A one-dimensional model is described for calculating the properties of plasma arcs in ablating, cylindrical capillaries. The basic assumptions and governing equations are presented and the results of some numerical solutions are discussed. These results are also compared with experimental measurements of the voltage across the arc, as well the pressure measured at a specific point in the capillary tube. The degree to which theory and experiment agree is discussed in some detail and possible reasons for the lack of agreement, where it exists, are pointed out.

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This paper presents a model that can be implemented to quickly estimate the resistive heating and the resulting transient temperature response. Quantifying the energy deposited in the rails and implementing an effective thermal management system will be key elements of an effective design for a large-scale electromagnetic launcher. The total current was divided between the inside, upper/lower and outside surface based on the results of a current distribution calculation. The diffusion of the magnetic field into each surface was modeled in order to determine the current distribution and the resistive heating. Cooling between shots was taken into account by solving the one dimensional transient heat diffusion equation within each surface. Repeating these calculations for a number of discrete segments down the length of the rail enabled the prediction of the total resistive rail heating and the temperature profile along the length of the rail. Experimental tests were conducted that verify the presence of localized heating in the corners of a U-shape conductor made of 7075 Aluminum. Taking into account the localized resistive heating near the surface of the conductor will become increasingly important with large-scale guns.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)October 2008 ARL-TR-4618 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTWe extend a previously developed, two-dimensional model for investigating current and heat transport in railguns. The new model permits the treatment of problems in which there are two components of the magnetic induction and a single component of the current density. In our previous models, there were two components of the current density and only one component of the magnetic induction. The basic mathematical formalism is developed and applied to a two-dimensional configuration in rectangular coordinates. The model is then used to investigate current diffusion into a pair of parallel rails such as might be appropriate in a railgun behind the projectile. The calculations produce the time and spatial distributions of the electromagnetic fields within the rails. Some physical discussion of the results is provided. SUBJECT TERMSrailgun, current diffusion, electromagnetic propulsion, electrodynamics, Maxwell's equations SECURITY

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