Limiting length in cooling design of HTS magnets

Regular operation of HTS windings is accompanied by a low-level heat (index loss), generated due to the low n-value of HTS materials. The paper shows that the index loss in conduction cooled magnets causes thermal instability and quench, when the cooling length exceeds certain critical value L*. This index conduction crisis is brought by the abrupt temperature growth of the index loss. The crisis can occur at rather small temperature gradients (of the order of a K), and should be among the major design considerations for a conduction cooled magnet. Stability criterion λ is derived in a one-dimensional conduction model with nonlinear index loss. Practical formulae are suggested defining maximum allowable current vs. cooling length. Effect of limited cryocooler capacity is modeled. The theory is illustrated by examples of a solenoidal coil and a solitary conductor (bus)