Thanks for the more detailed description Verpies. I think what actually threw me off was I expected the field between a pair of coils/loops to repel rather than attract.
Since the force between two conductors is attractive when the currents in these conductors flow in the same direction and repulsive if they flow in opposite directions, the coaxial rings will attract each other axially when carrying currents in the same direction. However, the same rings will be expanded radially by the diametrically opposite currents. So if you had a long narrow elastic superconductive tube and you forced a permanent magnet inside it, then this tube would tend to change its shape into a large Hula-Hoop.  Still brings some interesting scenarios when we charge/discharge this unique capacitor and what that does to the surrounding field patterns.. 
If you take the experiment depicted below and insert a capacitor in series with the loop and rotate it with the angular frequency 1/√(LC) then the amplitude of the alternating current induced in that loop will increase without bound when R=0. 
|