Schwinger Particle-Production Mechanism for a Finite-Length Flux Tube   with Transverse Confinement
  Previous results for the pair production probability in a strong electric field with a finite longitudinal separation are generalized to the case of a finite-length flux tube with transverse confinement. The threshold length of the flux tube, below which pair production cannot occur, increases as a result of transverse confinement. 
Cheuk-Yin Wong, Ren-Chuan Wang, and Jian-Shi Wu