Design of Unipotential lens Operated Under space charge effect and low aberration

The present work includes acomputational investigations in the field of charged particles optics using numerical analysis methods. The recent research concentrated about design of aunipotential lens operating under the effect of space charge and zero magnification mode. The axial electrostatic potential was presented by using apolynomial of fourth order which form it ,The equation of paraxial ray was solved to get the trajectory of charge particles which satisfies the suggested potential function, and by solving the equation of paraxial ray, the optical properties like spherical and chromatic aberration and focal length were measured and then getting the shape of poles of electrostatic lens by solving the equation of Poisson.