We show that nucleation of vortex loops in superfluid He-3 by rapid thermal
quench in the presence of superflow is dominated by a transverse instabili
ty of the moving normal-superfluid interface. Exact expressions for the ins
tability threshold as a function of supercurrent density and the front velo
city are found. The results are verified by numerical solution of the Ginzb
urg-Landau equation. (C) 2000 Elsevier Science B.V.