Using a Bi-based small high Tc superconductor (HTSC) coil, we have studied its stability against a local disturbance and current-induced quench in the helium gas cooling condition. While the stability margin of HTSC coil against a local disturbance was very large, quench current was limited by a catastrophic temperature rise which originated from the nonlinear characteristic of the Joule heating. The crucial parameter for the quench becomes the nonlinear resistance in HTSC as a function of temperature and transport current. It has been shown that the dynamic characteristics of the quench can be described quantitatively by the simplified one-dimensional heat balance equation.
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