# An Electromagnetic Circuit Design to Improve a Multi-Stage Coil-Gun's Energy Conversion Efficiency
###### Abstract  
We present in this paper a method of improving a coil gun circuit's energy efficiency and acceleration performance. Particularly, the improvement was performed by designing a solenoid coil and capacitance for projectile velocity enhancement in a multi-stage coil gun, based on simulations and experiments. A projectile decelerates in coil guns when passing through the solenoid coil's center by being subjugated to a force opposing the launch direction. Thus, we achieved the efficient distribution of the electromagnetic power delivered from the circuit to the projectile by adjusting the capacitance according to the solenoid coil's shape. This produced a current shape suitable for projectile acceleration, consequently enhancing its performance. Designing the coil using 1.3 mm diameter copper wires, among the coils using copper wires of various diameters, to increase the number of turns and reduce the capacitance improved the energy efficiency while enhancing the acceleration performance. Finally, each stage's measured and simulated velocities in the coil gun were analyzed and compared. Accordingly, we arrived at an efficient design method for multi-stage coil gun systems.  
capacitor; electromagnetic launcher (EML); finite elements method; multi-stage coil gun; solenoid coil +
Footnote †: journal: Applied Sciences  
increasing the number of turns and the supplied current may decrease the energy distribution efficiency, even if the electromagnetic force generated in the coil is high, potentially decreasing the projectile's acceleration efficiency. Therefore, in this research, we designed the solenoid coil and capacitance to improve the projectile acceleration performance and the electrical to kinetic energy conversion efficiency. Notably, in this research, not only did we set the used copper wire's diameter as a design variable, but also the number of turns of the solenoid coil was set as well. Accordingly, we selected the suitable capacitance depending on the coil's shape to efficiently convert the generated electromagnetic force into kinetic energy. Additionally, not only do the coil gun's electric circuit components act as important design factors, but also the projectile's location during operation [7]. This is because the force received by the projectile continuously varies according to the distance and time between it and the solenoid coil. For this reason, it is difficult to directly calculate the projectile velocity [8; 9]. Therefore, using a computation program might be the best idea for efficient designs. Moreover, we simulated the designed coil gun model by FEA using ANSYS Maxwell, an electromagnetic analysis FEA software [10]. Based on the simulation results, a prototype was fabricated and the projectile velocity was measured for the prototype. Since a single-coil gun's acceleration performance is limited due to its solenoid's magnetic saturation point, multi-stage coil guns are studied to increase the projectile velocity [11; 12]. Therefore, we also considered in this study a situation where the projectile had an initial velocity at each stage, except for the first and last ones. A multi-stage coil gun (with 9 stages) was designed, and the design method, which was based on that of a single-coil gun, was presented.