  I present the results of the analytic plane strain optimization of the
structure and conductor grading in the inner leg of a Tokamak toroidal field
coil. The coil is assumed to be made of regions of soft conductor inside a
stiff grid of conduit. Calculus of variations is used to determine the optimal
profile of this structure. The optimal solution is found to be two-layered. An
outer layer is bucked only, not wedged, and the structure fraction is graded so
that all structure is at a uniform stress. An inner layer is an advanced
bucking cylinder, similar to a Florida Bitter plate, whose radial stiffness is
tuned so that its azimuthal stress is uniform. Such an advanced bucking
cylinder would require advanced manufacturing to fabricate. These results
should be seen an upper limits rather than achievable performance. Concepts
that arise from this optimization, such as selectively softening layers of the
bucking cylinder by drilling or cutting, may be of use to real designs in a
less-optimized form.
