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Arc-Driven Rail Gun Research

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ARC-DRIVEN RAIL GUN RESEARCH PREPARED K)R LEWIS RESEARCH CENTER NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GRANT NAG 3-76 Pradosh K. Ray Department of ~echanicalEngineering Tuskegee Institute Tuskegee Institute, Alabama .- . REPRODUCED BY U.S. DEPARTMENT OF COMMERCE NATIONAL TECHNICAL INFORMATION SERVICE' SPRINGFIELD, VA 22161 .. - -. I - -- - -- .- -.- 1, lierro~tNo 2. Goverrlnien~ Access~onNo. 3. Acc~p~enl'sCa~aloy No. blAy\-CR 174816 L 4 11t11: llllcl S,IIIIIII~ 5, Il~,~>~brtL1,11,! Uecciilber 1Yd5 Arc 3rivcri Rai 1 Gun l!escarct~ G. t'crfor~n~ny-- - Crga~~~z~;~on -- ~orlc ---- e 7. A~rllor~sl 0. Per(orn~.rir,O:gsn~zat,on Rer,orr P,o Pradosh li. I?dy - 10 %'ark VIIII No 9. Purlorrnlng Oryan~~ilttoriNanie and Address YOS 2415 RTO? 506-55-22 I.:ccli~r~ical Eliqi lieeri rig Uepartii.ent 11. Con~ractor Grant No. Tusieyee Ir~stituLe Tuskcgee Insti tule, AL 36033 f4AG 3-76 13. Tyw of Repu-1 and Perlod Covered I 12 S~rorisorinqAil~,firy Nzrilc arid ,~~ltlt,?ss Ar~riua1 Report tla t ior~alireroliauli cs arld S;race hdiiii n i st1.s ticill to Cec., 1954 Lcwi s Kesedrch Cerlter 14. Sponsoring Agency Code 2 1032 8r'oo~.1~al'kRoad LeHC Code 5323 rii.~;~;illauL~011 114135 15. Su~~l>lentu~ilary Pdolrs Grar~tihn i tor: Lhli 11 ial;~I;cl-s 1aI:r. Iid2S/'~-Lch i s ?.ese;l~.cIl Cerltc!r Cleveland, 011 54\35 IG Abrrracr rlic crl~rdlio~~sdt!scl.ibi II~li~e l:cr.ror-ll,;ll~cc or at1 i~~ductiv~ly-drivenrai i sun are alld lyrcd iib~ilericdl I;'. Ft-icL ior~L~etuecn tile projectile arid rsi1s is inclbded tnrouyh a11 ei:ipi rical foriil~~latiori. The ecluations are applied to tlie experi~ientof Rashleiqh ai~tlI.la1-sl1~11 to obtairi ail est i~lialc! of eriel.!l;y distl-ibution in rail qhlis as a function or ti111c. Tt~ec!fFect OF ft-ic:tioridl t~eiltdissil~atio~~ 011 the bore of the gbrl is ca Icu lated in the exlieri~~ienl:of Lau~!r- et a1 . Ttie ~:ccl\anis~nof ;iias~i.d and [!I-ojectile accelerstion in a dc rail gun is dcscr-ibed f1.01.i a ~i:icr~oscol?ic~!oir~t of view Ll~roucjilthe establ ish~~icntof tile Hal 1 f ielcl. Ttip p1as111acc>i~cluctivit,;i is sliown tu he a ter~sorindicatirlg that there is a sllla I I co~~,[lol~e~itof currenL para1 lel to trlc di rectior~of acceleration. Tllc p1asll;a ct!drdcteristics arc evalu;~tccl in tt~ccspcri~~~cn: of 3auer et ai. as a function of l,I,~s~iaIII,I~S t11t-uug11a 5 il,il>l~rlui~l I~IL-:~I,III iiill arlalysis of tt>e 111as1~1a. Ey cqusting tl~ccllel-!ly dissil!ated Ill tl~e111asl:ia wiLh the I-adidtion heat loss, the properties I of Llie pl as,i~aare deteniiirled. I 17. Kev Y~o~rlriSil(l!~c,red t~i.Aurhor(s) l 18 D~str~but~onS~a~ernun: Rrl i1 C,,III L Ii!c t~.oil~d!jr~elicACCC I il1.d tu~' Ur~classified--9111ii~ii Led Iligh-'icloc ity Projcctilc Acccleratirlg P1as1,ia 1. 19 Sccurilr Class11 lo1 1h8s reporti 20. Secur~trCIdss~l. (of rt115s,lqci 21. No cl Pagcs 22. Pr,ce' Uriilils~ified 1 JIIC I dssi fied 5 3 L - TABLE OF CONTENTS Topic Page Abstract i Energy Partitioning in an Inductively-Driven Rail Gun Introduction Rail Gun Systern Mathematical Formulation Energy Partitioning Results and Discussion Conclusions Nomenclature Friction in Rail Guns Introduction Origin of the Retarding Force Results Dissipation of Energy Concl usion Nomencl ature Plasma-Projectile Interaction in an Arc-Driven Rail Gun Introduction Mechanism of Acceleration Plasma Conductivity Characterization of Plasma Induced Magnetic Field Pressure Temperature and Degree of Ionization Density Conductivity and Resistance Results and Discussion Conclusion Nomenclature References Distribution List LIST OF FIGURES Figure No. Title Page 1 Schematic diagram of a rai 1 gun system 5 2 Equivalent 1umped-parameter electric circuit 6 3 Acceleration length as a function of time 12 4 Percentage of energy distribution as a function of time Effect of accelerator length on projectile exit velocity Efficiency and projectile exit velocity as a function of (L0/L1X) Plasma resistance and current as a function of time Percentage distribution of resistive losses versus time Acceleration length as a function of time Lorentz force and friction force as a function of acceleration length in the experiment of Bauer et a1 . Lorentz force and friction force versus accel- eration length in the experiment of Rashleigh and Marshall Frictional energy dissipation as a percentage of total energy delivered to the gun versus acceleration length in the experiment of Bauer et al. Charge separation at the edges of plasma due to a magnetic field Migration of electrons in the electric and magnetic fields Geometry of plasma for modeling Variation of pressure along the length of the plasma and average pressure Figure No. Title Page 17 Average plasnia temperature and average degree of ionization as a function of plasma mass 54 18 Variation of electron and plasma density with the plasma mass 55 19 Effect of variation of plasma mass on plasma length and conductivity 5 6 LIST OF TABLES Table No. Title Page 1 Input data 9 2 Input data 3 3 3 Input data for estimating plasma conditions 58 4 Estimated plasma parameters in the experiment of Bauer et al. 59 ENERGY PARTITIONING IN AN INDUCTIVELY-DRIVEN RAIL GUN Introduction There are a number of applications that require macroparti- cles moving at very high speeds. Equation of state measurements can be extended with suitable projectile travelling at speeds in excess of 10 km/s [I]. Effects of micrometeoroid impact on space vehicles can be simulated at speeds exceeding 20 km/s [2]. Payloads can be directly launched from the earth's surface to earth orbit or beyond at speeds in the range of 15 to 25 km/s [3] whereas impact fusion might be achievable at speeds greater than 150 km/s [4]. Also there are space propulsion applications [5] and many military applications [6] of projectiles moving' at high speeds. With current technology, projectile speeds in excess of 10 km/s can be obtained only by the use of electromagnetic energy [7]. The simplest of the electromagnetic launching devices is the dc rail gun where the accelerating force is the Lorentz force resulting from a current flowing orthogonally to a self-generated magnetic field. There has been a resurgence of interest in rail guns since Rashleigh and Marshall (hereafter referred to as R & M) success- fully accelerated a 3 gm projectile to a velocity of 5.9 km/s in a 5 m long rail gun by using a plasma armature and an intermediate storage inductor for pulse shaping [8]. Inductively-driven rail guns were found to have superior performance characteristics to those 1 2 driven with other types of power sources. In the intervening years, a considerable amount of work has been done to explore various aspects of rail gun systems. Limits of rail gun performance have been evaluated by Hawke et al. and velocities up to 10 km/s have been obtained for 3 gm projectiles in a 1.8 m long rail gun 191. Even so, the experiments by R & M remain one of the most successful ones to date. In this article, the energy partitioning in an inductively-driven rail gun is analyzed as a function of time after the gun is energized and the parameters of R & M experiments are used in this numerical simulation. From a fundamental point of view, the nature of friction between the projectile and rails was found to be rather complex [lo]. In view of this, it was explored in this study if the effect of friction on rail gun performance can be adequately expressed through an empirical factor as a function of the velocity of the projectile. This can be shown to be proportional to the square of the projectile velocity. However, a recent study indicated that rail gun performances could be explained by taking into account an increase in the mass of the arc as it ablates materials from the rails [Ill. Rai 1 Gun System The rail gun consists of a pair of para1 lel conductors separated by a distance and connected by a movable conductor. A large dc current (ki lo-amperes) flows in a short burst from one rail to the other through the interconnecting conductor. The interconnect- ing conductor is normally a thin metallic fuse which becomes a plasma when the large current is discharged through it. 3 The current flowing in the rails generates a magnetic field B between the rails and this magnetic field interacts with the current flowing in the armature. The resulting Lorentz force J x -B acting on the armature accelerates the plasma along the rails. If the plasma is confined behind a projectile made of dielectric materials, the pressure of plasma will accelerate the projectile along with the plasma. The confinement of the plasma can be provided by the conducting rails on two sides and dielectric material on the other two sides. During launch operations there are high peaking loads which can be met with a suitable energy storage system. The power sources that are currently being used to supply the primary energy to rai1 guns include homopolar generator [8], capacitor bank [12] and magnetic flux compression generator [lo]. The rail gun functions essentially as a linear dc motor.
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