Otto H. Zinke - University of Arkansas Physics Department

THE PHYSICS OF FLUIDS VOLUME 14, NUMBER I JANUARY 1971Snowplowing in a Plasma Rail GunD. W. COLLIEB* AND 0. a. ZINKEDeparfmenl of Physicb, Un6era of Arkanm, Pay~lls,Arkamas 78701(Reoeiied 4 September 1988; final manuscript rewived 4 Msy 1970)Agreement between data from a plarmra rail yn aa analysed by a timeof-flight technique andpredicted by ~wplow theory indimtea that there is no necessity for any theory of drag force in thegun end seema to indiarte that om theory for drag force which also accounta for the conduotion ofelectrical current into a moving plasma ahould be re-eanmined.INTRODUCTIONOne poasible technique for studying the mannerin which electric current is conducted into a plasmfrom conducting walls is to determine the behaviorof the plasma aa it moves with respect to the wallsin a device such as a plasma gun. It has been notedby Thom, Norwood, and Jalufka' that movingplasmas never achieve expected flow velocities insuch devices. In the same article it has been postulatedthat a moving plasma may be slowed if theconduction of electric current into the plasma fromthe walh occurs through the positive ions of theplssma. The efiect has been celled drag force.'Lovberga has offered a postulate which depends on"whether the current front in the gun acts as atight piston or whether it displays permeability."Apparently technical literature by Lovberg,Gooding, and, Haywortha as quoted by Thom,Norwood, and Jaluflca' attribute the di5culty tothe "maseloading problem" which, according, tothe latter authors, "describes the technical problemof matching the inertia of the mass of the plasmato the inertia of the electrical circuitry whichpowers the gun."hae been described in some detail by Msnka4 andRoss' and used by Manka, Crawford, and Zinke'and Rosa and Zinke.' The technique yielde thetemperature (2') of the positive ions of the plaema,the flow velocity (V) of the plasma as it exit, therails, the ion population of the plaama (N), andthe time the plasma is relessed from the rails.Manka4 estimates that oscilloscope reading mrs,the principal source of error, give a 50% variationin the measured temwature and a 15% variationin the memured flow velocity. Reading errors maycause pbma releaee times to be off 6 these databy as much as several microseconds. For similarreasons the ion population may be off by a factorof 2 and is, additionally, subject to the assumptionof a fully 'ionized plasma being present. Snowplowtheory ie modified here to predict, in addition tothe flow velocity of the plasma, the temperature,the ion population, and the plasma release time.SNOWPLOW THEORYThe theory will assume that a plasma of initialpositive ion population n~ originates at one endof a rail gun and ie accelerated to the other throughIn any event, the energy lost to drag force is a neutral gas of n, atoms or .moIeculee per unitexperimentally of the same order of magnitude of length. The point of plasma initiation will be takenthe flow energy and the various theories would as z = 0. The plasma is sssumed created in aapparently have to predict loaaea of lie order of breakdown of neutral-gas caused by the dischargemagnitude. It is the purpose here to report that of an energy storage capacitor. The plasma fomif plasma drag occurs with a simple rail gun, the one component of a simple series circuit. Theenergy transferred to the drag mechanism must mowplow equation derived here will be Bimilar tobe at least an order of magnitude less than the that derived by Hart? However, the nobtion ofplasma flow- energy. Indeed, simple snowplowing Mostev, Neuringer, and Rigneyo will be d.seems to account for dl aspects of plasma behavior Kirchoffla law for a plasm8 driven by a diechargingobserved. Therefore, the variom theories for plasma capwitor is [see, e.g., Eq. (1) of Ref. 91drag should be re-examined and, in particular, thetheory of Thom, Notwood, and JaLufks1 which d(LOz +accounts for the flow of electric current into thedl+ (go + Rr + RJIplasma should be, reviewed. + e/1 ' Zdl = Vo. (I):Measurements of plssma characteristics weremade through the time-of-fight technique which The inductance L, ia ~ssociated with the oircuit i72