Optimal Bitter Coil Solenoid
  Bitter coil is an electromagnet used for the generation of exceptionally strong magnetic fields. The upper bound of magnet flux density is restricted by several factors. One principal restriction is the high stresses due to Lorentz forces in the coil. The Lorentz forces generate the distributed body force, which acts as the pressure of magnetic field. The common radial thickness profile of the Bitter coil is constant. In this paper the possibility of optimization by means of non-constant radial thickness profile of the Bitter coil is studied. The close form expression for optimal thickness profile is obtained. Both designs are compared and the considerable improvement of magnetic flux density is demonstrated. Moreover, the optimal design improves the shape of cooling channels. Namely, the highest cross-section of cooling channel is at the most thermally loaded inner surface of the coil. 
V. Kobelev
physics.ins-det physics.acc-ph