# Turned to steel in the great magnetic field

This is obviously a "fun" question, but I'm sure it still has valid physics in it, so bear with me.

How great of a magnetic field would you need to transmute other elements into iron/nickel, if that's in fact possible?

The magnetic field near a neutron star, roughly of order 10^10 tesla, is so strong that it distorts atomic orbitals into thin "cigar shapes". (The cyclotron energy becomes greater than the Coulomb energy.) Certainly if a solid crystal were placed in such a field it would become very anisotropic, and at some field strength the lattice constant in the direction transverse to the field could become small enough for nuclear fusion rates between the nuclei to become non-negligible.

How high do we need to crank up the field before the nuclei all equilibrate to the absolute energy minimum of iron and nickel in, say, a matter of hours or days?

Update: From http://dx.doi.org/10.1086/152986 it appears that matter in strong magnetic fields forms into strongly-bound 1D chains along the field lines, which are only weakly bound to each other, and the parallel and transverse lattice constants are actually comparable.

• +1 for suggesting the mechanism by which this could happen, in enough detail that it's clearly out of my area of expertise ;-) Without that I'm sure I would have downvoted and/or voted to close. – David Z Dec 5 '10 at 2:47
• +1, hopefully the answers will be as good as the question. – Sklivvz Dec 5 '10 at 11:38
• +1, I would say in the order of Gigateslas, however I do not have sufficient expertise in the subject to conduct a mathematical analysis. – Cem Dec 5 '10 at 14:42

a great topic. First, ten gigatesla is only the magnetic field near a magnetar - a special type of neutron star. They were discussed e.g. in this Scientific American article in 2003:

https://web.archive.org/web/20120204052553if_/http://solomon.as.utexas.edu/~duncan/sciam.pdf

Ordinary neutron stars have magnetic fields that are 1000 times weaker than that.

It is true that in the magnetar stars, atoms are squeezed to cigars thinner than the Compton wavelength of the electron - which is in between the radius of the electron (and also the radius of the nucleus) and the radius of the atom.

However, it is such strong a field that many other things occur. For example, there is a box interaction between 4 photons, caused by a virtual electron loop. This is normally negligible - so we say that Maxwell's equations are linear in the electromagnetic fields. However, at such strong magnetic fields, the nonlinearity kicks in and one photon often splits into two, or vice versa.

So there's a lot of new stuff going on in such fields. A magnetar that would be 1000 miles away would kill us due to diamagnetism of water in our cells.

Magnetars and fusion

Your idea to use magnetars to support fusion is creative, of course. But I think that to start fusion, you have to squeeze the nuclei closer than the Compton wavelength of the electron which is still $$2.4 \times 10^{-12}$$ meters, much longer than the nuclear radius. You would need to add two or three more orders of magnitude to the squeezing. A magnetar is not enough for that.

When you have such brutally deformed atoms, you can't neglect the nuclear reactions involving electrons - which are usually thought of as "irrelevant distant small particles" that don't influence the nuclear processes. However, if their wave functions are squeezed to radia that are substantially shorter than the Compton wavelength, their kinetic energy substantially increases. At the width of the wave function comparable to the Compton wavelength, the total energy/mass of the electron increases by O(100%) or so. This increase comes from the "thin" directions only but it is enough.

Now, note that the difference between the neutron mass and the proton mass is just 2.5 masses of the electron. So if you squeeze the electron so that its total energy increases more than 2.5 times, it becomes energetically favored for the protons inside your (not so) "crystal" to absorb the electron and turn into neutrons.

So I believe that all the matter in a near proximity of the magnetar will actually turn into the same matter that the neutron star itself is made of. That will happen before the protons will have any chance to create new bound states such as iron nuclei (that you wanted to produce by fusion). You will end up with neutrons and almost no protons - the same state of matter that the star is built from itself. In some sense, I think that this shouldn't be surprising - if it is surprising for someone, he should have asked the question why there is no ordinary matter left on the neutron stars.

What is the timescale after which the electrons are absorbed to turn the protons into neutrons? Well, it's a process mediated by the weak nuclear interaction - like beta-decays. Recall that the lifetime of the neutron is 15 minutes but it is anomalously long a time because of some kinematical accidents. The normal objects of the same size - such as the extremely squeezed cigar-shaped atoms - would decay more quickly (into neutron and neutrinos, in this case). On the other hand, the electrons in the cigar-shaped atoms occupy a bigger region than the quarks in the neutron. But this can only add at most 4 orders of magnitude. To summarize, I think that within days or months, if not more quickly, the electrons would get swallowed to create neutrons.

All the best Lubos