A computer theoretical s1udy has been carried out in field of opto - clcctroniccs, to design  an electron  gun using the space charge effect.

The   distribution  of   axial  potential    upon   the  two   -electrode

immersion  lens  of  (L=l4mm)  has been  carried   out   using   Poisons equation and the  tinite  clement  method;  knowing  the first 11nd second derivation  of  the    axial   potential   and  the  solution   of  paraxial   ray equation, the  optical   prop

The inverse problem is important method in the design of electrostatic lenses which is used in this work, with new technique by suggesting an axial electrostatic potential distribution using polynomial functions of the third order. The paraxial-ray equation is solved to obtain the trajectory of particles that satisfy the suggested potential function.In this work design of immersion electrostatic lens operated under zero magnification condition. The electrode shape of sthe electrostatic lens was the dermined from the solution of laplace equation and plotted in two deimensions . The results showed low values of spherical and chromatic aberrations , which are considered as good criteria for good desigh.

 Theoretical study computerized has been carried out in electron optics field, to design electrostatic immersion lens , the inverse problem is important method in the design of electrostatic lenses by suggesting an axial electrostatic potential distribution using polynomial function. The paraxial –ray equation is solved to obtain the trajectory particles that satisfy the suggested potential function. In this research, designed immersed lens length L = 10mm operated under zero condition, as it was obtained the electrode shape of this lens solutions using the Laplace equation The results of the search showed low values of spherical and chromatic aberrations, which gives a good indication of the design of the lens.   It was

 Computer theoretical study has been carried out on the design of five electrode immersion electrostatic lens used in electron gun application. The finite element method (FEM) is used in the solution of the Poisson's equation fro determine axial potential distribution, the electron trajectory under Zero magnification condition .      The optical  properties : focal length ,spherical and chromatic aberrations are calculated,From studying the properties of the designed electron gun. we have good futures for these  electron gun where are abeam current 4*10-4A    can be supplied by using cathode tip of radius 100 nm.

  In this paper,  design computationl investigation in the field of charged-particle optics with the aid of numerical analysis methods  under the absence of space charge effects. The work has been concentrated on the design of three-electrode  einzel electrostatic  lens accelerating and decelerating operated under different magnification conditions.     The potential field distribution of  lens has been represented by exponential function.  The paraxial-ray equation has been solved for the proposed field to determine the trajectory of charged-particles traversing in the lens.  From The axial  potential distribution and its first and second derivatives, the optical propertie

The presentwork is a theoretical study in the field of charged particle optics. It concentrates on the design of electrostatic enzil lens for focusing charge particles beams, using inverse method in designingthe electrostatic lens. The paraxial ray equation was solved to obtain the trajectory of the particles, the optical properties such as the focal length and spherical and chromatic aberration coefficients were determined. The shape of the electrode of the electrostatic lens were determined by solving poison equation and the results showed low values of spherical and chromatic aberrations, which are considered as good criteria for good design.

  Theoretical study computerized has been carried out in field electron optics , to design electrostatic unipotential lens , the inverse problem is important method in the design of electrostatic lenses by suggesting an axial electrostatic potential distribution using polynomial function. The paraxial –ray equation is solved to obtain the trajectory particles that satisfy the suggested potential function. In this research , design electrostatic unipotential lens three-electrode accelerating and decelerating L=5 mm operated under finite and infinite magnification conditions. The electrode shape of the electrostatic lens was then determined from the solution of the Laplace's equation's. the results showed low values of spherica

Abstract
A two electrode immersion electrostatic lens used in the design
of an electron gun, with small aberration, has been designed using
the finite element method (FEM). By choosing the appropriate
geometrical shape of there electrodes the potential V(r,z) and the
axial potential distribution have been computed using the FEM to
solve Laplace's equation.
The trajectory of the electron beam and the optical properties of
this lens combination of electrodes have been computed under
different magnification conditions (Zero and infinite magnification
conditions) from studying the properties of the designed electron
gun can be supplied with Abeam current of 5.7*10-6 A , electron
gun with half acceptance

A computerized investigation has been carried out on the design of six electrodes electrostatic lenses used in electron gun application. The Finite-Element Method (FEM) was used in the solution of Laplace equation for determine the axial potential distribution. The electron trajectory under zero magnification condition. The optical properties, spherical and chromatic aberrations, the object and image focal length and object and image position are calculated. A very good futures for the electron gun with these lenses have been computed where are a beam current of 8.7*10-7A can be supplied using cathode tip of radius 10nm.

The present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w