Mechanical forces in superconducting windings of toroidal magnet systems

A new computer code is briefly described which can be advantageously applied to superconducting toroidal systems with complicated coil shapes. The guiding idea is to use the same geometry for the current elements and the stress model. Furthermore, a short review shows that more work is necessary for elucidating the influence of mechanical stress on the critical current density of the superconductors and on the physical properties of the non-superconducting stabilizing material. Values for the centripetal force acting on each torus coil can be easily calculated when the "1/r approximation" for the magnetic flux density is assumed. The influence of the magnetic flux leaking out between the coils is discussed and it is shown that for tori with large numbers of coils (say, 32 to 64) and with not too large aspect ratios (say, 1.5 to 2) the above mentioned approximation for the calculation of the centripetal forces yields values which are only a few percent too large. Finally, the consequence of a coil failure in a toroidal magnet is discussed under the assumption that each superconducting coil operates in persistent mode. Due to the re-arrangement of the currents and of the magnet fields, centripetal forces and perpendicular force components result whose asymptotically reached values are appreciably larger than the static values calculated for a torus with one coil missing.