The simulations of the electrostatic confinement fusion unit have been presented in low magnetic field case, which is produced by a central wire system inside the grid system of the chamber. The time-dependent simulations have been realized by the time integration together with the finite difference elements (FDE). Especially, FDEs have been used to compute the chamber potential and magnetic field interaction of the particles, namely electrons and ions with the chamber structures. The central wires exert a magnetic field in the azimuthal direction inside the central grid. It is found that this field induces helical trajectories on the particles. The model unit has six cathodes around the center. The system is simulated in a Deuterium media which is fully ionized. Considering the boundaries of the unit, the electrical and magnetic forces are determined by using the many-body technique with the particle-chamber and particle particle interactions. According to the results, many of the electrons can be repelled by the negative potential; however the ions have changeable trajectories with slower attitudes. The ion temperature has been found as T-i = 6.9 keV at the end of 6 mu s. The ion distribution proves that 45% of ions exist inside the grid however the increasing trend of ion temperature proves that this value is to be increased further. The velocity distribution shows a maximum around 5 x 10(5) m/s, however there are also highly energetic particles. (C) 2015 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.