Can magnetic field blocking be used to improve magnetic accelerators?

Question

There are some materials that block magnetic fields from going to the other side. I was wondering if it was possible to make a coil gun and block the magnetic fields that exist on the back half of the coil. As the coil pulls the projectile towards it initially, and after the projectile passes, it will try to pull it back, causing losses.

In my experience with physics, I see many parallels between liquids, electricity, gravity, and magnetism. Examples being, someone made a computer based on liquid diodes. Also heat increases conductivity with clamping pressure, so does electricity.

This makes me believe that the magnetic field is similar to electivity. Flowing in a direction. Therefore if half of the field was blocked, it would interrupt the field and weaken it, making magnetic field blocking useless.

However, I suppose that if you would insulate the projectile tube only, the outside magnetic field would be largely unaffected and would still complete its circuit. The projectile would just stop being effected by magnetic fields after entering the insulted tube.

If so you could likely get rid of all the complex hardware with multiple coils and timing mechanisms, and just have one giant coil, that could be cooled with liquid gas, and one tube that is half insulated.

Answer 1

Considering these problems non-mathematically is not very useful because electromagnetism follows Maxwell's laws, which are much stricter than the laws of hand-waving.

So let's do some math! You've left off the timing mechanisms, so the coil you describe would have a constant magnetic field, $\vec B(x,y,z)$ Let's suppose it's also rotationally symmetrical (this doesn't change the result, but it makes the math easier). And let's suppose you are accelerating a fixed dipole magnet through the coil, with a dipole moment $\vec m$, straight through along the $z$ axis so $x=y=0$.

The magnetic force on this dipole magnet is given by $\vec F=\nabla(\vec m\cdot\vec B)$. By symmetry, $\vec m\cdot\vec B=m_zB_z$, and $\vec F_x=\vec F_y=0$. So $F=\left|\vec F\right|=F_z=m\frac{\partial B_z}{\partial z}$.

Now, let's find the work that our coil gun does on the magnet as it travels along the axis. This is given by the simple integral below.

$$ W=m\int^{\infty}_{-\infty}dz \frac{\partial B_z}{\partial z}=m(B_z(\infty)-B_z(-\infty))=0$$

Note that $\lim_{z\to\infty}B(z)=0$ unless the coil is infinite. And if the coil is infinite then $B(\infty)=B(-\infty)$.

There's no work done! That is, regardless of what materials you make the tube out of, or how much current you use, or anything else, this device can't possibly do work. The "timing mechanisms" are 100% essential to the operation of a coil gun, because the magnetic field fundamentally pulls the magnet back just as much as it pulls it forward. The only way to around this is to replace the constant magnetic field with a time-varying magnetic field.

Actually, you might note that the work done in this case depends only on the difference between the magnetic field at the starting point and at the ending point. Which means in the situation you have described, it can't even enter the insulated part of the tube. Since the magnetic field decreases to zero in the tube, there must be a large magnetic field gradient before the entrance, and this gradient stops the magnet in its tracks.

Equivalently, this force can be described as a potential energy, $U=\vec m\cdot\vec B$. When the projectile is far away from the coil, its potential energy goes to zero. So any kinetic energy it gained going through the coil is lost. Again, this doesn't depend on the specific geometry or materials of the setup. It only depends on the fact that the field does not vary in time.