Accurate analytical expression of the electrostatic potential close to a grid placed between two plates

The potential distribution between a grid and two plates is an electrostatic problem already solved for MultiWire detectors used in Nuclear Physics, where theoretical expressions are obtained assuming linear charge distributions. In this paper, the accuracy of the line model is investigated close to the wires, using both analytical and numerical approaches. In the symmetric case where the grid is at equal distances between two grounded plates, it is shown that the error can be modeled using a quadrupole charge. After solving the electrostatic problem for the asymmetric case, a larger discrepancy is found, and is interpreted as a consequence of a dipole charge on the electrode. Two different models of this dipole are then implemented, leading to an accurate theoretical expression of the potential. (paper)