Engineering design solutions of flux swing with structural requirements for ohmic heating solenoids

Here a more detailed publication is summarized which presents analytical methods with solutions that describe the structural behavior of ohmic heating solenoids to achieve a better understanding of the relationships between the functional variables that can provide the basis for recommended design improvements. The solutions relate the requirements imposed by structural integrity to the need for producing sufficient flux swing to initiate a plasma current in the tokamak fusion machine. A method is provided to perform a detailed structural analysis of every conducting turn in the radial build of the solenoid, and computer programmed listings for the closed form solutions are made available as part of the reference document. Distinction is made in deriving separate models for the regions of the solenoid where turn-to-turn radial contact is maintained with radial compression or with a bond in the presence of radial tension, and also where there is turn-to-turn radial separation due to the absence or the loss of bonding in the presence of would be radial tension. The derivations follow the theory of elasticity for a body possessing cylindrical anisotropy where the material properties are different in the radial and tangential directions. The formulations are made practical by presenting the methods for reducing stress and for relocating the relative position for potential turn-to-turn radial delamination by permitting an arbitrary traction at the outer radial surface of the solenoid in the form of pressure or displacement such as may be applied by a containment or a shrink fit structural cylinder