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v3.3.2-pre
In this unit we will discuss the main challenges posed by magnet protection and the constraints induced on the magnet design. We will first describe the equation that balances the Joule heating and the heat capacity in the conductor. After setting the limits for the higher temperature during irreversible transition to normal conducting state (quench), we give the dependence of specific heat of the conductor components and the copper resistivity on the temperature.
The stored energy in the magnet has to be discharged safely, and therefore is an essential parameter of protection. We give a few element to have back of the envelope estimates of stored energy, and we show how magnetic field is a quite inefficient way of storing energy.
Energy can be extracted via a dump resistor: this approach has intrinsic limits given by the voltages that can be withstand by insulation. The alternative is to bring the whole magnet to normal state, and dump the stored energy in the coil. The intrinsic limits of this approach are also discussed, through the definition of a protection time margin. This parameter give the maximum time required to bring the whole coil to resistive state, before the final temperature goes above the limits. It is of the order of 50-100 ms for high field, large current density accelerator magnets. Its dependence on energy density in the coil, copper fraction, and, last but not least, current density are given.