1392 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 5, MAY 2013 Simulation of a Two-Turn Railgun and Comparison Between a Conventional Railgun and a Two-Turn Railgun by 3-D FEM Asghar Keshtkar, Leila Gharib, Mohammad Sajjad Bayati, and Mohammadhosain Abbasi Abstract—The use of a multiturn railgun is a method for decreasing the current without reducing the electromagnetic force on the projectile. The objective of this paper is to study a novel multiturn railgun that can launch several separated projectiles launching synchronously or asynchronously. In addition to dis- tributing the force on the projectiles, this method prepares the projectiles to be launched in time. The railgun has two barrels stacked in series and is powered by one pulse power supply. In this paper, by using a finite-element method, we simulate a 3-D railgun. The projectiles are in different positions. It is investigated by obtaining the self-inductance gradient and mutual inductance gradient for each position of armatures by which time of launch can be regulated through changing the configuration of the launcher. In addition, we explore how the launching time is directly proportional to the propulsive force, their relation and its limitation by the rails and armatures geometry, armatures initial positions, and armatures mass and material. Finally, with simulation results, we conclude that a two-turn railgun has a higher effective inductance gradient than a simple railgun. Index Terms— Current density, electromagnetic launcher, FEM, inductance gradient, railgun. I. I NTRODUCTION T O DATE, the increase in the inductance gradient of railguns has been intensively analyzed [1]. Utilizing aug- mented rails, segmented rails, multisupply sources, and some other methods confirmed a significant effect on inductance gra- dient [2], [3]. A practical solution to the problem of launching massive projectiles to high velocities with existing limitations on a railgun length requires increasing the driving electromag- netic force while providing the necessary mechanical, thermal, and electrical performance and erosion resistance of the barrel and armature [4]. By using completely separate armatures, effects of induction leads to a better force distribution in the model and it will make possible multiprojectiles [5]. The current density distribution in a two-turn railgun is more Manuscript received November 10, 2012; revised March 3, 2013; accepted March 3, 2013. Date of publication April 12, 2013; date of current version May 6, 2013. This work was supported by grant 1/56020 from the Imam Khomeini International University. A. Keshtkar and L. Gharib are with the Imam Khomeini Interna- tional University, Qazvin 34149-16818, Iran (e-mail: akeshtkar@gmail.com; gharib_leila@yahoo.com). M. S. Bayati is with Razi University, Kermanshah 08314274535, Iran (e-mail: s.bayati@gmail.com). M. Abbasi is with Zanjan Regional Electric Company, Zanjan 45195-115, Iran (e-mail: m_abbasi@zrec.co.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2013.2251910 uniform with one better magnetic field diffusion into rail, and the armature surfaces augmented by the insulating gaps available [6]. In this paper, the effects of stacked rails as a multiturn railgun are analyzed. Thus, a two-turn railgun is simulated with finite-element analysis (FEA), which exploited two distinct armatures. Through a power supply to two rail pairs, the results of the modeling confirm a relative increment in inductance gradient. II. GOVERNING EQUATIONS The electromagnetic analysis of a railgun is complex and its simulation needs time transient analysis. The differential equation for magnetic vector potential  A in the transient state are [1] ∇×  1 μ ∇×  A  + σ ∂  A ∂ t =  J (1) ∇×  A =  B (2) where  B is the magnetic flux density, μ is the permeability, σ is the electrical conductivity, and  J is the applied current density. The interaction between the magnetic field density produced by the rail current in the armature position and the passing current from the armature causes its acceleration in the rail length. This force is produced from the Lorentz law  F =   J ×  Bd v. (3) By knowing the applied force on the armatures in moving direction, self- and mutual inductance gradients can be calcu- lated using the following equation [2]: F 1 = 1 2 L  11 I 2 1 + M  21 I 1 I 2 (4) F 2 = 1 2 L  22 I 2 2 + M  12 I 1 I 2 (5) where F 1 , F 2 are the electromagnetic propulsive forces acting on the armatures in moving direction and I 1 , I 2 are the excitation current flowing through the railgun. In this case, the rails are series and I 1 = I 2 . III. RAILGUN STRUCTURE AND I NPUT CURRENT Initially, we considered a two-turn railgun with two rail pairs where each rail is from copper with a length of 100 cm, 0093-3813/$31.00 © 2013 IEEE