Subject: How to construct an ideal Induction coil ?

For a scientific Project we want to construct an induction coil. I checked the 
formulas for a magnetic circuit, where the magnetic current (flux) flows in a 
closed ferromagnetic loop without an air gap. Our target is to minimize the 
reluctance as low as possible, that is why we plan to use a closed circuit 
which is made of permalloy.
But, the  conventional induction coil is wound on a bar shaped core (open 
circuit : however the flux follows the air path) but in such a coil, the 
reluctance would be very high, for the  same mmf, the magnetic flux (current) 
would be very low, if so why are standard coils wound on magnetic bars ?
For a bar shaped coil how can I evaluate the reluctance for the air path ?
Are there any methods to nullify the reluctance at all ? 

Could you please give us a rich book list for our project.

Re: How to construct an ideal Induction coil ?