Scaling Laws for Electromagnetic Launchers Considering Pulse Power Supply Limitations

In all areas of engineering, testing a full-scale model is costly, risky, and time-consuming. The scaling laws can be implemented in electromagnetic launchers (EMLs) to reduce the risks of a full-scale implementation. The objective is to obtain temperatures, magnetic induction, and stress fields (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i>, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i>) similar to the full-size geometry. EML dimensions such as cross section, rail separation, and length should be selected appropriately to obtain accurate results. Pulsed power supply (PPS) parameters require adjustments as well. In this study, scaling rules are studied utilizing an existing PPS. EMFY-4, with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50\times 60$</tex-math> </inline-formula> mm concave bore and 6-m length, is scaled to be used with 250-kJ capacitive PPS. A multiobjective optimization study is conducted to get a minimum rail length to seek higher energy density and less volume/mass prototype and to minimize the muzzle current to the peak rail current ratio for higher efficiency. The effect of armature mass, capacitor charging voltage, and the required number of PPS modules on the objective functions are discussed. The study showed that when the existing PPS is used, the scaling with the higher scaling factor, denoted as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {\lambda }$</tex-math> </inline-formula>, gives better results. It is observed that the efficiencies of the scaled launchers with 2-m rail length are 10.5%, 13%, and 17.9% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {\lambda }=0.2$</tex-math> </inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {\lambda }=0.3$</tex-math> </inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {\lambda }=0.4$</tex-math> </inline-formula> cases, respectively.