Jad H. Batteh

Plasma dynamics of an arc‐driven, electromagnetic, projectile accelerator

A model is analyzed to study the electromagnetic acceleration of projectiles using a device known as the rail gun. Current is conducted between the rails by a plasma arc which drives the projectile. The analysis includes determining the electromagnetic fields within the gun and solving the fluid‐mechanical equations of the plasma under the assumption that the flow parameters are steady in a frame that accelerates with the arc. Specifically, a set of coupled equations is derived which, when solved, yields the properties of the arc and the acceleration of the projectile. A limiting‐case analytic solution to the equations is found, and an iterative technique is employed to solve the equations numerically in the more general case. The results of the calculation are applied to analyze the arc in an experiment recently carried out by Rashleigh and Marshall. Some approximate scaling relations, which indicate how the properties of the arc vary with the dimensions of the rail gun, the mass of the projectile, the m...

Two‐dimensional plasma model for the arc‐driven rail gun

A previously developed one‐dimensional model for studying the fluid‐mechanical electrodynamical properties of the plasma in an arc‐driven rail gun is extended to two dimensions. The analysis includes deriving a set of general, time‐dependent equations, the solution of which yields the associated properties of the arc. These equations are then solved under the assumptions that the flow variables are steady in a frame of reference which accelerates with the arc, and that the effect of the arc’s acceleration upon these variables can be neglected. Numerical calculations are carried out to analyze arcs in recent experiments. In addition to the numerical calculations, some approximate analytic solutions, which are applicable under certain limiting conditions, are also worked out. These limiting‐case solutions are then used to derive a set of scaling relations which indicate how the arc properties vary with gun size, projectile mass, and acceleration characteristics. Considerable discussion of the assumptions an...

Shock propagation in the one‐dimensional lattice at a nonzero initial temperature

Recent studies of shock propagation in a one‐dimensional discrete crystal lattice are extended to include the case for which the lattice is at a nonzero intitial temperature. The lattice is assumed to be monatomic, and its atoms are assumed to interact via a Morse‐type interatomic potential. Behind the shock front, a spectrum of well‐defined stable pulses (solitons) is observed to propagate amid the thermal background of the lattice. The solitons have varying amplitude and propagation velocities, and the different velocities introduce a spreading effect which prevents the shock profile from approaching a steady state. The velocity distribution function of atoms well behind the front is calculated and indicates an approach to thermal equilibrium at an elevated temperature in this region of the crystal. The implications of the nonsteady behavior and the slow approach to thermal equilibrium for currently used theories of detonation are noted and discussed.

Momentum equation for arc-driven rail guns

In several models of arc‐driven rail guns, the rails are assumed to be infinitely high to simplify the calculation of the electromagnetic fields which appear in the momentum equation for the arc. This assumption leads to overestimates of the arc pressures and accelerations by approximately a factor of 2 for typical rail‐gun geometries. In this paper, we develop a simple method for modifying the momentum equation to account for the effect of finite‐height rails on the performance of the rail gun and the properties of the arc. The modification is based on an integration of the Lorentz force across the arc cross section at each axial location in the arc. Application of this technique suggests that, for typical rail‐gun geometries and moderately long arcs, the momentum equation appropriate for infinite‐height rails can be retained provided that the magnetic pressure term in the equation is scaled by a factor which depends on the effective inductance of the gun. The analysis also indicates that the magnetic pr...

Analysis of experimental data from a 50-mm railgun driven by a 5-MJ capacitor power supply

The Compact High Energy Capacitor Module Advanced Test Experiment (CHECMATE) barrel coupled with a 5-MJ capacitor power supply has become a primary testbed for conducting armature research CHECMATE is a nominal 50-mm square-bore EM launcher that is 5 m in length. Recent testing on this hardware was conducted using molybdenum coated rails, G-9 insulators, and a plasma armature. Eight firings were performed at various charge voltages and with various power supply triggering schemes. Muzzle velocities achieved with the 93-g projectile ranged from 3.6 to 4.2 km/s. The analysis performed on this test series is summarized. The primary focus of this analysis was to identify and assess the potential mechanisms which lead to performance degradation at high velocities. Results presented indicate that the Electric Gun Circuit Analysis Code (EGCAC) demonstrates good agreement with experimental B-dot data up to approximately 3.5 km/s; however, on the higher voltage shots, EGCAC overpredicts the expected velocity. >

A methodology for computing thermodynamic and transport properties of plasma mixtures in ETC injectors

This paper describes the development of a numerical model for computing the thermodynamic and transport properties of plasma mixtures characteristic of those found in plasma injectors. The species currently considered in the model are H, C, Cu, Al, Fe, O and N; however, the model is designed such that other species can be added as needed. The calculation of plasma properties employs a methodology that makes it particularly well-suited for incorporation into computational fluid dynamic models for the injector. The paper describes the theory and the methodology used to compute the plasma properties. The authors compare the results of the mixture model with results from more restrictive models as a means of validating the methodology. They also report results from a study conducted with the model to examine the effect of variations in plasma composition on plasma properties. >

Effect of in-bore gas on railgun performance

Acceleration of a projectile in a nonevacuated railgun bore produces a series of shock waves traveling through the gas in front of the projectile which retards the projectiles motion. A model is presented which describes the three components of this retarding force-the force required to accelerate the gas to the projectile velocity as it is entrained by the shock front, the force required to continue to accelerate previously shocked gas as the projectile accelerates, and the force required to overcome the viscous drag which arises from the interaction of the shocked gas and the gun tube. The authors address the relative contributions of the three components of the force and the significance of the retarding force when compared to the net accelerating force. The validity of the strong shock approximation for computing the retarding force is discussed. >

A time‐dependent model for railgun plasma armatures

In this paper a one‐dimensional, time‐dependent model is described for the analysis of railgun plasma armatures. The model assumes that the armature is isothermal, and that the electrical conductivity and degree of ionization in the plasma are uniform and constant in time. The model is applied to the analysis of three problems—armature initiation, armature response to a change in current, and armature response to a change in mass. In each case, the perturbation induces damped oscillations in the armature length and projectile acceleration about the corresponding steady‐state values. The period of the oscillations is, for early times, approximately equal to 3leq/a0, where leq is the equilibrium armature length corresponding to the steady‐state solution and a0 is the acoustic propagation velocity in the plasma. The exponential decay time for the cases studied ranges from 140 to 200 μsec. Although most calculations are completely numerical, a partly analytic, limiting‐case perturbation solution of the govern...

Effects of solitary waves upon the shock profile in a three‐dimensional lattice

Shock propagation in a three‐dimensional monatomic fcc lattice is studied using a computer‐molecular‐dynamic technique. It is demonstrated that compression of the lattice gives rise to a spectrum of well‐defined longitudinal pulses (solitary waves) which propagate in the vicinity of the shock front amid the thermal background of the lattice. The properties of these pulses are examined in some detail and it is demonstrated that they are not completely stable. Rather, they tend to decay as they propagate into the lattice, producing both random thermal motion and, in some cases, transverse solitary‐wave motion. The effects of the solitary waves upon the temperature, density, and stress profiles and upon the approach to thermal equilibrium behind the shock front are investigated. Our results are compared with those of others and some indication of desirable future work is given.

Atmospheric effects on projectile acceleration in the rail gun

The manner in which projectile velocity in a rail gun is limited by the presence of atmosphere in the gun tube is studied. In particular, we solve the equation of motion for the acceleration of the armature and projectile, accounting for both the decelerating force exerted by the atmosphere and the time decay of the current profile. From the solution, a characteristic time is derived which indicates quantitatively when the effect of the atmosphere can be expected to be significant. Results of the calculation are then compared qualitatively with results from two recent experiments: one in which atmospheric effects are nearly negligible and one in which they are not.