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TECHNICAL REPORT BRL-TR-3014

PLASMA PROPERTIES OF A LARGE-BORE,I.O ARC-ARMATURE RAILGUN

KEITh A. JAMISON

]HNYS. BURDENDTIJOHN D. POWELLJUL 0 3

JULY 1989

APPROVED MOR DUC DISIrDUMIIO UNLUMMW.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

Go .9 125

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BRL-TR-3014

6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATIONUS Arny Ballistic Research (f alicabk)

Laboratory SLB_-T_-_EPEc. ADDRESS (Cty, State, and ZIP Code) 7b. ADDRESS (City, State, and ZIP Code)Aberdeen Proving Ground, MD 21005-5066

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Sc. ADDRESS (C7y, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERSPROGRAM PROJECT TASK WORK UNITAberdeen Proving Ground, MD 21005-5o66 ELEMENT NO. NO. NO. ACCESSION NO.62618A AH80 00 00OIAJ

11. TITLE (IWcude Security Classification)

(U) Plasma Properties of a Large-Bore, Arc-Armature Railgun

12. PERSONAL AUTHOR(S)

WA.. Tnm1 Ty, 1m-v CZ Thivilnn san, .TAhri T)_ PewaV13a. TYPE OF REPORT |13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) 115. PAGE COUNT

FROM TO

16. SUPPLEMENTARY NOTATION

17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if neceuary and identify by block number)FIELD GROUP SUB-GROUP -,Railgun, Plasma Armature, Electromagnetic Propulsion,'20 03 Plasma iagnostics, .

19. ABSTRACT (Continue on reverse if necessary and identify by block number) (iak)

Diagnostic measurements on the plasm armature of the large-bore railgum, CHECHATE,have been made for four separate firings. These measurements include time-dependent valuesof the currenl, light output, and breech and muzzle voltages. In addition, signals obtainedfrom!B-dot" data are used to infer the armature induction field, current-density profile,and arc length. The measured results are then employed in conjunction with a one-dimensional, steady-state model to calculate properties of the arc which cannot be measureddirectly. Among the quantities calculated are the armature mass and the temperature andionization state as a function of position in the arc. As a result of this analysis, it isconcluded that the armature mass remains nearly constant and that the arc temperature issomewhat lower than had been expected previously. Both these factors lend some credence tothe use of plasma armatures for a wide variety of applications.

20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION) UNCLASSIFIED/UNLIMITED 0 SAME AS RPT. 03 DTIC USERS UNCLASSIFIED

22a. NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE (Include Area Code) 22c. OFFICE SYMBOLHenry S. Burden 301127h- 4363 SLCBR-Th-rP

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ACKNOWLEDGMENT

The results of this investigation were heavily dependent upon the re-sponse provided by Maxwell Laboratories; this proved extremely gratifying.The state-of-the-art facility was competently designed and reliably and re-petitively provided the shot performance requested. The professional staffgave clear guidance in setting up the operation, unstinting support duringits term, and a full and thorough assessment of test parameters after itscompletion. The technician staff was enthusiastic and cooperative, pliablein the face of changes, and always ready to give the extra measure of help.The entire operation was one characterized by interest and helpfulness. Wetruly enjoyed every minute of it.

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TABLE OF CONTENTS

Page

ACKNOWLEDGMENT ........... ......................... .iii

LIST OF FIGURES ........... ......................... .vii

LIST OF TABLES .......... ......................... . ix

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

II. EXPERIMENTAL RESULTS .......... ...................... 3

1. Diagnostic Probes .......... ...................... 32. Measured Quantities .......... ..................... 93. Data Analysis ........... ........................ 23

III. MODEL CALCULATIONS ........... ....................... 311. Governing Equations ........ ..................... .. 322. Results of Calculations ....... ................... .. 37

IV. CONCLUSIONS AND RECOMMENDATIONS ...... ................. .46

REFERENCES ........... ........................... .. 47

DISTRIBUTION LIST ........... ........................ 49

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LIST OF FIGURES

Figure Page

1 Schematic Illustration of CHECMATE Railgun and Power Supply . . . 2

2 Schematic Circuit for Breech and Muzzle Voltage Probes .. ..... 5

3 Orientation an, Voltage Response of B-Dot Coils .... ......... 6

4 Induction Field and Light Emission Probe Assembly .... ........ 7

5 Cross Section View of Probe Mounting Location in CHECMATE BarrelStructure......... . . . . . . . . . . . . . . . . 8

6 Schematic Circuit of PIN Diode Light Detectors ............. 10

7 Railgun Current Versus Time Waveforms for Shots 94-97 . . . ... 11

8 Breech and Muzzle Voltage Traces for Shots 95, 96 and 97 . ... 13

9 Four Station B-Dot Loop Voltage Signals; Shot 94 .......... .. 14

10 Four Station B-Dot Loop Voltage Signals; Shot 95 ...... .... 15

11 Four Station B-Dot Loop Voltage Signals; Shot 96 ........ ..16

12 Four Station B-Dot Loop Voltage Signals; Shot 97 ............ 17

13 Light Intensity Versus Time Traces from Four Probes; Shot 95 •. 19

14 Light Intensity Versus Time Traces from Four Probes; Shot 96 . . 20

15 Ideal and Interpolated Accelerations for CHECMATE Railgun Shots94 and 96 ...... ........................... . 21

16 Ideal and Interpolated Accelerations for CHECMATE Railgun Shots

95 and 97 ........... ............................ 22

17 Parametric Description of Armature Current Density Function . . . 25

18 Sample Distribution of the Arc Current Density at Four DifferentTimes; Shot 94... ... .... ... . . . . . . . . . . . . 27

19 Armature Length Versus Armature Current ......... . . . .28

20 Comparison of Current Density and Light Emission; Shot 95 .. . 29

21 Comparison of Current Density and Light Emission; Shot 96 . ... 30

22 Calculated Armature Mass Versus Time of the Carbon Arc ...... .38

23 Peak Temperature Versus Current for Carbon Arc ... ......... .. 39

vii

LIST OF FIGURES

Figure Page

24 Average Temperature Versus Current for Carbon Arc .......... .40

25 Average Ion Concentration Versus Current for Carbon Arc ....... 41

26 Comparison of Temperature Profiles for Carbon Arc from DataAnalysis and Theory ........ ....................... .. 43

27 Neutral Concentration Averaged Over Trailing Edge of Carbon Arc . 45

28 Armature Mass Versus Time for Different Arc Materials ........ .47

29 Mean Arc Temperature Versus Time for Different Arc Materials . 48

ix

I. INTRODUCTION

The possible applications of railguns for military uses have been givenconsiderable attention in recent years. Of the many classes of electric guns,the simple linear railgun has received the most study. Within this class, byfar the most successful has been the plasma armature type exemplified by theCHECMATE railgun.1 In this device, a thin aluminum foil on the rear face ofthe projectile is subjected to a large current and rapidly vaporizes. Thatcurrent is initiated in the circuit, which includes a substantial inductor,by the discharge of a capacitor. At the instant of complete discharge, thecapacitor is then shunted out of the circuit by a low resistance "crowbar".Driven by the energy stored in the field around the inductor, the current con-tinues to flow through the vapor left by the explosion of the foil, heatingand ionizing it to produce an arc or plasma. The driving force applied to theprojectile arises from the pressure accrued in the gaseous plasm as the dif-fuse current of density J flowing through it from rail to rail reacts with theaccompanying, intense magnetic induction field, B. The term plasma (or, alter-natively, arc) implies a hot, ionized, highly luminescent, gaseous conductionpath for the railgun current; the term armature relates to the motive part ofan electric motor. While the exact environment between the rails behind theprojectile is not known in great detail, several theoretical descriptions2 - 5

of its state have been offered and numerous experimental studies have beenperformed on various small railguns.

Most of the projected uses of railguns do not involve small devices, butrather railguns whose bore dimensions are several centimeters and whose lengthsare several meters. The CHECMATE railgun has a square bore 5 cm by 5 cm and alength of five meters. It has been used to fire projectiles having massesbetween 100 and 350 grams at velocities between one and three kilometers persecond. At the time of this writing, it has been fired nearly 100 times. Thesuccessful operation of the CHECMATE railgun represents a significant advancetoward practical applications of railgun technology. A schematic illustrationof the railgun and its power supply are shown in Fig. 1.

In this report, we describe a set of diagnostic measurements made on theCHEC1ATE railgun in an attempt to quantify some of the properties of the plasmaarc armature. In addition, these measurements are used in conjunction with a

iHolland, M.M., Wilkinson, G.M., Krickhuhn, A.P, and Dethlefson, R., "SixMegajoule Rail Gun Test Facility," IEEE Trans. Magn. MAG-22, 1521 (1986).

2 powell, John D. and Batteh, Jad H., "Plasma Dynamics of an Arc-Driven Elec-tromagnetic Projectile Accelerator," J. Appl. Phys. 52, 2717 (1981). Seealso, "Plasma Dynamics of the Arc-Driven Rail Gun," Ballistic Research Labora-tory Report No. ARBRL-TR-02267, September 1980.

3Powell, John D. and Batteh, Jad H., "Two-Dimensional Plasma Model for theArc-Driven Railgun," J. Appl. Phys. 54, 2242 (1983). See also Powell, JohnD., "Two Dimensional Model for Arc Dynamics in the Railgun," Ballistic Re-search Laboratory Report No. ARBRL-TR-02423, October 1982

4Sloan, M.L, "Physics of Rail Gun Plasma Armatures," IEEE Trans. Magn. MAG-22,1747 (1986).

5Thio, Y.C. and Frost, L.S., "Non-Ideal Plasma Behavior of Railgun Arcs," IEEETrans. Magn. MAG-22, 1757 (1986).

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one-dinensional, steady-state model to infer certain properties of the arcwhich cannot be measured directly. The report is organized as follows. InSec. II we describe the diagnostic probes constructed especially for theseexperiments, indicate the specific measurements made, and analyze the data toinfer the current density and arc length. In Sec. III, we indicate some re-visions undertaken on a model previously developed by Powell and Batteh,2

and then use the revised model to calculate properties of the plasma thatcannot be measured directly. In Sec. IV are contained our conclusions andrecommendations for further study.

II. EXPERIMENTAL RESULTS

l. Diagnostic Probes

The measurement of electrical quantities on a railgun requires particularcare to minimize the interactions of its characteristically intense electricand magnetic fields. Probes must be provided with the maximum practicableinsulation possible and multiple grounds, establishing loops in which currentsmay be magnetically induced, must be diligently avoided. All of the diagnos-tic techniqu s employed have been previously used and refined on the smallBRL railgun.9 The voltages produced by the probes were digitally sampled ata preset rate using Nicolet oscilloscopes. These histories were then storedon floppy discs after each firing. The discs were later read into the BRL-LFD VAX 8600 for analysis. Each type of probe and its response characteris-tics are briefly described in the sections following. The only additionaldata used in this analysis were railgun current-time histories and the shot-start locations. To obtain the gun's current-time histories, signals7 wererecorded from calibrated Rogowski loops encircling each of the five power-supply module-output leads. These signals were integrated and summed to givethe total current delivered to the railgun.

The conditions and performance parameters of each of the four firings aresummarized in Table I. For reference we shall utilize the shot number fromthe Maxwell firing log.

TABLE I. Description of Shot Parameters

Maxwell Projectile Peak Injection Capacitor ChargeShot# Mass Current Velocity Velocity Voltage

94 120 g 1.210 MA 2.37 km/s 680 m/s 35 kV95 233 g 1.214 MA 1.86 km/s 500 m/s 35 kV

96 120 g 1.215 MA 2.36 km/s 680 m/s 35 kV97 233 g 1.4 4 MA 2.105 km/s 500 m/s 39 kV

6Jamison, K.A. and Burden, H.S., "A Laboratory Arc Driven Rail Gun," Ballis-tic Research Laboratory Report No. ARBRL-TR-02502, June 1983.

7Wilkinson, G.M. (unpublished data).

3

a. Voltage Probes

Since very different voltages exist at the two ends of the railgun,the breech and muzzle ends of the rails were each shunted by a resistive chainthat wes .inked through a terminated Pearson current transformer (see Fig. 2);the voltage output of the Pearson was thus proportional to the source voltage.Series diodes isolated the probe circuits from the discharge of CHECMATE'snegatively charged sense capacitor on passage of the projectile.

b. B-Dot Loops

In these measurements, the time rate of change of the armture induc-tion field is sensed in a coil oriented to be insensitive to the fields pro-duced by the currents in the rails. Essentially, the coil axis must be para-llel to the rail currents and perpendicular to the armature current. When anarmature carrying megampere currents, with accompanying 10 to 25 Tesla induc-tion fields, passes a point at speeds of the order of I km/s, the rising andfalling field intensity can develop a significant induced voltage in even asmall conducting loop. The relative orientations and typical output for sucha coil are shown schematically in Fig. 3 together with the governing equationsfor the induced signals. Table II denotes the locations and dimensional de-tails for each of the stations mounted in the CHECMATE barrel for these experi-ments. With five-turn coils less than one centimeter in diameter, we havemeasured inductive signatures up to seven volts in amplitude using the probeassembly shown in Fig. 4. This assembly was designed particularly for com-pactness so that the hole in the sidewall of the CHECM4ATE barrel needed to ac-commodate it would cause the least possible weakening of the structure. Themodification of the CHECMATE sidewall to accept the probe is shown in Fig. 5.The view of the probe shown in Fig. 4 is rotated 900 with respect to the per-spective in Fig. 5.

TABLE II. Probe Stations and Dimensions

Station 1 Station 2 Station 3 Station 4

Distance from Arc Initia-tion; Shots 94 and 96 58.4 cm 83.8 cm 109.2 cm 134.6 cmDistance from Arc Initia-tion; Shots 95 and 97 68.6 cm 94.0 cm 119.4 cm 144.8 cmNumber of Turns 5 5 5 5Center of Bore to LoopCenter 5.30 cm 5.36 cm 5.33 cm 5.40 cmLoop Diameter 0.876 cm 0.876 cm 0.876 cm 0.876 cm*NOTE: The exact location of arc initiation varies with the injection veloc-

ity which is different for each projectile mass.

c. Fiber-Ontic Light Probes

The plasma armature is, to understate the case, highly luminous.Our experience in routing light from the bore to a reverse biased PIN diodehas indicated that, even without drilling completely through the insulating

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sidewalls of the railgun, a satisfactory signal will be generated as theplasma armature passes. Figures 4 and 5 show the method of positioning thefiber optic. The thickness of insulator separating the bottom of the fiberoptic cavity and the bore surface was 0.64 cm; the choice of this thicknessrepresents some conservatism over that originally specified.

The fiber optics were routed to a well-shielded box, physically and elec-trically separated from the gun barrel, and which enclosed the PIN diodesused to sense the light. The remainder of the circuit is shown in Fig. 6.The battery was connected with polarity such that the diode blocked currentflow. As the diode is illuminated, however, liberated electrons constitute acurrent proportional to the incident light flux and the voltage drop acrossthe diode. This current produces a voltage drop in the load resistor nearlyproportional to the light intensity. Because the amplitude of this voltagevaries over a range limited by the supply voltage, the original 9-volt batterywas changed to 67 volts to compensate for the increased cavity wall thicknessdiscussed above.

2. Measured Opantities

The probes described in the previous section were utilized to measure thefollowing quantities:

o Rail (armature) currento Breech voltageo Muzzle voltageo Time derivatives of the armature induction fieldo Light emission to the insulating portion of the barrelo Armtiire loestion ver us time.

a. Current

Figure 7 is a representation of the current-versus-time plots measuredby integrating and summing the Maxwell Rogowski coil signals from each of thefive capacitor banks. The waveform is typical of a crowbarred inductor cir-cuit which is characterized by a rapid rise to peak current followed by anearly exponential decay. Current waveforms from Shots 94 and 96 are nearlyidentical and are indistinguishable in Fig. 7. Table I above lists for eachof the four shots a value of peak current. In practice, for the times whenthe armature is near the probe array, the current may be accurately modeled by

I(t) = 1(0) exp (-t/T) . (W)

This equation allows two quantities, 1(0) and -, to be used in the computationof the instantaneous current at times when the armature is close to the probe

array. Table III, in Sec. e below, gives values for both the scaling con-stant and the decay constant which describe the railgun current for all fourshots.

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b. Breech and Muzzle Voltage

The voltage across the extreme tip of the arc drives the currentsensed in the muzzle voltage circuit. This circuit contains only portionsof the rails in which no propulsive current is flowing so self-inductiveand resistive effects of these large currents are not superimposed on themeasurement. (Mutual inductance between the propulsive and the measuringcircuits may also be shown to be very small.) The voltage seen is, then,the resistive voltage across the leading edge of the arc. The breechmeasurement path, on the other hand, includes both current carrying railsand the trailing edge of the armature. This path surrounds a growingvolume of flux driving the armature. The resulting inductive voltagesare, thus, added to the resistive voltage developed across the rear por-tion of the armature. Figure 8 shows breech and muzzle voltage traces forShots 96 and 97. The rapid fall of both voltage traces during the earlyportion of the shot, 0 to 300 microseconds, signals the formation of thearmature plasma. After 500 microseconds the voltage drop becomes relativelyconstant at or near 300 V. The muzzle voltage of only 300 V is lower thananticipated for a 5 cm bore railgun. Of particular interest are the muzzlevoltage jumps at 2.4 ms and 2.9 ms for Shots 96 and 97, respectively. Thesejumps are characteristic of the armature exit from the railgun when thereis still sizable field energy in the inductor and between the rails. We alsonote the lack of such jumps in the breech voltage suggesting that the armaturewas quite long near the end of the shot.

c. Armature Induction Field

The armature induction field, B, is not directly sensed; instead, itstime derivative, "B-dot," is measured at four locations. This measurementconstitutes the standard against which a modeled counterpart is compared as atest of the success in the modeling procedure developed to unfold the armaturecurrent density. The characteristic form of a B-dot trace is a relativelysharp negative peak followed by a wider, lower amplitude positive peak. Thepolarity of these peaks is tied to the chosen orientation of the B-dot coil.As the distributed current in the arc approaches the array of coils, each ofits elements is contributing to each respective fall in voltages sensed. Asthe midpoint of the distribution passes a given coil, the effect of the por-tion of the current which has already passed and is receding matches the eff-ect of the portion still to come and the response passes through zero. Finally,as the bulk of the current is receding down bore, the polarity reverses.

Figures 9 through 12 show the B-dot traces for each of the four stationsfor Shots 94 through 97. The individual points are the digitized voltages in-duced in the loops imbedded in the barrel and smooth lines are those calculatedby the fitting procedure to be discussed in the next section. The randompoint-to-point variations are apparently real and the disturbances superimposedon the later portions of the traces may be caused by small arcs behind theoriginal one. The nearly equal amplitudes from the different probes suggestthat the increasing length of the arc and the decay of the total current whichreduce the B-dot signals are nearly balanced by the increase in velocity whichboosts the B-dot signals.

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The observed intensity of emitted light as a function of time at eachof the four probe stations is plotted for Shots 95 and 96 in Figs. 13 and 14.The differences in vertical scale maxima are an indication of the variationin sensitivity of the uncalibrated PIN diodes, and should not be used to in-fer relative intensities among stations. For Shot 95, the initial sharp risein light intensity indicates passage of the armature-projectile interface;for Shot 96, however, luminosity ahead of the sharp rise indicates leakage ofluminous material past the projectile into the bore ahead of it, from 500 to700 microseconds at probe station 2. The extended leakage path and greaterstability of the longer, heavier projectile used in Shot 95 offer an explana-tion of this observation. On Shot 94 our digitizing instrument was set ontoo sensitive a scale and the signals saturated the amplifiers. On Shot 97the recording equipment failed to record all but one of the light emissionsignals.

e. Armature Location Versus Time

Our method of analysis of armature current density from B-dot signa-tures requires knowledge of the location of the leading edge of the arc ver-sus time. Normally, we would use the sharp rise in the fiber optic data todetermine the position-versus-time function; however, the loss of some fiberoptic data and the uncertainty introduced by the precursor luminosity describedabove, have led us to use the time of the first negative peak of each of thefour B-dot stations to determine the coefficients of the cubic equation

X (t) =A1 t3 + A2 t

2 + A3 t + A4 . (2)

Here Xp(t) denotes the position of the projectile-armature interface. Fromthis information (see Table III), the acceleration may be derived and plotsof acceleration versus time are shown in Figs. 15 and 16. The accuracy ofthis method is probably only on the order of 10 percent, but it is goodenough to show that the ideal accelerations, predicted from the effect of thecalculated armature forces on the projectile mass, are too high. Bore fric-tion and energy required to drive a shock ahead of the projectile could ac-count for most of this discrepancy.

TABLE III. Shot Parmeters Used in Data Analysis

Shot 94 Shot 95 Shot 96 Shot 97

1(0) 1.30 Ma 1.28 Ma 1.30 Ma 1.49 Ma

T 2.17 ms 2.55 ms 2.17 ms 2.50 ms

A1 -1.1802 X 108 -4.9575 x I07 -7.254 x 107 -3.4926 X 107

A2 7.0107 X 105 3.9912 x 10S 6.5462 X 105 4.1452 x 105

A 944.27 757.80 938.40 801.34

A4 -0.12780 -0.14770 -0.13405 -0.11603

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3. Data Analysis

a. Current Density from B-Dot Signatures

A source of further understanding of the plasma armature properties maybe found by setting the time derivative of the Biot-Savart integral (Fig. 3)equal to instantaneous values of the field derivative sensed by a B-dot coil.Then, an unfolding operation may reveal the kernel of the integral J(x,t) whichis the distribution of current within the armature. Because there is no reasonto believe that only one distribution of current is capable of producing theobserved field distribution, not enough information is available to allow aunique analytic solution to this problem. In our previous work,8 however, wehave developed a computer technique for modeling a moving, current distribu-tion and the effect of its magnetic field on a stationary B-dot coil. Weartificially provide added information by using a modification of the Gaussiancurve function, truncated at the plasma-projectile interface (see Fig. 17):

J(x,t) = (1o/cn) exp [-(x-X 0 ) 2/2W2]

where X = Xp-X(t). Figure 17 and Eqs. (3) - (5) define the five adjustableparameters, P..

The procedure systematically varies the parameters until the calculated coilresponse closely fits the B-dot signatures we have measured; in this sense,the distribution is "unfolded" from the B-dot signature.

We have attempted the modeling procedure with a number of different func-tions but were most successful in matching the set of B-dot traces when usinga truncated Gaussian curve function. This Gaussian (or statistical normal)representation of the current-density distribution was chosen for several rea-sons: First, it contains several parameters whose variation manipulates itto the desired shape. Second, the shape is qualitatively similar to standardtheoretically derived profiles.2 Third, the formality for normalizing the areais well known and easily usable. The latter requirement is in accordance withthe practical necessity that the area (i.e., the integral of the current den-sity over the distribution) should be normalized to the value of the instant-aneous, total current. This current is computed using the values of T and1(0) (an adjusted initial current value) and the given value of time. Thevalue for 1(0) is fitting parameter P5 and is adjusted to improve the fit.The value for T is fixed at the experimentally measured quantity. A seriesof calculations, each at a new position as determined from the digitizer timestep and Eq. (2), describing this moving distribution's magnetic field, weremade using a Biot-Savart volume integral. The time derivative, B-dot, at theposition of a given coil was then calculated. With each trial set of para-meters, a test of the fit between the calculated B-dot and that seen by thecoil was made. The process then directed appropriate changes in the parame-ters and was repeated iteratively until no further improvement in goodness offit could be obtained.

8 Jamison, K.A., Marquez-Reines, M. and Burden, H.S., "Measurements of the Spa-tial Distributions of Current in a Rail Gun Arc Armature," IEEE Trans. Magn.MAG-20, 403 (1984).

23

The parameters used to describe the current-density distributions whichfit the data best are listed in Table IV. Referring to Fig. 17, we see thatX(t), the distance between the peak of the Gaussian and the front truncationpoint representing the back of the projectile is given by

X(t) = P2 1(0)P4 = P2 e P4/

TABLE IV. Current Density Parameters for Acceptable B-Dot Fit

Shot 94 Shot 95 Shot 96 Shot 97

P1 0.o6924 0.07375 0.06800 0.06646

P2 0.03701 0.04986 0.03945 0.03699

P3 1.0717 1.1l04 1.2726 1.1527

P4 -0.0902 0.5518 0.00186 0.4706

P5 1.374 X 106 1.430 X 106 1.377 X 106 1.66 x 106

where P4 expresses the power of the current ratio which modulates P2 , the zerotime value of X. The second equality was derived from the first by substitu-tion of Eq. (I).

The characteristic width of the Gaussian is given by

W(t) = P1 ( P3 = P1 e /T (4)

where P3 again expresses a power of the current ratio, this time modulatingPI, the initial Gaussian width. (W is analogous to the variance of the normaldistribution.)

P5 is the calculated, zero-time value for the decaying current wave form.Though not a measured quantity, it does permit use of an analytic formulationwhich gives current

I(t) = P5 exp (-t/T), (5)

accurately representing the measured current when the armature is near theprobes. - "

P2 and PI are continuously modulated by the factors defined. This repre-sentation was chosen primarily to allow comparison between experiment andmodels whose arc length varies as a power of the inverse of the ratio, instan-taneous current to peak current. Note that Xp(t) is given by Eq. (1). Thevalues for T were not used as fitting parameters, but were taken directlyfrom the data. In this way the time dependence of the current was forced tomatch the experimental conditions.

After numerous iterations of the five parameters listed above, minimiz-ing the differences between the measured and calculated B-dot signals, we

24

u 00) N .,

441)

CD

-co

440-

00

Z)

06

44.

I I I- 25

observed the parameters shown in Table IV. All of the parameters except P4were very sensitive to the fitting procedure. Since P2 is not a large number, itis evident that its modulator, P4, would not be a critical parameter in deter-mining the calculated B-dot signal. The Gaussian width, PI, and its modu-lator, P2 , were sensitive fitting parameters and their values for all shots arequite similar.

The parameters above, together with the position-versus-time equation,completely define J for all points in space at all times. The results can beexpected to describe J accurately only in the regions of time when some signalis present on the B-dot probes. Because J is a function of two variables, weare able to display the current density in two different ways. The currentdensity J may be plotted either as a function of position at a fixed time oras a function of time at a fixed position. The former is the so-called snap-shot view of the armature current; the latter is representative of the arma-ture "flying by" a point on the barrel. Figure 18 graphically displays thespatial distribution of J for four different times during Shot 96. The timeshave been arbitrarily chosen to correspond to 100 kA intervals as the currentdecays and the projectile is accelerated down the bore. It is evident fromthese curves that the arc length is between 20 and 40 cm. Therefore, the peakcurrent density does not exceed 150 MA per square meter.

b. Arc Length

Since the arc length is not defined for a Gaussian function, we havearbitrarily chosen to define the length as the distance from the rear of theprojectile to a point in space at which the current density has fallen to onetenth its peak value. For computational purposes, we actually include J whereit was larger than one percent of the maximum. This corresponds to a pointthree Gaussian widths, W(t), behind the maximum value. Figure 19 displays the"arc length," calculated in this manner, versus total current in the armaturefor each of the four shots. While the cutoff point of our distribution isarbitrary, the trends in time and current variation are real. We see fromthis plot that the armature length scales nearly as the inverse of the cur-rent.

c. Comparison of Current Density and Light Intensity

Figures 20 and 21 show plots of the current density, J(t) versus timefor the fixed locations of each of the probes. We have also arbitrarily scaledthe light intensity measurements to the peak value of J as it flies by eachprobe location and plotted it for comparison. It is evident that luminous ma-terial not only outruns the projectile in Shot 96 but also lags behind thecurrent carrying portion of the armature in both shots.

Fine structure in the light output is also evident in both shots, particu-larly at later times. This type of structure was previously observed in datataken from the BRL railgun and can possibly be explained by the existence ofRaleigh-Taylor instabilities in the arc. 9

9Powell, John D., "Interchange Instability in Railgun Arcs," Phys. Rev. A,34, 3262 (1986). See also Ballistic Research Laboratory Report No. BRL-TR-2776, January 19F7.

26

~0

C14

(NV~I1) r. e

-Y 00l (N 444

0

4.3

00

0) 4.0

0' 4)

C; 4)CN (A

0-

C0 LO 0

00

27.

LO (D Nl i

-6-- .4- -4-- -

U) V)V) (n

09 0 0 +

U) >a

/ / 04J

a) N

Z 41~4J V) 4) 1

00 b4J q

r-0;

(UO~ HION31 3dV

28

125

100Probe Station # 1

75

50

25

100

L 75Probe Station #275 -

E 50

. 25

0

U)100

< 75 A , Probe Station #3S50

'- 25

0 _

75 ,Probe Station # 4

50

I A

600 800 1000 1200 1400 1600 1800 2000 2200

TIME ( microseconds )

Figure 20. Comparison of Current Density and Light Emission; Shot9.

29

150 -

125

100100-- Probe Station # 1

75

50

25

0 -

S125

-~100

Probe Station N 2E 75

50D•50

3 250 0

125

o100 A75 .Probe Station #3

4.- 50-

0

100

2550

400 600 800 1000 1200 1400 1600 1800 2000

TIME ( microseconds)

Figure 21. Comparison of Current Density and Light Emission; Shot 96.

30

III. MODEL CALCULATIONS

In the earlier parts of this report data obtained from several shots onCHECMATE have been discussed in some detail. It is obviously desirable to ob-tain in addition some estimate of properties of the arc which cannot be meas-ured directly. Such properties include, for example, the arc mass, the tem-perature as a function of position and time, and the extent of ionization inthe arc. In this section of the report we discuss some calculations that wehave undertaken to determine these properties.

The model used for the calculations is basically the one-dimensional,steady-state model previously developed by Powell and Batteh.2 The model willbe applied at each instant of time under the assumption that time-dependentchanges in the arc properties occur in a quasi-static manner. This assumptionis felt to be reasonable for purposes of analyzing the data discussed heresince the arc is rapidly formed and experimental measurements are made wellafter the acceleration process is underway. If, instead, one wished to studyarc formation or, say, the collision of the arc with a projectile, then highlytime-dependent effects are important and must be accounted for. These effectshave been studied by usl0 and othersll in previous work. There are, of course,additional effects such as instabilities and turbulence, not yet investigatedin great detail, and these effects are not included in the model or calcula-tions.

A number of modifications have been made to the steady-state model bothto improve the calculations and to make best use of the experimental results.The most significant change is that we have omitted entirely the theoreticalcalculation of temperature, a calculation previously based on the assumptionthat ohmic heating in the arc is balanced at any time by radiative cooling.Instead, the temperature within the arc is inferred from the measured (fitted)current density as a function of position and the measured muzzle voltage.This modification has been introduced because theoretical temperature calcula-tions, particularly in one dimension, are not felt to be reliable. Not onlyare there numerical difficulties, but there may also be additional energy loss/gain mechanisms not accounted for and difficult to quantify. These difficul-ties are avoided by simply using the experimental data directly. For purposesof comparison, however, we have undertaken some purely theoretical calculationsin which temperature is calculated via energy-conservation considerations,and these results will also be discussed in the ensuing pages.

Two other minor modifications have also been introduced. First, theelectrical conductivity in the model has been extended to include not onlyelectron-ion scattering (Spitzer), but electron-neutral scattering as well.The latter contribution was included when arc temperatures were found to be

lPFowell, John D. and Jamison, Keith A., "One-Dimensional, Time-DependentModel for Railgun Arcs," Ballistic Research Laboratory Report No. BRL-TR-2779, Feb 87. See also Jamison, K.A., Burden, H.S., Powell, J.D., andMarquez-Reines, M., "Non-Steady Phenomena in Railgun Plasma Armatures,"IEEE Trans. Magn. MAG-22, 1546 (1986).

llBatteh, Jad H. and Rolader, Glenn E., "Modeling of Transient Effects in Rail-gun Plasma Armatures," Ballistic Research Laboratory Contract Report No.BRL-CR-567, March 1987.

31

sufficiently low that this scattering mechanism might in some cases be impor-tant. The second change in the previously used model is that we have attempt-ed to account very approximately for the finite rail height, h (see Fig. 3).In previous work the rails were assumed to be infinitely high, but this assump-tion is known to overestimate substantially the acceleration and pressureof the arc. To account for the finite rail height we have used Batteh'sapproximation12 in which the magnetic permeability is simply replaced by aneffective value.

In Sec. III.1 we outline the governing equations for the model, discuss-ing in particular the changes noted above. In Sec. 111.2 we present resultsof the data analysis, indicating properties of the arc not directly measured,and compare the results with those obtained from some purely theoretical work.We also indicate reasons for the lack of agreement and suggest ways in whichfuture models can be improved.

1. Governing Equations

We take directly from the experimental data at each instant of time valuesof the nuzzle voltage Vm, the arc length La, the current i, the projectilelocation down the bore Xp, and the projectile mass mp. We also essentiallytake as given the experimentally determined current-aensity profile,

1 (x-xo f

J = C-- e 2W2 (6)N

where values of W and x0 are also provided by the experiment (see Fig 17).In general, however, theoretical expressions for the arc conductivity vanishat the back of the arc where the density vanishes so that it is convenient toreplace Eq. (6) near the back of the arc with a function which vanishes atx = X - La. For simplicity we choose a quadratic function to representJ in ?his region. In the notation of previous model calculations where Eis a dimensionless distance defined by

x-X + kp a 31 (7)ta

we therefore have

1W -e- (&&- 0 ) 21eN, for 2 > * (8)N 0

j(W)= C 1E + C 2 E2 for < E*

Note that in this notation 0 (x =Xp - Ia) corresponds to the trailingedge of the arc and E = 1 (x X ) corresponds to the projectile surface.The value of E* is a'bitrary, b~t should be fairly small, and we have consist-ently chosen * = 0.1. 'The constants W0 and 0 in Eq. (8) are given by

1 2 Batteh, Jad H., "Momentum Equation for Arc-Driven Rail Guns," J. Appl. Phys.56, 3182 (1984). See also, "Arc-Dynamic Calculations in the Rail Gun,"Ballistic Research Laboratory Contract Report No. ARBRL-CR-00521, Nov 83.

32

W = W/1a

and (9)x 0-X +

0 = aa

the constants Cl, C2 and CN follow from the requirement that J and A be

continuous at &* and from the current-conservation relation

1f JdE = Jl a " (10)0

Here j is the rail current per unit height. We easily determine from theseconditions that

C- = 2k a E* R 1 za E*R 2 Wo0 a 7r 12 - E0 er *- 029- £a +--W - (r) [erf (--) - err (0 mr)] (n)N 3i 2 i (7) 42o

2R 1 R2Cl 2Bc-* c' (12)

N N

and

C R 2 R102 C (13)

In these expressions

-( = e - 0 )2 /2W02

- ) - )2/2 W2 0R=

(14)

0

and erf (x) is the error function

erf(x) = -I e 2 du (15)

Once the current density has been obtained, expressions for the magnetic-induction field B and pressure P follow immediately from results derived inRef. 2. In particular, we have

C-

B(&) = - - a f J( )d (16)

0

33

which yields after employing (8) and integrating

B(C) = Vj - vk a (CI&2/2 + C2 &3/3) , for & < E*

and (17 )

B(&) = Uj - lita (CI&*2/2 + C2E3/3)lita W0 E -O E,-

(1) [erf ( 0 erf for E > *.C, 2 /2-W0 r2W 0N

If we further assume that the projectile mass is large compared to the arcmass, as we will find to be the case in all our analysis, then the hydro-static pressure P is given in terms of the B field by

p = j2 B 2 (18)2 2p "

In Eqs. (16)-(18), u is the standard, free-space, magnetic permeability.These equations, however, have been derived under the assumption that therails are infinitely high, an approximation that is known to overestimatethe pressure and accelerating force of the arc.2 Batteh12 has argued thatapproximate account can be taken of finite rail height provided p in theseequations is replaced by an effective value U*. In a tedious calculationhe has worked out the appropriate value and finds

1* = 4 [S tan-' (S) + S2/4 log (1 + 1/S2) -- log (1 + s2)] (19)

where S = h/w, i.e., the ratio of the rail height to rail separation. Wewill employ this approximation in the remainder of our analysis.

The position-dependent conductivity within the are can also be inferredfrom the experimental data, namely the current density in (6) and the measuredmuzzle voltage. It has been notedIk that in the steady state J/a is indepen-dent of position in the arc and is given by

J/0 = V P/w . (20)

Here a is the arc conductivity and V is the potential drop across the plasma.Consequently, we have

C= wJ/VP . (21)

3L

. . .. . . . . -, a I I II I i II I iI i

In terms of the measured voltage Vm, Vp is given by

V = V - V (22)

where Vc is the total contact potential at the two rail-arc interfaces. Un-fortunately, values of Vc are not known, so we have analyzed the data forvarious reasonable estimates.

The remaining properties of the arc that must be determined are thetemperature T, the concentration of singly and doubly charged ions xI and x2,the density p, and finally the arc mass ma . To determine the first three ofthese quantities we invoke the theoretical expression for the arc conductivityalong with the Saha equations which predict the ionization state as a functionof temperature and pressure. For the conductivity we assume

1 3

I = 1 + 1 (23)y aL aH

where oH is the conductivity of a completely ionized gas and OL that for aslightly ionized gas. For OH the standard Spitzer expression is used

2.3 x i0-2 YE T3/2 (24)

OH = Z logA T24

where Z is

z X1 + 4x2 (25)x + 2x2

and YE is a constant given by 0.587 for a singly ionized gas and by 0.683 fora doubly ionized gas. For arbitrary ionization we have assumed for simpli-city a linear relation

YE = o.096 Z + o.491 . (26)

The shielding parameter A in Eq. (24) can be written in terms of T, P, xI andx2 as

A = 1.23 x 107 T3/2 (1 + xI + 2x2 )kBT (27)

Z P(x1 +

where kB is Boltzmann's constant.

For the case of slight ionization we use the relation

1 3Cambel, A.B., Plasma Physics and Magnetofluidmechanics (Mc-Graw-Hill, NewYork, 1963), Chap. 7.

35

4.5 x 10- 1 2 (x1 + 2x2 )0L =(I - x2 - x2 ) (28)

where Q is the electron-neutral scattering cross section. Values of Q aregenerally not known in all temperature ranges for materials of interest so wehave assumed a constant value of 10-18 M 2 . At most temperatures a is not aparticularly sensitive function of Q.

The ion concentrations xI and x2 follow from solutions to the Saha eq-uations as discussed in Ref. 2. Thus, we have the relations

xI (xI + 2x2 )

( -x I - x2)(l + x1 + 2x2) =K 1 (TP)

and (29)

x2 (x1 + 2x2 )

x1(l + x1 + 2x2 ) 2

Calculation of the functions K1 and K2 has been discussed elsewhere2 and willnot be discussed here. We should point out, however, that these functionsdepend only on the temperature and pressure and on the the properties of thematerial which constitutes the arc, i.e., the ionization potentials andelectronic partition functions.

It is now apparent that Eqs. (23) and (29) along with the supplementaryrelations discussed and the experimentally inferred conductivity can be solvedsimultaneously to yield values of T, xl, and x2 at all points of the arc. Thissolution must be carried out numerically. Once the values are known, however,the density follows from the ideal-gas equation of state assumed in allour previous work, namely,

+m (30)P~ ~ ~ 1 i+x + 2x2)kBT (0

where m0 is the atomic mass of the ions or neutrals making up the arc. Fin-ally, the arc mass follows directly from the calculated density and measuredarc length via the relation

1m = h w k f p(E)d' (31)

where h is the rail height.

36

The foregoing analysis is sufficient to determine all the arc propertieswithout our having to employ any relationship relating to energy conserva-tion. We now turn to a discussion of some of the calculations.

2. Results of Calculations

We have undertaken numerous calculations using the formalism of thepreceding section and discuss here only some of the more typical results.The calculations fall basically into two groups. In the first, certain aver-age or position-independent properties of the arc were computed; in the sec-ond, spatially dependent quantities were calculated at a given point in time.All data were taken from three of the shots on CHECMATE discussed previously,those numbered 95, 96 and 97. The projectile mass for Shots 95 and 97 was233g, while that for Shot 96 was 120g.

The material which constitutes the arc was not, of course, known in anydetail and most of our results are based on the assumption that it consistsof carbon vapor. Carbon was chosen for most of the calculations for reasonswhich will be explained when the analysis is presented. We have, however,undertaken some computations for copper and aluminum-vapor arcs and theseresults are briefly discussed primarily to indicate some of the more salientdifferences. We have also assumed in most calculations that no contact poten-tial existed at the rail-arc interfaces. Thus, the total measured muzzle voltagein Eq. (22) is assumed to be a bulk voltage drop across the plasma. We do,however, indicate in some of the later discussion what effect a nonzero contactpotential should have and how it can bring experimental and theoretical resultsinto better agreement.

Shown in Fig. 22 is the calculated armature mass for the carbon arc asa function of time for each of the three shots. For Shots 95 and 97 the massappears to remain nearly constant at about l.5g for the entire accelerationtime. Thus, if a significant amount of ablation is occurring during the shot,the resulting mass does not appear to be entrained in the arc. This pointwill be discussed further when a comparison with some purely theoretical re-sults is made. For Shot 96 the arc mass is slightly smaller than for theother two cases. One possible explanation for the slightly smaller mass inShot 96 is that the injection velocity for this case (smaller projectile mass)is higher than that for Shots 95 and 97 and the dwell time at any given pointon the rails is also smaller. Consequently, less time is available for railand insulator material to become vaporized and entrained in the arc if infact such an effect occurs at very early times before the nearly steady values,seen in Fig. 22, are achieved. It should also be noted that there are fairlysignificant drops in the armature mass at about 0.7 and 0.9 milliseconds.These times are Just subsequent to the times at which light-output data fromShot 96 indicated luminous material being blown past the projectile (see Sec.II.2.d). At each time, however, the equilibrium value of the mass appearsto be quickly restored.

We have also computed as a function of the pulsed current i both meanand peak temperatures within the arc as well as the mean concentration ofsingle ions . The peak temperature occurs just to the left of the pro-

jectile surface as will be seen when some spatially dependent results arepresented. These results are shown in Figs. 23-25 and exhibit largelyself-explanatory behavior. Both temperature profiles increase with increasing

37

0(

0

0

000

00

*0

* 0 10

*0 _04-

0 0

0 c 4)

* b 0# 4)0

th 0 Q E40 0

*0 0 Wua 0 0

* 0 0 L* 0 0 (I* 0 0 >.

a 0 4* 0 0E

a 0 -d4.00 0

0 0 * 0 0 00

0 0; 0 '.0i

LO (D. 0 00ol 0) () a 0-

*0 0F-00 0

000 00 000 co

0 r0 co

0 0 4q 1CC

o L 0 U*) 0 LO 0 .4.

(5 SSVPN

38

00

*Q I

* 4

0

.00 0

000

0%

000%

0.* 00~ a.

000 o\ %I .m -r-I m% 0

000

0/C) ) C) 0

0 0 0

co (DI ~ C I I0

0 0 0 0 0 0i

39

clq

0')0) ) u-

000000

0 V() V) V)*00

0'44

009

0 Z* 0))

0 be z

0 1, ,

0 C)

N; >000

o00 0

3dflivd3dh31

40

*~a o,) )

0 00

*0

0 00 ~.

5,.4C; p;

0~0

N))

41.

current, the increase resulting primarily from erhanced ohmic heating athigher currents. It is of interest to note that very approximate scaling re-lations,3 derived under the assumption that w

0

1r4

5.4 ED

IM -.o

14

C; (AU

eJ 5.4 HC4 Al

5.44r4

04

C0 C 4

o C0 C 0o 0 00

o 0 0 0 UdV431

43'

was chosen so that the potential drop across the plasma Vp was the same asthe value predicted from the theory.

TABLE V. Comparison of Theoretical and Data Analysis Results

A B C D

ma 0.95 R 1.46 g 1.25 g 0.81 g

V - 28TV 28TV 28TV

V 0 75V 16Tv

V 120V 28TV 212V 120V

2.77 x 104 2.03 x 10 2.19 x 10 2.72 x 104

TMAx 3.74 x 104 2.52 x 10 2.76 x 104 3.62 x

104

0.74 o.48 0.59 0.77

0.034 0.003 0.004 0.025

It is evident from Fig. 26, curves A and B, that there is substantialdisparity between theory and experiment if one assumes that no contact poten-tial exists at the rail-arc interfaces; at some points the two temperaturesdiffer by as much as 50%. As Vc increases, however, as shown in curves C andD, the experimental temperatures also increase and approach the theoreticalprofile. The increase in T with increasing Vc results from the consequentsmaller values of Vp. These smaller values can result only if the -onducti-vity, and thus the temperature, also increases. It seems probable wat thecontact potential lies somewhere between the extreme values of 0 and 167 voltsso that a realistic curve from the data analysis, accounting accurately forthe contact potential, would still lie somewhat below the theoretical profile.If so, it appears that the theory probably overestimates the temperature ofthe arc by a few percent. One likely source of error in the model is theneglect of some energy-loss mechanism. Recently, it has been proposed thatneutral atoms may diffuse out the back of the arc, while mass is added viaablation in such a way that the total arc mass remains nearly constant. Ifso, the neutrals will carry energy with them and this loss mechanism is notpresently accounted for in the theory. That there is high concentration ofneutrals near the back of the arc can be seen in Fig. 27 in which the neutralconcentration, averaged over the back 25% of the arc, is plotted as a func-tion of current. The data used to compute this curve are identical to thoseused in the computation of results in Figs. 22-24. It seems unlikely thatsuch large numbers of neutrals, particularly at low currents, could be car-ried along with the arc without some significant loss out the back.

44

C-4

0

* '-.

00

0 >oF 0

C;z

0 0 0Na ,

0

LO~*l 01 0 4

00

00

4)

z

cJi

(fCi_( to N -)

0 00 00 c ,

00 C; C C

45

Unfortunately, we cannot determine unequivocally the cause for the dis-crepancy between the theoretical and experimental temperature profiles. Nodoubt both effects discussed in the preceding paragraph contribute to someextent to the lack of agreement. Crude estimates which we have made suggestthat the energy lost via neutral diffusion is probably fairly small (at mostof the order of 10% of the arc's internal energy) but these studies requiremore analysis. We are not aware of any reliable estimates, theoretical orexperimental, of the contact potential.

We should also point out that it would obviously be more desirable to com-pare results of the data analysis with theoretical calculations obtained froma model in which the contact potential was specifically included. One couldthen determine to what extent the existence of such a potential affected theinternal properties of the plasma. Unfortunately, no such model exists. Itdoes seem reasonable, however, to expect that such effects would not be toosignificant since the potential is localized near the rail surfaces. Further,studies are nonetheless appropriate when the nature and magnitude of the con-tact potential are better understood.

We have also carried out some calculations under the assumption that thearc was composed of aluminum and copper ions. A summary of the results ofthese calculations is indicated in Figs. 28 and 29 in which we have plotted asa function of current the arc mass ma and the mean temperature T for the threedifferent types of arc materials. All data were taken from Shot 95 so thatthe curves for carbon were shown in Figs. 22 and 24. For reference the firstand second ionization potentials and atomic masses of the materials involvedare shown in Table VI. As can be seen in Fig. 28, the masses of the differentarcs are substantially different and scale very roughly with the atomic mass.Furthermore, It is noteworthy that the mass computed for the aluminum arc (= 4g)is significantly higher than was the mass of the fuse initially blown to createthe arc (= 0.3g). Since no other source of aluminum was present, it then ap-pears that only a very small percentage of the arc actually consists of alumi-num vapor. Similar statements cannot be made about the other materials. How-ever, since copper has a thermal conductivity higher than the insulating mater-ial, and is therefore harder to vaporize, it appears likely that the arc iscomposed primarily of elements from the insulators, i.e., carbon, hydrogen andoxygen. The temperatures of the various arcs are not nearly so different astheir masses but in general increase with increasing ionization potential.The result can be understood if it is remembered that all three arcs have acommon conductivity and pressure and thus higher temperatures are needed to.ionize the materials which have higher ionization potentials. However, theextent of ionization is a sensitive function of the temperature so fairly smallchanges in this parameter mean large changes in ion concentration.

TABLE VI. Ionization Potentials and Atomic Masses of Arc MaterialsMaterial I (ev) I 2(ev) mo(amu)

C 11.26 24.38 12

Al 5.98 18.82 27

Cu 7.72 20.29 64

46

a 0

o ao

o 44

o 0o 0

o 0 0o a 0

o 0

0 0 Z

o 00

o 00 0 (%CL

0 0 ~.

o 0a 0L.4-

B a Ci)

o 0 (47

0(4 0

0 0

< 0 0 -4

lII I II 4 0 000

0 0 4 0 0 $4

a 0 0* 0 0

* 0 0

0 0 0 o

0 0

s0* 0 a

. 0 00* 0 0 4

0 C14* 0 0* 0 a0

* 0 0 .* 0 0(

* 0 0 0

* 0 0

* 0 E

0 0

* 0 0 >

* 0 DS0 0 4

* 00 m..$ 4o

* 0 O 0* o a

(

* 0 0 L0

o 0 0 40 00 0 0

4 0 00

0 0

* 0 0 00

0 0 0 00 0

o 0 0 0 0 0) .)$

Co 0 0 0.,

0 cO (0 c'Joo ~V 4 -

3flnVd3dV431

48

IV. CONCLUSIONS AND RECOMMENDATIONS

The diagnostic measurements and analysis undertaken here have led to anumber of conclusions concerning plasma arcs in large-bore railguns. Theseconclusions may be summarized as follows. First, it appears that the totalmass of the arc remains nearly constant over the acceleration time. Such aneffect could occur if there were no ablation from the rails or insulators and,in addition, no mechanism for losing mass from the arc. It is more likely,however, that some ablation does occur, particularly from the insulating ma-terials, and the resulting increase in mass is compensated for by some lossmechanism. Two possible mechanisms are diffusion of neutrals out the back ofthe arc apd losses at boundary layers whose velocity must vanish at the railsurface. 1 Both these problems merit further study as do efforts to quantifythe extent of ablation as a function of the other arc properties.

Second, it appears that theoretically derived temperatures are still sig-nificantly higher than those inferred from experiment. This observation per-sists even though the one-dimensional, theoretical model has been revised toaccount approximately for radiation losses from the sides of the arc. It ispossible that the theoretical results fail to account for some energy-lossmechanism (such as would accompany the mass loss described above) and thusoverestimate the temperature. It is also possible, however, that there is asignificant contact potential at the rail-arc interfaces so the measured muz-zle voltages are much higher than the potential drop across the plasma. Ashas been seen, postulating a contact potential and subtracting its value fromthe muzzle voltage before undertaking the data analysis leads to substantiallybetter agreement of theory and experiment. Undoubtedly, both these factorsare present and the extent of each can be determined only by further study.Of particular importance are experimental efforts to measure the contactpotential and theoretical studies of the mass diffusion postulate.

Finally, it does not appear possible to gain much information concerningthe composition of the arc from the work undertaken here. It is fairly evi-dent that there is very little aluminum present but the dominant material can-not be inferred. Presumably, the arc is formed at very early times, beforeits apparently steady mass is achieved, by material ablated from the projec-tile, rails, or insulators. Experimental efforts to determine the compositionof the arc would obviously be worthwhile and, then, theoretical models couldbe revised to account for the appropriate mixture. It does appear, however,that many arc properties are not significantly affected as the arc composi-tion is varied among several reasonable alternatives.

14Barber, John P., private communication.

49

REFERENCES

1. Holland, M.M., Wilkinson, G.M. Krickhuhn, A.P., and Dethlefsen, R., "SixMegajoule Rail Gun Test Facility," IEEE Trans. Magn. MAG-22, 1521 (1986).

2. Powell, John D. and Batteh, Jad H., "Plasma Dynamics of an Arc-DrivenElectromagnetic Projectile Accelerator," J. Appl. Phys. 5 2717 (1981).See also, "Plasma Dynamics of the Arc-Driven Rail Gun," Ballistic ResearchLaboratory Report No. ARBRL-TR-00267, September 1980.

3. Powell, John D. and Batteh, Jad H., "Two-Dimensional Plasma Model forthe Arc-Driven Railgun," J. Appl. Phys. 5.4, 2242 (1983). See also,Powell, John D., "Two Dimensional Model for Arc Dynamics in the Railgun,"Ballistic Research Laboratory Report No. ARBRL-TR-02423, October 1982.

4. Sloan, M.L., "Physics of Rail Gun Plasma Armatures," IEEE Trans. Magn.MAG-22, 1747 (1986).

5. Thio, Y.C. and Frost, L.S., "Non-Ideal Plasma Behavior of Railgun Arcs,"IEEE Trans. Magn. MAG-22, 1757 (1986).

6. Jamison, K.A. and Burden, H.S., "A Laboratory Arc Driven Rail Gun,"

Ballistic Research Laboratory Report No. ARBRL-TR-02502, June 1983.

7. Wilkinson, G.M. (unpublished data).

8. Jamison, K.A., Marquez-Reines M. and Burden, H.S., "Measurement of theSpatial Distributions of Current in a Rail Gun Arc Armature," IEEE Trans.Magn, MAG-20, 403 (1984).

9. Powell, John D., "Interchange Instability in Railgun Arcs," Phys. Rev. A,34, 3262 (1986). See also, Ballistic Research Laboratory Report No.BRL-TR-2776, January 1987.

10. Powell, John D. and Jamison, Keith A., "One-Dimensional, Time-DependentModel for Railgun Arcs," Ballistic Research Laboratory Report No. BRL-TR-2779, Feb 87. See also Jamison, K.A., Burden, H.S., Powell, J.D., andMarquez-Reines, M., "Non-Steady Phenomena in Railgun Plasma Armatures,"IEEE Trans. Magn. MAG-22, 1546 (1986).

ll. Batteh, Jad H. and Rolader, Glenn E., "Modeling of Transient Effects inRailgun Plasma Armatures," Ballistic Research laboratory Contract ReportNo. BRL-CR-567, March 1987.

12. Batteh, Jad H., "Momentum Equation for Arc-Driven Rail Guns," J. Appl.Phys. 56, 3182 (1984). See also, "Arc-Dynamic Calculations in the RailGun," Ballistic Research Laboratory Contract Report No. ARBRL-CR-00521,Nov 83.

13. Cambel, A.B. Plasma Physics and Magnetofluidmechanics (McGraw-Hill, New

York, 1963), Chap. 7.

14. Barber, J.P., private communication.

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