When producing rare-earth magnets they map out what is needed to achieve either the maximum or intended focus sets in flux projections of the pole faces and quench that onto the blank's 'memory' with a huge pulse of electromagnetism - thus a standard neodymium mag will already be resistant to bleeding over onto adjacent magnets by design (also a smaller non-pole surface area with the mags we use)

There will be some lateral attraction since in an alternator the adjacent magnets poles alternate but it is only a fraction of what is present on the true pole faces of the magnet. Having an iron backing seriously helps too.

What was missing in your question might have been the scale of the tube - 16-inch diameter outer pipe and 14-inch inner pipe, etc.. This idea is where a lot of pioneers in home built wind power started by using junk brake drums on their original spindles/hubs/bearings.

Where this gets difficult is there is no adjustment possible of the air-gap, the coils formed need compound curve winding to match radius and the magnets themselves need to have complete iron backing contact so would need to either be custom formed, have machined flats on the rotors, or adapter pillow segments that mate evenly with the curving steel pipe. That is not counting the increase in difficulty of finding material and making a whole assembly and balancing that one-up piece if you aren't using automotive parts that is vastly simplified by using trailer hubs and plate steel.

This sounds like a radial configuration, like a soda can spinning inside a slightly larger can. (if an "axial" is like one pancake spinning next to a stationary pancake)

"Zubbly" was the master of the radial motor conversion to PMA. When building a radial from scratch, it may be useful to look at some zubbly conversion pics. Here's some from my file:

http://www.fieldlines.com/story/2008/4/18/14151/1216
Good pics of rotor, Coils are skewed, so mags are straight.

http://www.fieldlines.com/story/2008/6/1/16542/40444
pics, 3/4 HP, 220/380 VAC/1440 RPM's, skewed rectangular magnets, 48 VDC at 340 RPM, ~560 watts.

http://www.fieldlines.com/story/2007/7/22/82515/9969
GOOD PICS !, 7.5 Hp 230 volt single phase, 36 slots, 54V@ 250rpm

http://www.fieldlines.com/story/2006/12/17/22270/167
good pics, British 3HP 380V, now 260V @ 1500 rpm