Not sure what is meant by multiply power. Do you mean increase it's current carrying ability? The main reason that hollow conductors are used Is due to skin effect. Since the current flows in the outer part of the conductor there's no need for it be solid. This can  translate into considerable savings in weight and expense.
Not sure about the magnetic field question. From what I've researched the magnetic field inside a hollow conductor is zero. Try searching " circular magnetic fields - ndt resource center". Hope this helps.

Good idea .  When I initially thought of this idea ( after many other people I assume ),  I thought that if it worked as I described it in the first post on this thread,   that another way of collecting the surpass energy would be to run a wire through the center of the cylinder,  I should have posted it, however,  your idea may have a better chance of functioning .

Permanent-Magnet-hollow-cylinder
You could run a wire through a  hollow-Permanent-Magnet-cylinder ( a permanent-magnet in the shape of a hollow cylinder ), to repel the current and make it flow inside the cylinder.  that may be an easier and more guaranteed way to test the concept .

Or, you could place the  hollow-metal-cylinder inside a a conducting-coil in order to repel the current and make it flow inside the cylinder,  to test the concept .

EDIT -  Surely this must be related to metamaterials, maybe consider testing carbon or materials made of lattices/honeycombs or whatever, I assume it is not related to crystals and their claimed power amplification if you run current through them, that effect seems definitely due to the same alignment of their atoms/molecules .

EDIT - Also, consider wrapping an   Insulation-Coated-Thin-Sheet-Of-Metal  into itself to from a spiral, that would be interesting,  a cylinder/tube version of a spiral,  or,   maybe even a  Bifilar or Multifilar version.

What if you used an aluminium-core in a coil, and only powered / pulsed the coil ( also try dc ) and attached wires to both ends of the aluminium-core to see the output of the aluminium

I don't know if I could answer your question with any real authority. There are too many gaps in my knowledge of electrical theory. I'll give and example of what has me scratching my head. Take pen and paper and draw a loop of wire with a positive and negative on each end. Along this wire draw your hollow copper tube. Then start drawing small circles all along your wire. Keep drawing ever larger circles around each one. These will represent the lines of flux of the magnetic field. What you will see is that the poles of your magnetic field is in the center of the loop. Not on either end or sides of your copper tube. This is part that has me stumped. Will there be a voltage induced or will it cancel out. This is probably very basic stuff for Engineers and more knowledgeable members. Maybe this post will catch someone's attention and they can answer for both of us.

Ok, I asked a some questions and it was suggested to me that a coax could be considered a conductor inside a hollow tube. I threw together a quick little test.