age and the ho r i zonta l ax i s is the f ina l ve loc i ty for th i r ty s t ages .

A c k n o w l e d g m e n t sT h i s w o r k w a s p e r f o rm e d f o r th e D e fe n s e N u c le a r A g e n c y u n d e r C o n t r a ct N o . D N A 0 0 1 - 9 3 - C - 0 0 1 4 . T h e v i e w sexpr es sed in th i s a r t ic l e a re those of the au thor and do no t re f l ec t the of f i c i a l po l i cy or pos i t ion o f the Dep ar tm ent o fD e f e n s e o r t h e U . S . G o v e r n m e n t .

R e f e r e n c e s1 . R . A . R i c h ar d s o n , W . R . C r a v e y , a n d D . A . G o e rz , P e r f o r m a n c e o f a 1 0 k V , 6 2 5 k A , 8 5 k J E n e r g y D i s c h a r g e M o d u l eUt i l i z ing a Sol id Die lec t r i c Swi tch . P resented a t the 8 th IEEE In te rna t iona l Pul sed Power Confe rence , San Diego, CA.

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