Approximation of the resistance in a solenoid consisting of alternating sheets
This is a well known design called the Bitter solenoid, see here on wikipedia. There are several links out from that article to analysis and design papers. It was invented in 1933 by, would you believe, Mr. Bitter.

A quote from that article ...


  Unlike a copper wire, the current density of a current carrying disc is not uniform across its cross-sectional area, but is instead a function of the ratio of the inner diameter of the disc to an arbitrary radius within the disc. The implications of this relationship is that the current density decreases with an increase in radius. As such, the bulk of the current is flowing closer to the inner radius of the disc. Large discs (i.e., disc with a large difference between their inner and outer radius) will have a larger discrepancy in the current density between the inner and outer portions of the disc. This will reduce the efficiency and cause additional complications in the system because there will be a more substantial temperature and stress gradient along the disc. As such, a series of nested coils is often used as it will more evenly distribute the current across a large combined area as opposed to a single coil with large discs.