Electronic – Simulating a magnetic field in Spice

Firstly, I do not think you can use a neodymium magnet as a projectile.

Coilgun

A coilgun (or Gauss gun, in reference to Carl Friedrich Gauss, who formulated mathematical descriptions of the magnetic effect used by magnetic accelerators) is a type of projectile accelerator consisting of one or more coils used as electromagnets in the configuration of a linear motor that accelerate a ferromagnetic or conducting projectile to high velocity.

And you should be more focused on the kinetic energy of the projectile as it leaves the tube. A 400 farad 2.7 v capacitor stores 1450 joules of energy, which given a efficiency of 1 percent translates to 14.5 joules of projectile energy. Plugging this in to the kinetic energy equation \$E = \frac{1}{2}mv^2\$, gives us a muzzle velocity of 170 m/s for a 1 gram projectile.

Now let's come to the question of force. The force depends on how much power you can pump through the coil. And this minimum force will be huge, because the projectile must reach muzzle velocity by the middle of the coil. (The coil must also be discharged by this time, or the projectile will slow down) For a one gram projectile, this will be 729 newtons or 73 kgs of force, assuming a coil length of 4 cm. (You can calculate acceleration from this equation - \$ a = \frac{v^2}{s}\$ where s is the barrel length and v is velocity)

And what does this mean? You need a strong projectile, definitely. And your capacitor must provide a vast amount of power. Taking the above parameters, the time before the projectile hits the middle of the barrel is 0.23 milliseconds, which you can calculate using the kinematic equation \$x = \frac{1}{2}at^2\$. Dividing the total energy by the time gives us a power requirement of 6.5 MW to be discharged. That's right. 6.5 MW.

With a 2.7 volt capacitor, the resistance must be below 1 micro-ohm. Definitely not possible. With a 400 volt capacitor, the minimum will be 24 milliohms. This is possible.

Now, your question specifies you are not interested in maximizing velocity. In that case, you can go through these calculations for your specific use case. The wire gauge depends on the current going through the wire and the voltage. Once you have that you can calculate the number of turns needed, and that gives you the resistance of the coil. You can add this to the resistance of the capacitor and the diode to give you the total resistance. This must be lower than the minimum resistance you calculated.

And of course, exercise caution. 1500 joules is a lot of energy.

Large pole pieces close together.

In your case one approach is a 10x20x(long) iron bar formed into an almost complete circle leaving a L=5 gap. This concentrates a relatively strong field enclosing your 10x20x5 volume in that gap. Wind copper round the bar, apply current.

Something like this...

Image from this page... Dimensions may not match your needs and material is ferrite rather than iron, but illustrates the principle.

EDIT : comparing this with your third option - there are some similarities if you concentrated the winding on the vertical arm of your core. (Spreading out the winding screens most of your cell from the magnetic field!). However this directs the flux almost equally across the gap, whereas with your "U" the RH end of the gap will see somewhat less field while the LH end next to the winding will see a bit more. You can probably reduce this effect by carefully shaping the core and pole pieces, and performing 3D simulations of the magnetic circuit...

Alternative form with a gapped E core...

Winding would be on the central limb of the E, and would be simpler if the gap was at one end of the central limb rather than in the middle. Image from this page though their focus is on creating efficient inductors rather than generating a concentrated magnetic field. Nevertheless, read their page - especially the section "Gap energy" - even though the magnetic path looks quite long, because iron (or ferrite) has such a low reluctance compared to air, its length is unimportant compared to the length of the gap.