Calculation of desired vertical ovality of SSC collars

If the collar material has a larger coefficient of thermal contraction than the yoke and the yoke is split on the horizontal mid-plane, it may be difficult to use the yoke to provide horizontal support to the collared coil. To be inserted easily into the yoke at room temperature the collared coil must be no larger in horizontal diameter than the yoke. When the magnet is cooled to liquid helium temperature the collars will contract more than the yoke and a gap may develop between the collars and the yoke at the horizontal mid-plane. If, however, the collared coil is oversize in the vertical direction, clamping it in the yoke will tend to make its horizontal diameter grow enough to contact the yoke. Thus it may be desirable to design the collars to generate a ''vertical ovality.'' In this note I discuss a method to calculate the desired ovality of the collared coil at room temperature and the (undeflected) collar shape needed to achieve this. I then calculate the skin stress required to push the collared coil into shape. In both calculations I show the range of values resulting from plausible variations in the calculation parameters and in the coal prestress