Three-dimensional magnetic reconnection is studied using magnetohydrodynamic simulations. Initial configuration is based on the two-dimensional Harris neutral sheet model that lies in the xz plane, and is extended in the y direction. Localized anomalous resistivity is applied to the central region and the subsequent evolution of spontaneous magnetic reconnection is observed. A special attention is given to the results with a finite $B_y$ superimposed on the Harris model. Significant changes are seen in the system structure when the $B_y$ component causes asymmetries. The reconnected field lines are skewed and the plasma flows, shock structures, and the current flows show peculiar asymmetries. Plasma sheet is also seen twisted. The reconnection region becomes broader and the strength of the current sheet grows more as $B_y$ increases. Thus, the energy conversion is more significant when $B_y$ is large, unless $B_y$ is the dominant component. The field-aligned component of the current, which initially exists because of the finite $B_y$ component, is enhanced off the central plane when reconnection develops, while it is reduced on the central plane. The spatial scale of resistivity affects the reconnection rate as in the previous studies of $B_y = 0$, yielding a small energy conversion for a very localized model resistivity.
Acceleration of particles in the fields obtained from the fore-mentioned three-dimensional MHD simulation of local magnetic reconnection is also presented by tracing test particles. The study is focused on the dynamics and acceleration of particles under the influence of a nonzero $B_y$ component and the results are compared with the $B_y = 0$ case. For the $B_y = 0$ case, most of the results are overall in good agreement with the previous studies that have performed with similar conditions. When the nonzero $B_y$ component is included, we find the extreme up-down asymmetry about the $z = 0$ plane in the particle acceleration features. The acceleration features above the $z = 0$ plane are quite similar to those in the $B_y = 0$ case, while the features below the $z = 0$ plane show significant differences. The energized particles occur over a significant portion inside the separatrices in both cases. However, the accelerated particles above the $z = 0$ plane mostly come from the negative y-boundary, while those below the $z = 0$ plane come predominantly from the positive $x$-boundary. The accelerated region above the $z = 0$ plane is distinctly divided into three regions according to the source positions of the constituting particles, with highly structured transition between these regions. On the other hand, source regions are not distinctly divided and show significant fluctuations below the $z = 0$ plane. The pronounced y-directional asymmetry appears in the distribution of the energy gain above the $z = 0$ plane. However, the distribution below the $z = 0$ plane no longer show such asymmetry. We suggest that these differences result from the presence of the $E_z$ component in this model. Because of the limited extension of the X line in this simulation, the energy gain obtained in this study is less than about 25 keV.
