Perhaps you've seen several articles on concept studies detailing how future spacecraft could be shielded from ionizing radiation using strong magnetic fields. Here I hope to explain how that works without getting into quite the technicalities that a published paper would.

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The Lorentz Force

When a charge is released in an electric field, the electric force causes the charge to move parallel to the field lines. Magnetic fields also produce forces on charges, but a little differently. Say I produce a magnetic field pointing up, with the same field magnitude at every point. Then I put a positive charge in this field and kick it to the right. There is no external electric field in this frame, but the charge will not move only to the right - it will curve into your screen! This force is given by the Lorentz force:

F = qv x B

F is the force vector, v is the velocity vector of the charge, q is the charge of the particle, and B is the local magnetic field vector.

The result is that moving charged particles curve in the presence of a magnetic field. Barring losses due to cyclotron radiation (braking radiation), the particle doesn't lose any energy: The direction simply changes.

Guess what most ionizing radiation found in space is? Really fast moving charged particles. We can use a magnetic field to stop them and protect a spacecraft.

Is that it for magnetic shielding?

So that's it then, right? If I put a big cylindrical magnet in my spacecraft, the field around the equator of the magnet will point straight up. If a charged nucleus comes hurtling towards the center of the magnet at near the speed of light, it will just curve away from the spacecraft and we're done. All we have to do is make sure the magnetic field is strong enough. Right?

Not quite. What I just said is true, but it's missing one major point. Yes, a charged particle fired directly at the center of such a magnet will indeed curve away and miss the magnet. But in space, radiation often comes from all directions. A field able to deflect a head-on radiation particle might also cause a different particle to hit the spacecraft that was otherwise going to miss - it came in from the side on a trajectory that would go past the spacecraft, but impacted the spacecraft due to the Lorentz force from the magnetic field.

So we can't say just yet that our magnetic field will actually do us much good. Yet.

Carl Størmer and the Størmer Radius

Carl Størmer, born in Norway in 1874, is responsible for a lot of the theory behind magnetic radiation shielding. Interestingly, he was not studying how to protect spacecraft from huge amounts of radiation (living before the first spacecraft), but was instead studying the natural polar aurora that form on Earth, partially recounted in his book The Polar Aurora (Here's more information if you're interested.).

Carl Størmer
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The following discussion draws mostly on content from this paper, as well as a little from the book above.

The Earth of course has a magnetic field which can be approximated as a magnetic dipole. Whereas electric charges (positive and negative) exist, no such magnetic charges (called monopoles) have never been observed. Magnetic dipoles, on the other, do exist: The ideal dipole consists of two opposite magnetic charge monopoles infinitely close together. I believe the electron is considered a perfect magnetic dipole. We can use the magnetic field of a dipole to approximate lots of magnets, such as permanent magnet cylinders, coils of wire with current running through them, and ... planets, like Earth.

Current loop magnetic dipole
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Størmer found, by analyzing the relevant differential equations, that a sort of excluded region exists around a magnetic dipole. That is, there is a region around a perfect magnetic dipole that a charged particle coming in from far away cannot enter, so long as the magnetic dipole strength is high enough. This region is determined by a parameter called the Størmer radius. It can be calculated quickly, of course (see the above paper if you're interested), and relies on a number of factors, including the dipole moment strength of the shielding magnetic dipole and the speed of the incoming charged particle. I'll refer to it as Cst.

As far as I know, Cst doesn't have much physical meaning on its own. What it does do is determine the maximum dimension of the shielded excluded region. This region takes the approximate shape of a torus, and the widest part of the torus has a length of about 0.4*Cst.

I highly recommend reading the Shepherd/Kress paper (linked again here) if you want to see how this is done in more detail.

The result: For any given ideal magnetic dipole, incoming charged radiation cannot enter this toroidal region given by Cst. Of course, Cst becomes smaller if the particle is moving more quickly, and becomes larger if the magnetic dipole strength increases. Thus more powerful ionizing radiation will require a bigger magnet to deflect it.

Notice the lack of dots in the toroidal region. No radiation below the given energy can enter this region.
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Remember: This only works for charged radiation! Photons (including gamma, XRay, and UV radiation) and neutron radiation are entirely unaffected by this scheme. On the other hand, alpha and beta radiation, along with many other particles (heavy cosmic ray nuclei, muons, positrons) will all be shielded - you'll just need a ridiculously large magnet to protect a reasonably sized region against something like Americium alpha rays.

Also remember that there's nothing special here. If you put a perfect magnetic dipole is a field and threw different charged particles at it from all directions while tracking where they ended up (using only the Lorentz force), you would see this shielded region start to take shape. Many magnets act like ideal dipoles from far away.

The short of it is that we can use a magnetic dipole to totally block charged radiation! I find it a really cool application of magnetic fields.

Use on Spacecraft

Now we return to the conceptual articles and papers on shielding spacecraft using magnets. To do this, you would simply put the area you want to protect (crew, payload, etc) inside the toroidal shielded region, power up a huge electromagnetic in the core of the torus, and enjoy a radiation-free ride through interplanetary space.

... Of course, it's not anywhere near that simple. For starters, blocking any significantly high energy radiation would require absurdly large magnetic dipole moments, which means absurdly large magnets. Since making a permanent magnet this big is not feasible, what this really means is that it would require massive amounts of current, and therefore massive amount of electrical power. Obscene amounts of power. And then you'd have to cool that magnet, keep it running, and find a way to actually generate this power. As such, it's not that feasible right now. But perhaps in the future!

Another article on this, if you're interested. And another on a far-future artificial magnetic field for the planet Mars.

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I hope you learned something from this post! Unfortunately there's nothing here that can be applied to a DIY situation (I think?) like most of the stuff I write about. But I found this concept pretty cool, so I hope you did too.

Thanks for reading!
All sources cited in text.