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Electromagnetic propulsion provides a non-contact way for delivering goods. The projectile typically does not contain explosives, which has apparent advantages over traditional methods. Due to the multi-physics nature, simulation is expensive and time-consuming. We established a simplified model in time domain incorporating mechanics and electromagnetics to study electromagnetic propulsion. Results show that important physical parameters such as force, velocity, acceleration, etc. can be extracted from the model without time-consuming efforts. We hope this model could help the exploration of electromagnetic propulsion.

Electromagnetic propulsion uses the physics of moving charge or current conductor in a magnetic field under the electromagnetic force (known as Lorentz force) to accelerate the projectile [

However, we found that a simplified but accurate simulation is not currently available for studying electromagnetic propulsion. Here, we build a transient electromagnetic propulsion model in three dimensions by employing multi-physical fields. An initial test with a simplified armature shows that the speed can be accelerated to 1836 meters per second in our model. This model is simple but provides enough details in an intuitive way.

The entire magnetic propulsion problem involves mechanics, electromagnetics, aerodynamics, heat transfer etc. However, we only focus on electromagnetics and mechanics in this work. Heat transfer and aerodynamics can be added in further investigations in more details.

Due to the quasi-static nature of the problem under study, we can decouple the electromagnetic problem into pure electric and magnetic parts. In the electric domain, the governing equation is the Gaussian law [

{ ∇ ⋅ J = Q J = σ E + ∂ D ∂ t E = − ∇ V (1)

where J is the current density in units of A/m^{2}, D is the electrical displacement in unit of C/m^{2}, σ is the electrical conductivity in unit of S/m and V is the scalar potential in unit of V. For the electrical part, we only consider the two rails and the space in between them with other space ignored, since the electric field outside this region is not of interest to us. Simulations on these regions can give us the correct results regarding total current and local current density.

In the magnetic domain, the governing equation is the Ampere’s law shown below with H and A being the magnetic field A/m in unit of and vector potential in unit of T·m, respectively [

{ ∇ × H = J B = ∇ × A (2)

Since magnetic field is generated by the current, there is no source nor sink for it. We incorporated a larger air region to cover the rails. The outer boundary of the air region is set to be magnetic insulation, namely, n × A = 0 , where n is the surface normal.

The mechanics part is governed by the Newton’s law below.

d 2 x d t 2 = F x M (3)

F x = ∫ V ( J × B ) d V . (4)

The schematic diagram of electromagnetic propulsion system is shown in

The armature travels about 7 meters in 4 milliseconds, reaching a speed of 1836 m/s. It gains tremendous acceleration during the interaction with electromagnetic wave.

In summary, we have built a simplified model for simulating electromagnetic propulsion with finite element method. The model incorporates mechanics and low-frequency electromagnetics. Numerical results show that the electrical projectile can be accelerated to 1836 m/s in a traveling distance of 7 meters. In the future, more details, such as heat transfer effect, could be added to give even detailed and accurate results.

The authors declare no conflicts of interest regarding the publication of this paper.

Chen, R.W. and Wang, K.C. (2020) A Simplified Numerical Approach for Simulating Electromagnetic Propulsion. Journal of Electromagnetic Analysis and Applications, 12, 1-5. https://doi.org/10.4236/jemaa.2020.121001