RD-Rle? 224 PULSED CURRENT TRANSFORMER FOR LOW INDUCTIVE LOADS(U) I/IARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND RDA ZIELINSKI ET AL. OCT B? BRL-MR-3626

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00 MEMORANDUM REPORT BRL-MR-3626

PULSED CURRENT TRANSFORMERFOR LOW INDUCTIVE LOADS

ALEX ZIELINSKI ZE fTKEITH JAMISON DEC 161W

JOHN BENNETT

OCTOBER 1987

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.

US ARMY BALLISTIC RESEARCH LABORATORY.; ABERDEEN PROVING GROUND, MARYLAND

87 12 9 051

UNCLASS I FI 1l)

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6a NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a NAME OF MONITORING ORGANIZATIONUS Army Ball ist ic Research (If applicable)L~a bo ra t o ry I LC BR-TB- EP

6i ADDRESS (City, State, and ZIP Code) 7b ADDRESS (City, State, and ZIPCode)

Aberdeen Proving Ground, MD 21005-5066

Ba NAME OF FUNDING/ SPONSORING 8b OFFICE SYMBOL 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION US Army Of applicable)

Ballistic Research Laboratory SLCBR-D "__

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PROGRAM PROJECT TASK WORK UN:'Aberdeen Proving Ground, MD 21005-5066 ELEMENT NO NO NO ACCESSION ."

62618A A1180 00 001 A.I11 TITLE (Include Security Classification)

(IJ) Pulsed Current Transformer for Low Inductance Loads

12 PERSGNAL AUTHOR(S)-ielinski, Alexander Jamison. Keith (BRL) and Bennett, John (ARDEC)Ila TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (Year, Month, Day) 15 PAGE COUNT p

FROM _ TO __

16 SUPPLEMENTARY NOTATION

1? COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP Electromagnetic Railgun, Pulse Transformer, Pulse Power,

I0) 01 High Current Transformer.I o3 -I

1) AVSTRAC T (Continue on reverse if necessary and identify by block number) (idk)

At the US Army Research, Development and Engineering Command (ARDEC), an effort was tu;tken to couple an array of five capacitor banks to a low inductance load. To achieve cur,hich exceed the limit placed on the capacitor banks, pulse current transformers were used.his power system, termed CAPSTAR, was ultimately used to electromagnetically stress a rol:.,i

)ore composite railgun barrel section.

A mathematical model has been developed to simulate a capacitor power supply drivinl,[)IIls(I transformer with various secondary loads. The model was first tested by compariso:•experimental results using a subscale pulse transformer. The calculated data points wcmugo'. ao, reInent with the experiment. Minor adjustments to some circuit parameters to :1c,.!or the transitory behavior of the circuit are described.

The AI(C system of five capacitor banks and pulse transformers was evaluated in thei,;i,, :is the subscale transformer. Measurements for evaluating the (Continued)

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Alexander 2 ielinski (311 )78-3889 SlCBR-'r -[I'00 FORM 1473, 8 4 MAR fPP tayn -e uso u-t* . -- ( 'C, ft ( F A

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b0 tvo -n:,c. antd experiment va.s no as c¢osc its th 5 t hc sah. . -t an " :i . Pc rf'ur-la cccuzves a !1,)wng load optimization for the CAPSI AR system are presented.

In the performance simulations, not only were constant inductive and resistive loads used,but a railgun was also modeled as a load. Performance has been plotted for two power sources;the five capacitor banks in parallel with a pulse shaping inductor and the CAPSTAR system.In a]l cases the capacitor banks were crowbarred. The pulse transformers perform best when 'dr~vi:,g &i short, large-bore railgun.

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ACKNOWLEDGEMENT

aThe authors wish to thank the personnel at ARDEC (Army Research, Develop-

ment and Engineering Command) for supplying the test data on the CAPSTAR sys-

tem.

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S. _.. . . .

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENT... .. .. .. .. .. .. .. .. .. .. .. . ..

LIST OF ILLUSTRATIONS. ....................... vii

I. INTRODUCTION .............................

II. CIRCUIT MODEL . .. .. .. .. .. .. .. .. .. .. .. .. ... 1

III. TRANSFORMER BEHAVIOR ......................... 4

A. Circuit Inductance ........................ 6

B. Circuit Resistances. ....................... 6

IV. CALCULATED PARAMETERS. ........................ 7

A. Circuit Inductances. ....................... 7

B. Circuit Resistances. ....................... 7

V. MEASURED QUANTITIES ......................... 8

VI. SIMULATION AND MODEL VERIFICATION .................. 8

A. Subscale Transformer . . . . . .. .. .. .. .. .. .. .. 11

B. CAPSTAR System .......................... 11

VII. PROJECTED PERFORMANCE WITH RAILGUN LOADS. ............. 16

VIII. CONCLUSION.............................21

REFERENCES.............................29

APPENDIX- COMPUTER PROGRAM .. .................... 31

DISTRIBUTION LIST ........................... 35

vN

LIST OF ILLUSTRATIONS

Figure Page

1 Photograph of CAPSTAR and Equivalent Circuit for Pulse Transformers 2

2 Transformer Topology ........... ....................... 5

3 Short (Top Curve) and Open Circuit (Bottom Curve) Circuit ImpedanceVersus Frequency ........... .......................... 9

4 Short (Top Curve) and Open Circuit (Bottom Curve) Circuit ResistanceVersus Frequency ........... .......................... 10

5 Primary - Secondary Current Ratios for Subscale Transformer . . . .12

6 Calculated and Measured Currents for Subscale Transformer (1 TurnCoil Secondary Load) ......... ........................ .13

7 Maximum Load Magnetic Energy Versus Load Impedance ............ .15

8 Bore Diameter Versus Maximum Barrel Length (1 ksi = 6.894 MPa) . . .17

9 Calculated and Measured Primary Current for CAPSTAR With a BarrelLoad (One Transformer) ......... ....................... .18

10 Calculated and Measured Barrel Load Current for CAPSTAR ......... 19

11 Primary - Secondary Current Ratios for CAPSTAR ... ........... .20

12 Barrel Pressure Simulation for Two Different Power Sources (1 ksi =

6.894 MPa) ............. ............................. .22

13 Velocity Simulation for Two Different Power Sources ............ 23

14 Velocity Versus Mass for Two Different Bore Sizes ... ......... .24

15 CAPSTAR Current Ratios Versus Time for Different Barrel Parameters .25

16 CAPSTAR Secondary Currents Versus Time for Different Barrel Para-meters ............ ............................... .26

vii

I. INTRODUCTION

The concept of accelerating particles using an electromagnetic railgunhas been pursued for many years. Railguns and their subcomponents are low im-pedance devices which require a power source capable of producing high currents.There are a limited number of sources which can meet these requirements. Amongthese are rotating machines, which often need constant, careful maintenanceand, typically, create a pulse with a long risetime. Capacitors are also ableto supply large currents. They are readily available and relatively mainten-ance free. They must, however, be used with a pulse forming network to pro-tect them from discharging too quickly. This protection is usually in the formof an internal impedance which limits the minimum discharge time and the peakcurrent delivered from the power source.

The ARDEC Electromagnetic Launcher Facility, Picatinny Arsenal, Dover,NJ, has five, 50 kilojoule, 10,000 volt, capacitor banks each having a maximumcurrent rating of 100,000 amperes. This current limit must be observed to pre-vent internal damage to the supply. It also makes tnese banks unsuitable forpulsing loads which have an inductance less than one microhenry. One methodto alleviate this, and achieve protection, is to operate the capacitor bankin conjunction with a pulse transformer. Five coaxial pulse transformers weredesigned and built at the University of Texas, Center for Electromechanics,Austin, TX. 1 The ultimate goal of this project was to operate all five pulsetransformers, each driven by a capacitor bank, in parallel, to deliver a cur-rent pulse of two million amperes to a short section of a composite railgunbarrel. The integrated system of capacitor banks and current step-up pulsetransformers has been named CAPSTAR. The laboratory set-up of the system isshown in the top of Fig. 1. As a means for validating CAPSTAR, a single, sub-scale pulse transformer was constructed to verify estimates of performance andto corroborate the mathematical model.

The purpose of this paper is to describe the mathematical model we havedeveloped, report the verification done with the subscale pulse transformerand CAPSTAR, and present the results from the initial testing of the CAPSTARsystem. In Sec. II of this report, we present an equivalent circuit for thepuise transformer driving an arbitrary load and outline the method we have usedto solve the equations. In Sec. III, the physical behavior of the pulse trans-former is dis-ussed. In Secs. IV and V, we show both calculated and measuredelectrical properties for each of the components in the transformer system.Section VI describes a simulation of the performance of both the subscale andCAPSTAR systems and the last section discusses the output from the simulationand expected performance if the CAPSTAR system were used to drive a railgunarmature.

II. CIRCUIT MODEL

Consider the equivalent circuit representation for a capacitor drivingthe primary of a current step up pulse transformer as shown in the lower por-tion of Fig. 1. The secondary winding of the transformer is connected to a1Pappas, J.A., Driga, M.D. and Weldon, W.F., "High Current Coaxial PulseTransformer for Railgun Applications," Proceedings of the 5th IEEE PulsedPower Conference, 1985.

1.

CAPACITOR PRIMARY PULSE SECONDARY LOADBANK LEADS X-FORMER LEADS

Rbank '1,ank Readi L leadi M~ 1,2 \V Rlead2 Llead2

cTprimary Rseco nd ary locad

iigurc 1. Photograph of CAPSTAR and Equivalent Circuit for Pulse Transformers.

2

load which comprises an arbitrary inductance and resistance. Summing voltagesaround the right and left hand loops by Kirchoff's Law yields:

c I(Ra R RdI 1 (2LML(L

Vca p 1 bank+Rleadl+pri d (Lbank+Lleadl+Lpri) dt 1,2

and

dI 2 dI10=I (R +R 1d Rld + dj- (Ld1L+_ 1 22 (seclead2+ (Lsec+Llead2+Lload) + - 1, H1 2 , (2)

where M1 ,2 is the mutual inductance between the primary and secondary circuits.From Eq. 2,

dI2 -I2 (R2tt) - (dI1/dt) M1,2dt 1(3)

L2tot

where

L =L +L +L"

L2tot Lsec Llead2 Lload a

and

R =R +R +RR2tot Rsec Rlead2 Rload

Substituting into Eq. (1)

dI V cap - 1I Rltt + (M1,2 12 R2tot/L 2tt) (4)Ltot - (H21 ,2/L2tot)

where

Lltot L bank + LleadI + Lpri

and

Rltot R bank + Rlead 1 + Rpri

The performance of the circuit may be easily solved numerically by making thesubstitution dI/dt % = Al/At for small At. The initial conditions I1 = , =and Vcap Vcharge are updated by calculating the current charge and the

3

capacitor charge. New values for II, 12 and Vcap are found iteratively byusing Eqs. (3) and (4) with

= I + -T (At) (5)

and

Vcap =Vcap - I At/C (6)

The time increment, At, was decreased until the output did not change. Avalue of 1 ps was found to be acceptable. A short computer code has been writ-ten to solve Eqs. (3)-(6) and is included in the Appendix.

III. TRANSFORMER BEHAVIOR

The pulse transformers described here, and shown in Fig. 2, are similarin geometry to a coaxial transmission line. The center conductor, or primarywinding, has radius a, and forms a single continuous helical winding whichpasses through holes drilled in both secondary output buss bars. The outerconductor, or secondary winding, is formed from tubular sections of thickness(c - b). Each secondary segment end is joined in parallel with buss bar toform the secondary output buss. This configuration produces a step up in cur-rent and a step down in voltage from the primary to the secondary side of thetransformer. The ratio of the number of turns in the primary to the singleturn in the secondary can be used to describe transformer performance only inspecial cases. Ideally, if the output of the secondary is shorted and thepulse is relatively short, the ratio of secondary current to primary currentshould equal the turns ratio.

Previous attempts to model the inductance and coupling of the CAPSTARsystem and the subscale transformer assumed that the magnetic field was com-pletely enclosed by the space bounded by the inner wall of the secondarytubes.2 This type of modeling is only applicable for very short time pulsesand a shorted secondary. With the addition of any load inductance the currentratio 12/Il is no longer equal to the number of turns, N.

When no load is connected to the transformer, an apparent contradictionarises in the field strength outside the secondary. The secondary tube can bemade quite thick to prevent magnetic field from the primary penetrating out-side the tube. If, however, one observes no secondary current when primarycurrent is changing, opposite flowing eddy currents must occur on the innerand outer surfaces of the secondary tubes and field will exist outside thesecondary even though none has penetrated into the conducting tube wall. Infact, significant magnetic fields are observed outside the secondary at timestoo short for field to penetrate the wall thickness of the secondary tube. Forthe purpose of this report, we will neglect eddy current losses in the second-ary tubes and assume that they are thin walled.2 ielinski, Alex E., "Design and Testing of a Pulsed Current Transformer,"ARDFC Technical Report ARLCD-TR-85005, April 1985.

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A. Circuit Inductances

The inductive quantities in our mathematical model are sometimes diffi-cult to measure. For this reason we wish to relate the model parameters tomeasureable quantities. From Eq. (1), with the secondary open circuited, the

inductance seen from the primary terminals, Loc, is equal to the inductanceof the primary coil, Lpri. Substituting Eq. (3) into Eq. (1), with the sec-

ondary short circuited, the inductance seen from the primary terminals, Lsc,

is:

Lsc = Lpri M21,2/Lsec (8)

Substantially all the flux produced by the secondary links the primaryand the mutual inductance, M 1 ,2 , is given by the secondary inductance timesN. Substituting in Eq. (8),

L = L - N2 L .(9)sc pri sec

Rewriting Eq. (9), the secondary inductance may be expressed solely in termsof measured quantities as

L LLse = o c (10)sec (0

Similarly the coupling constant defined as k = Ml,2/[Lpri Lsec j , may alsobe written in terms of measured quantities as:

k =[1 - Lsc/Loc] .(11)[1 sc /Loc

B. Circuit Resistances

For the primary coil, resistance is calculated based on full current pene-tration in the winding (DC). This assumption is acceptable because of the

filamentary nature of the wire winding. The minimum secondary resistance is

calculated from the geometry of the secondary tubes. Again, from Eq. (1),with the secondary open circuited, the resistance seen from the primary ter-minals, Roc, is equal to the resistance of the primary coil, Rpri. Substi-tuting lFq. (3) into E(. (1) with the secondary shorted, the resistance seen

from the primary terminals, Rsc, is:

R c= 1 Ri + N2R ec(12)s~c pri (12)

Rcwriting in terms of measured quantities:

0 .

R -RSC OCR =sec N (13)

Since Roc must always be greater than Rpri , Rsec given in Eq. (13) issomewhat less than actual value.

Equations (10) and (13) show that the secondary impedances referred tothe primary side of the current step up transformer are reduced by the squareof the turns ratio.

IV. CALCULATED PARAMETERS

A. Circuit Inductances

Shown in Fig. 2 is the geometry used for the pulse transformer. The pri-mary inductance can be calculated from Ref. 3 as,

L [.002 7 2 (R/AxN) N 2KI]-[.004 7R N [1.25 - in (Ax/a)] (14)pr 1

Where R is the mean radius of the helical primary coil, Ax is the spacing be-tween turns, a is the radius of the primary conductor, and K1 is an end effectcoefficient given in Ref. 3. From the subscale transformer dimensions L =11.89 pH.

In Ref. (1) the inductance seen from the primary terminals with the sec-ondary shorted was verified to be that of straight coaxial tubes with length27RN. This is expressed as:

L = N p R [.25 + ln(b/a)] . (15)sc o

The short circuit inductance calculated from Eq. (15) only includes themagnetic energy of the coaxial configuration. Hence for the subscale transfor-

mer:

L = 1.17 pH.sc

From Eq. (11), the coupling constant is .949. From Eq. (10) the secondary in-ductance is 670 nH.

B. Circuit Resistance

The DC resistance for the primary coil was calculated based on the hand-

book value for No. six gauge stranded copper wire as,

R= 1.29 milliohm/meter

3 Grover, F.W., Inductance Calculations, D. Van Nostrand Co., Inc., NYC, 1946.

- .

giving

R = 9.7 milliohmspri1

The minimum resistance for the secondary tubes (see Fig. 1) may be calcu-lated based on the cross sectional area of conductor which has been penetrated

by current as,

Rtube = 2 7rR/[a(i(c 2 -b 2 )

The total for all four tubes in parallel is,

R = 335 pS2sec

V. MEASURED QUANTITIES

The parameters of interest Loc, Lsc, Roc and Rsc, are measured as a func-tion of frequency. These inductances are shown in Fig. 3 while the resistancesare shown in Fig. 4. For peak current times in the 60 to 100 microsecondrange, a frequency of 4000 Hertz was selected to evaluate the inductances.The corresponding open circuit and short circuit inductances are 12.4 H and2.11 01. The measured short circuit inductance does include, however, the

output buss of the transformer as well as the inductance of a short composedof a foil. The secondary inductance from Eq. (10) yields 643 n and thecoupling constant, k, from Eq. (11) is .91.

In considering the resistances, it was best to use the lowest possiblefrequency measurement (100 Hertz). The corresponding open circuit and shortcircuit resistance are 10.1 milliohms and 13.1 milliohms. The secondary re-sistance calculated from Eq. (13) yields 188 pQ.

VI. SIMULATION AND MODEL PERFORMANCE

The circuit model was found to be very useful in understanding the per-formance of the pulse transformers. The quantities used in the model may beobtained in three different ways: they may be derived from measured quanti-ties as shown in Sec. III; calculated from physical principals as shown inSec. IV; or derived from iterations of parameter variation to best obtain goodagreement between the experiment and transformer model. Departures are made

* from DC values that are consistent with the circuit geometries and currenttime dependence.

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A. Subscale Transformer

The first load used to characterize the transformer was a foil short.The load inductance and resistance were measured on a Hewlett Packard LRCBridge (Model 4274A). Since the foil is thin, the values for inductance andresistance are fairly constant over a wide frequency range. Also, since in-creasing the load inductance has a major effect on the transformer's perform-ance, the results obtained with the least amount of secondary inductance wouldbest characterize the transformer's behavior. The model capacitor power sup-ply used to pulse the transformer had been characterized previously.2 Allvalues in the model were adjusted until good agreement between simulation andexperimental data were obtained under short circuit conditions. Once thetransformer's output could be predicted with a short circuit load of finiteinductance and resistance, a one turn coil was used as the secondary load.Again, impedance measurements were made of the load at 4000 Hertz. The simu-lation was run using the adjusted numbers determined under the short circuitconditions. Figure 5 shows the ratio of primary to secondary currents forthe two different load cases. For the coil load case, the model uses a meas-ured resistance at a frequency which corresponds to the time for current topeak (4000 Hertz). From skin depth calculations the current will fully pene-trate the coil's cross section at 230 microseconds. Since the load coil'scross sectional dimensions are much greater than the transient skin depth oneexpects the coil's resistance to be significantly higher at early times andmuch lower at later times. The effect of the high coil resistance (needed to31mu~ate the experiment at short times) can be seen in Fig. 6. At 150 micro-seconds the calculated secondary current starts to fall from the experimentalcurve. This implies that the load resistance used in the calculation is toolarge for that region of time. The code does not take into account the timedependence of these circuit elements. Table I summarizes the calculated, ex-perimentally measured and the adjusted parameters used for characterizing thesubscale transformer circuit.

B. CAPSTAR System

The detailed design and construction for the full scale transformers arepresented elsewhere together with some initial test results. 1 Because of theconfidence in the circuit model and its validation, the CAPSTAR system wassimulated in the same way. The capacitor bank's internal parameters were cal-culated from experimental data; Lbank % 1 WH and Rbank % 10 milliohms and thecrowbar turn on voltage % -400 v. As in the subscale pulse transformers test-ing, a short was used initially to evaluate the transformer's parameters.The inductance and resistance for the secondary common load plate connectionwere calculated from the voltage drop and secondary dl/dt traces. This wasalso done for the aluminum short load.

Table II shows the adjusted and calculated parameters used for character-izing CAPSTAR.

Figure 7 shows the amount of magnetic energy transferred to an inductiveload for two configurations: One in which the five capacitor banks are usedin parallel and one in which they are used in conjunction with the pulse trans-formers. The cut-off point for use of CAPSTAR to drive an inductive load tomaximum energy appears to be 240 n~l with 10 Z2 of resistance and, 125 nil with1000 p6 of resistance.

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TABLE I - Subscale Transformer

CALCULATED MEASURED ADJUSTED

Open Circuit Inductance (pH) 11.95 12.4 11.89

Short Circuit Inductance (pHI) 1.17 2.11 --

Secondary Inductance (Eq. 10) (nH) 670 643 643

Primary Resistance (mQ2) 9.7 10.1 9.7

Secondary Resistance (pW2) 335 188 955

Coupling Coefficient (Eq. 11) .949 .91 .905

Bank Capacitance (pf) -- 1306 1300

Bank Resistance (ma) -- 36 36

Bank Inductance (nH) -- 440 440

Load Inductance (nH) 4.48 <4.1> ".1

Load Resistance (j.Q) 67 (min.) <60.7> 65

*< > Time Averaged

TABLE II - CAPSTAR

Calculated Adjusted

Bank Capacitance (pf) 1100 1050

Bank Inductance (phI) 1.0 1.0

Bank Resistance (mS2) 10 10

Primary Lead Inductance (nM) 7.2 8.0

Primary Lead Resistance (pSQ) 19.8 20.0

Primary Inductance (pH) 12.89 12.89

Primary Resistance (mQ2) 1.6 1.6

Secondary Inductance (nfl) 408.4 375.5Secondary Resistance (.2) 26.0 300.0

Coupling Constant .89 .853

Load Plate Inductance (nil) 4.46 [<6.2'] 8.5

Load Plate Resistance (p2) 5.01 1<4.45>] 5.0

Short Load Inductance (nil) 2.0 [<2.94>] 3.0Short Load Resistance (IZ2) 4.02 [<5.5>1 5.5

* Time Averaged

14

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Defining efficiency as the ratio of maximum delivered magnetic energy to storedelectrostatic energy, one finds that CAPSTAR becomes more efficient than thefive capacitor banks separately only for loads less than 75 nH with 10 ps ofresistance and, 25 nH with 500 pQ of resistance. This is because, with thepulse transformers and any inductive secondary load, the banks can be operatedat the maximum charge voltage (10 kv) without going over the maximum currentrating (100 kA). This is not the case when the capacitor banks are used sep-

arately. The maximum current rating for use with low inductive loads isreached with charge voltages much less than 10 kv.

The goal of the CAPSTAR system was to electromagnetically stress a com-posite round bore railgun barrel section. One such barrel had a measured timeaveraged inductance and resistance gradient of .374 pH/m and 964 pR/m, respec-tively.4 Assuming that the inductance gradient has no dependence on the boreradius, and that the resistance gradient scales as one over the bore radius,then suitable barrel dimensions can be found to achieve a peak barrel pressure.Barrels with lengths of at least two bore dimensions are only considered.Figure 8 illustrates how the barrel length limits the maximum peak pressurefor a given bore diameter. This graph is for the CAPSTAR system at full-ratedvoltage. The time for the pressure to reach its peak for the CAPSTAR parame-ters in Fig. 8 is in the range of 40-100 microseconds. This type of pressureprofile may be more severe than that experienced by a railgun barrel when driv-ing a railgun armature.

Experimental and calculated data of currents and current ratios with abarrel load are shown in Figs. 9 through 11. Because of the size of the CAP-STAR system, the data was not as abundant as that taken on the subscale trans-former. Only one out of the five capacitor banks was instrumented; measuredquantities included the primary-side voltage (outside the capacitor bank) andthe primary dI/dt. Since the charge voltage on every bank is set by a separ-ate potentiometer there was some uncertainty in the value of the initial chargevoltage. One way to determine the initial charge voltage is to add the capa-citor bank's internal impedance drop to the measured peak primary-side voltage.As a result, there is uncertainty due to the unknown contribution of currentfrom the remaining four transformers. In the model it was assumed that allfive capacitor banks were charged to the same initial value and each transfor-mers' secondary output supplied 1/5 the total load current.

VII. PROJECTED PERFORMANCE WITH RAILGUN LOADS

In addition to modeling the pulse transformer with constant inductiveand resistive secondary loads, it was thought to model the CAPSTAR system witha variable load such as a railgun with a moving armature. A solid armaturewould contribute a smaller loss than a plasma armature, but would have to main-tain it's mechanical integrity throughout the high secondary current pulse.'he armature used in the simulation is assumed to be solid and lossless. Al-though this is not an attempt to optimize a railgun to a pulse transformer itlocs provide some insight into currents and velocities attainable. In orderto assess the CAPSTAR power source driving a railgun load, the 5 capacitor

:lIaboratory Notebook No. LCA 375, ARDF.C, Picatinny Arsenal, Dover, NJ.

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banks in parallel are used as a reference point. Since the maximum currentoutput of each bank is 100,000 amperes, a 1.4 pH inductor with a 20 millisecondtime constant is used to current limit the banks at the maximum charge voltageof 10,000 volts. This will produce a maximum load current of .5 Megamp. A12.7 mm square bore, 1 meter long railgun barrel is used as the secondary load.The resulting pressure waveforms for both power sources are shown in Fig. 12.The launch package mass for both configurations is 3 grams. The velocity foreach of these two power sources is shown in Fig. 13. The transformers workquite well in multiplying the primary current even with a railgun load; how-ever, the launch structure still has to contain the high peak pressure. Forthe load currents that can be produced by CAPSTAR power source an acceptablebore size that limits the peak pressure to approximately 40,000 psi is 60 mm.Correspondingly, for the same pressure, the bore size for the 5 parallel banksis 15 mm. The minimum Lexan launch package mass for the 60 mm bore is roughly250 grams. The mass was varied around that point and this variation is plottedagainst the velocity obtained using both power sources in Fig. 14.It can be seen that CAPSTAR power source can be best utilized to drive a largebore railgun. This is solely to limit the bursting pressure to an acceptablelevel. Correspondingly, large projectiles can be launched. The heavy launchmass keeps the load inductance and resistance quite low early in the currentrise. This allows the current ratio to remain close to the number of turns.After the armature has moved some distance the barrel load inductance (L'z)and load resistance (R'z + L'v) reduce the coupling. This can be seen in Fig.15. Similarly, the secondary currents are shown in Fig. 16. Also, shown inFig. 16 is a railgun driving a 200 volt drop plasma armature. The velocitiesattained are of no consequence for bore size less than 60 mm since it is doubt-ful whether a barrel could contain the high pressures produced by the CAPSTARpower source. Since the pressure pulse has a high peak and a relatively shortwidth, short barrel lengths (300 mm) could be used as a railgun load. Peak toaverage accelerations of 4 are obtainable.

VIII. CONCLUSION

We have developed and tested a model for a capacitor driven, air corepulse transformer. The model has been verified on both the subscale transfor-mer and with preliminary data from the CAPSTAR system. Knowing the initialcapacitor bank voltage in the CAPSTAR system proved to be the greatest sourceof uncertainty in matching the simulation to the experiment. One of the mostsignificant findings is that the load impedance must be quite small if thecurrent ratio is expected to approach the turns ratio. For EM launcher com-ponents the self inductance is often too large for the pulse transformers tobe beneficial. This is evident from the fact that EM launchers generally muststore significant amounts of magnetic field energy in order to perform usefulwork. Furthermore, any great effort spent in enclosing the primary in verythick walled tubing to contain the magnetic field simply makes the transformerheavier without necessarily improving performance. The equivalent circuitmodel does not take into account the eddy current losses in the secondarytubes. For very high impedance loads we expect these losses to be significantand should be included in future modeling.

21

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With the verified transformer model, we have undertaken a brief study ! ,the use of pulse transformers directly driving railguns as a load. Our fin'!-ings show that the transformers are worthwhile only for short times and forcorrespondingly short barrel lengths. The maximum utility of the pulse trans-formers appears to be in applying strong magnetic forces to low inductancestructures for very short times. When the power source switchgear or an i:-ternal impedance limits the maximum current, the pulse transformers will pr.-vide much larger peak currents if the load is carefully chosen and the troni-;-former losses are acceptable.

: -5

,'

REFERENCES h

1. Pappas, J.A., Driga, M.D. and Weldon, W.F., "High Current Coaxial Pulse

Transformer for Railgun Applications," Proceedings of the 5th IEEE PulsedPower Conference, 1985.

2. Zielinski, Alex E., "Design and Testing of a Pulsed Current Transformer,"ARDEC Technical Report ARLCD-TR-85005, April 1985.

3. Grover, F.W., Inductance Calculations, D.Van Nostrand Co., Inc., NYC, 1946.

4. Laboratory Notebook No. LCA 375, ARDEC, Picatinny Arsenal, Dover, N.J.

%1

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292

9i

APPENDIX

COMPUTER PROGRAM

31

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