Electromagnetic projectile acceleration utilizing distributed energy sources

Circuit equations are derived for an electromagnetic projectile accelerator (railgun) powered by a large number of capacitive discharge circuits distributed along its length. The circuit equations are put into dimensionless form and the parameters governing the solutions derived. After specializing the equations to constant spacing between circuits, the case of lossless rails and negligible drag is analyzed to show that the electrical to kinetic energy transfer efficiency is equal to σ/2, where σ=2mS/ℒq20 and m is the projectile mass, S the distance between discharge circuit, ℒthe rail inductance per unit length, and q0 the charge on the first stage capacitor. For σ=2 complete transfer of electrical to kinetic energy is predicted while for σ>2 the projective-discharge circuit system is unstable. Numerical solutions are presented for both lossless rails and for finite rail resistance. When rail resistance is included, >70% transfer is calculated for accelerators of arbitrary length. The problem of projectile startup is considered and a simple modification of the first two stages is described which provides proper startup. Finally, the results of the numerical solutions are applied to a practical railgun design. A research railgun designed for repeated operation at 50 km/sec is described. It would have an overall length of 77 m, an electrical efficiency of 81%, a stored energy per stage of 105 kJ, and a charge transfer of <50 C per stage. A railgun of this design appears to be practicable with current pulsed power technology.