The effect of a $B_y$ field on ions in {\it 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 $B_y$. The current sheet with $+B_y$ produces less energetic ions than that with $-B_y$. At $B_y=0$, the exit positions of ions after acceleration from the current sheet are scattered almost equally above and below the current sheet. A finite $B_y$ breaks this symmetry. The non-zero $E_yB_y$ produces $E_\|=E_yB_y/B$. The finite $E_\|$ makes the electrons move so as to create a cancelling electrostatic potential difference along the magnetic field line. Based on this fact, we estimate the self-consistent electrostatic field. In addition, we have calculated the distribution functions generated from the modified Harris type geomagnetotail with a dawn-dusk magnetic field ($B_y$) using the Liouvilles' theorem. To find time-dependent z = 0 distribution functions, we start with two distribution functions at t = 0, the inner (z = 0) and the outer ($|z| > 4δ$). When a trajectory arrives at a phase space location at $z = 0$, the inner region distribution function is replaced by the outer region distribution function. From those simulations, we have seen the fact that $B_y$ fields ($1~3nT$) comparable to $B_z$ makes the anisotropic distribution isotropic and that as $B_y$ field increases and reaches 4~$6nT$, new anisotropic distribution functions and temperatures ($T_y ≥ T_x > T_z$) appear. But they are caused, not by the effect of resonance energies ($\hat{H} = 6.0$ and $\hat{H} = 50.8$), but by $B_n\hat{e}_z + B_y\hat{e}_y$.
