  We theoretically analyze the effects of Cu/SC (superconductor) ratio, strain,
and the ramp path on thermomagnetic instabilities of the superconducting coil.
By considering the multi-filamentary structures, we find that a lower Cu/SC
ratio leads to higher temperature peaks. The strain causes a higher frequency
of flux jumps and higher voltage peaks. The temperatures recover to working
temperature more difficultly and SC wires quench earlier in the presence of
strain. For the jagged ramp cases, few flux jumps occur at the decreasing
branch, whereas frequent flux jumps can be observed promptly when the applied
current exceeds the pre-existing peak. Our simulated results agree well with
experimental observations in Nb3Sn coils. Additionally, unlike the pulsed flux
jumps observed in linear ramp cases, giant and prolonged flux jumps are
observed at the increasing branch with a sinusoidal ramp path when the applied
current is sufficiently large.
