The effects of a By field on ions in unbounded transient orbits in the current sheet of the geomagnetic tail are studied. The trajectories and the energization of ions injected at the north edge of the current sheet (z=+L) are investigated varying the dawn to dusk magnetic field strength By. The current sheet with +By produces less energetic ions than that with -By. At By=0 the exit positions of ions after acceleration from the current sheet are scattered almost equally above and below the current sheet. Finite By introduces a helicity to the magnetic tail structure that breaks this symmetry. When the By field reaches 3 nT, almost all of the tailward streaming ions injected with initial velocities (0<V0<2000 km/s and a given initial kinetic energy 1/2 mV20) are ejected above the current sheet after acceleration. However, a current sheet with a negative dawn-dusk magnetic field ejects all of them below itself even for small negative By(-1 nT) values. The nonzero EyBy produces E∥=EyBy/B with E⋅B being a Lorentz scalar invariant. The finite E∥ makes the electrons move so as to create a cancelling electrostatic potential difference along the magnetic field line. On the basis of the ion orbits found here for the standard model E and B fields we estimate the self-consistent electrostatic field expected from the difference in the large ion orbits and the well-magnetized electrons. We suggest that the onset of geomagnetic activity may be correlated with the By field and the associated electrostatic field in the central plasma sheet. ¿ American Geophysical Union 1995