Lindsey D. Thornhill

Scaling study for the performance of railgun armatures

A model is developed for investigating the performance of solid, plasma, hybrid, and transitioning armatures as a function of railgun geometry and gun operating conditions. The two figures of merit used in the calculation are the armature efficiency and the maximum velocity. Effects investigated include armature parasitic mass, armature resistance, friction, ablation drag, and, for the hybrid armature, gap growth. The model is applied to study how armature performance scales with projectile mass, or correspondingly bore dimension, and with gun current per unit rail height in the hypervelocity regime from 7 to 15 km/s. The model indicates that armature efficiency generally increases with projectile mass, whereas the maximum velocity for plasma and transitioning armatures is relatively insensitive to projectile mass. Calculations are also performed to determine the sensitivity of the models predictions to uncertainty in key parameters, such as the ablation entrainment fraction, the skin friction coefficient, and the contact potential. >

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. >

Current distribution and plasma properties in injectors for electrothermal-chemical launch

Various designs of injectors for electrothermal-chemical launchers involve a periodic array of solid and plasma conductors. A two-dimensional model to determine both the conduction characteristics and plasma properties for a generic injector of this type is developed. The governing equations, which consists of the coupled Maxwell and energy-transport equations, are presented, and the methodology for solving them is discussed. Some specific calculations that determine how the electrical and thermodynamic characteristics of the device are affected by geometry and operating conditions are carried out. Possible further extensions of the model, as well as behavior that those extensions might elucidate, are also indicated.

Current distribution and resistance characteristics in plasma injectors for electrothermal-chemical launch

A two-dimensional model is developed for investigating electrical conduction in plasma injectors that consist of a periodic array of solid and plasma conductors. The model studied is general but the basic analysis applies to a variety of devices and experimental situations. Calculations are undertaken to determine the preferred conduction pathways as well as the impedance in such an injector as a function of several relevant parameters. These parameters include the relative dimensions of the solid and the aspect ratio of the conduction domain. It is shown that under some conditions the current will flow predominantly in the plasma and bypass the low-resistance path provided by the solid. Such an event is undesirable for several reasons discussed, and methods for preventing its occurrence are suggested. Additional calculations include the resistance of the injector and the fractional amount of current that flows through the solid. These quantities are shown to depend on the various length scales pertinent to the problem.

Scaling laws for plasma armatures in railguns

A methodology for deriving the electrical and thermodynamic properties of plasma armatures in railgun launchers is presented. The methodology is based on the solution to the one-dimensional, quasi-steady equations for the plasma armature. It is shown that the thermodynamic and transport properties for typical armature materials can be adequately represented by power-law curve fits in the temperature and pressure regimes of interest. To illustrate the methodology, detailed computations for both copper and aluminum armatures are performed. Some discussion is also presented for hydrogen armatures. It is shown that the armature properties predicted by the scaling laws agree very well with those derived from more detailed numerical solutions to the governing differential equations. It is shown that, for both aluminum and copper armatures, the electrical conductivity is a strong function of the current per unit rail height and a weak function of launcher geometry. This dependence is shown to be in reasonable agreement with experimental data compiled over a wide range of gun bore dimensions and operating conditions. >

Electromagnetic gun circuit analysis code (EGCAC)

A system engineering code that simulates the performance of a railgun/power supply system is described. The code, named EGCAC (electromagnetic gun circuit analysis code), accounts for many performance degrading effects, including viscous drag on the armature, viscous drag on the gas being pushed in front of the projectile, entrained gas that must be accelerated in front of the projectile, time-dependent rail resistance, armature resistance, system resistance, and ablation drag. EGCAC has been utilized to predict railgun performance up to a velocity of approximately 4 km/s for experiments at several laboratories. The theory of EGCAC is described, and sample calculations are presented. >

End-to-end modeling of electrothermal launchers

The authors describe the development and illustrate the utility of end-to-end models of electrothermal launcher systems. The end-to-end model is composed of a component that models the power supply, a component that models the plasma injector, and a component that models the interior ballistics processes. Appropriate coupling conditions are applied at the interfaces between the component models in order to make the end-to-end model self-consistent. The component models are made modular so that models with varying degrees of complexity can be interchanged as needed for resolution. The authors illustrate the use of the end-to-end model to analyze experimental results using two different levels of interior ballistics models. First, they use a control volume model of the interior ballistics process to simulate a test firing. Then, they illustrate the resolution that can be achieved with a two-dimensional model of the interior ballistics. >

Electron emission at the rail surface

The processes by which current is transferred from the cathode rail to the plasma armature in an arc-driven railgun are examined. Three electron emission mechanisms are considered, namely thermionic emission, field-enhanced thermionic emission (or Schottky emission), and photoemission. Calculations show that the dominant electron emission mechanism depends, to a great extent, on the work function of the rail surface, the rail surface temperature, the electric field at the rail surface, and the effective radiation temperature of the plasma. For conditions that are considered to be typical of a railgun armature, Schottky emission is the dominant electron emission mechanism, providing current densities of the order of 10/sup 9/ A/m/sup 2/. >

Determination of jerk, acceleration, and magnetic field loadings on a projectile launched from an electromagnetic railgun

The development of the numerical procedures that provide a first-order estimate of the jerk, acceleration, and magnetic field loadings are presented. Various power schemes, including inductively driven, distributed energy system (DES), and compulsator driven railguns, are studied. The development and use of nondimensional profiles that may be used to scale the loadings for various performance levels are described. The most severe loads on the projectile are likely to occur while the projectile is in one of the three transition regions in the launcher (preinjector breech, railgun breech, and muzzle). Determination of these loads is dependent on launcher design; schemes for estimating the exit loadings at the muzzle are presented. >