8 cleation, using a Coulomb gauge condition to obtain ordinary differential equations, from which we found instanton-like solutions for the electromagnetic field in the region of the bubble wall. We calculated the electromagnetic field produced in the EWPT bub- ble nucleation with electron currents as well as the W ± fields, and found that although the electron cur- rent did not affect the em field near the bubble wall, they play an important role within the bubble, which could be quite important for bubble collisions. Although our present work is a very limited phys- ical problem, it explores new physics which can arise from nucleation before collisions starting from a MSSM electroweak Lagrangian with leptons. This will be investigated in a continuation of our cur- rent research[21, 22] on magnetic field creation in EWPT bubble collisions. In the future we shall in- vestigate whether the resulting magnetic fields could serve as seeds for gallactic and extra-gallactic large- scale magnetic fields. This work was supported in part by the NSF grant PHY-00070888, in part by the DOE contracts W- 7405-ENG-36 and DE-FG02-97ER41014. The au- thors thank Prof. W.Y. Pauchy Hwang and Dr. S. Walawalkar for helpful discussions, and Los Alamos National Laboratory for hospitality. Acknowledgements 78 , 3610 (1997). [1] D. Grasso and H.R. Rubinstein, Phys. Rep. 348 , 163 (2001). [2] B. Cheng and A.V. Olinto, Phys. Rev. D50 , 2421 (1994). [3] G. Sigl, A.V. Olinto and K. Jedamzik, Phys. Rev. D55 , 4582 (1997). [4] S. Koh and C.H. Lee, Phys. Rev. D62 , 083509 (2000). [5] J. Barrow, P. Ferreira and J. Silk, Phys. Rev. Lett. [6] R. Durrer, P.G. Ferreira and T. Kahniashvili, Phys. Rev. D61 ,043001 (2000). [7] M.M. Forbes and A.R. Zhitnitsky, Phys. Rev. Lett. 85 , 5268 (2000); JHEP 0110 , 013 (2001). [8] T.W.B. Kibble and A. Vilenkin, Phys. Rev. D52 , 679 (1995). [9] J. Ahonen and K. Enqvist, Phys. Rev. D57 , 664 (1998). FIG. 5: jWr=W current for r=2.0, 3.0, 4.0, and 5.0 The horizontal lines are the electron current = -0.084 r 2 1.5 2 2.5 3 3.5 4 t GLYPH<LParen1> r$_{GLYPH<Equal>}$2.0 GLYPH<RParen1> -0.8 -0.6 -0.4 -0.2 jW2 GLYPH<LParen1> t GLYPH<RParen1> 1 2 3 4 5 6 t GLYPH<LParen1> r$_{GLYPH<Equal>}$3.0 GLYPH<RParen1> -1.2 -1 -0.8 -0.6 -0.4 -0.2 jW3 GLYPH<LParen1> t GLYPH<RParen1> 1 2 3 4 5 6 7 t GLYPH<LParen1> r$_{GLYPH<Equal>}$4.0 GLYPH<RParen1> -2.5 -2 -1.5 -1 -0.5 jW4 GLYPH<LParen1> t GLYPH<RParen1> 2 4 6 8 10 12 t GLYPH<LParen1> r$_{GLYPH<Equal>}$5.0 GLYPH<RParen1> -5 -4 -3 -2 -1 jW5 GLYPH<LParen1> t GLYPH<RParen1>