[Phys-L] Halbach arrays (was: magnetic braking). Also pedagogy

[John Denker <jsd@av8n.com>]

Hi --

1) In general: If you're building anything with magnets in it,
you need to know about *Halbach arrays*

I can't do much better than to quote wikipedia:

> A Halbach array is a special arrangement of permanent magnets that 
> augments the magnetic field on one side of the array while 
> cancelling the field to near zero on the other side.

This allows you to make the field especially uniform *or*
especially non-uniform.

> The crucial point is that the flux will cancel below the plane and 
> reinforce itself above the plane. In fact, any magnetization pattern 
> where the components of magnetization are π / 2 out of phase with
> each other will result in a one-sided flux. The mathematical
> transform that shifts the phase of all components of some function
> by π / 2 is called a Hilbert transform; the components of the
> magnetization vector can therefore be any Hilbert-transform pair
> (the simplest of which is simply sin ⁡ ( x ) cos ⁡ ( y ), as shown
> in the diagram above).
https://en.wikipedia.org/wiki/Halbach_array

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2) In particular: Back on 9/24/24 1:45 PM, Zeke Kossover asked
about magnetic braking in a uniform field versus a non-uniform
field.

The key idea is that you want to make the field as non-uniform
as you can without unduly weakening it.

The Halbach idea should allow you to make the field stronger and
make it stick out farther before it washes itself out.

I should have mentioned this earlier.

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3) Pedagogical story-telling:

Students may imagine that everything worth knowing about permanent
magnets and electric motors was figured out hundreds of years ago.
But that's certainly not true of Halbach arrays. They're a relatively
recent development.

More generally: There is such a thing as green-field research. That
includes looking in places where nobody has ever looked before. For
example, if you build the world's first radio telescope, or the
world's first IR telescope, you're guaranteed to discover stuff that
nobody could possibly have seen before. Sometimes such an instrument
is called your "secret weapon".

I've done some of that. But that's not the whole story.

Once I had an obnoxious pooh-bah ask me what *my* secret weapon was.
I told him that at the moment I didn't have one and didn't need one.
He gave me a dirty look. I explained that there is such a thing as
brown-field research, which involves looking at things that have
been around for hundreds of years, and saying "Hey, wait a minute.
Every textbook on earth says that the laws of physics make it
impossible to do any better than this ... but I'm not convinced."

This doesn't involve breaking the laws of physics. It's just
realizing that the laws don't actually say what everybody thinks
they say.

4) This is relevant to current events, namely the mining and
distribution of rare-earth metals, which are used to make strong
permanent magnets, which are needed for making powerful, efficient,
lightweight electric motors.

Good discussion of such things, from a year ago:
https://www.mheavytechnology.com/news/mining-of-rare-and-rare-earth-metals/