*3.1. Electrical Model*

A model of the electrical part of the first coil of the electromagnetic launcher is described in Figure 19 in the case of a single coil launcher, and in Figure 20 in the case of a four-coil launcher. Electrical differential Equations (1) are implemented using discrete blocks because coefficients of the equation are not constant due to the dependence of inductance *L* on the current and position of the plunger.

**Figure 19.** Electrical model of the first coil of an electromagnetic launcher with 1 coil.

As shown in Figures 19 and 20, the only difference between both models is the number of inputs of the inductance look-up table (LUT) block interpolating linearly the value of *L* using the simulations performed with *FEMM 4.2*. In the case of a four-coil EML, there are five inputs: plunger position, and the currents on each of the four coils.

It is important to note that there is a trigger input in each block. This input corresponds to an electronic trigger supplied by a pilot board and used for piloting the MOS transistor commutating the capacitor on the coil. There is one trigger input per coil, so that it is possible to drive them independently.

**Figure 20.** Electrical model of the first coil of an electromagnetic launcher with 4 coils.
