Electron orbits under the external vertical field (B(V)) and the self poloidal field of the toroidal plasma current in a toroidal geometry are investigated by using analytic model fields in order to search for the conditions of occurence of appropriate confinement asymmetry of fast electrons along the field lines. This asymmetry efficiently and quickly generates a toroidal current, which may close the field lines in ECH-started plasmas. It is analytically shown that the characteristics of confinement asymmetry depend on the product of the major radius and the strength of the external vertical field. The results suggest that in large devices B(V) should be lowered and also some artificial means to speed up the pitch angle scattering for the fast electrons at a higher energy range are beneficial to generate the toroidal current in order to close the filed lines.