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.

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 to design an immersion lens
with low aberration operating under zero magnification condition using inverse problem.
The aberration is highly dependent on the shape of electrodes, for a preassigned electron
beam trajectory the paraxial-ray-equation is solved to determine the electrostatic potential
and field distribution.
From the knowledge of the potential and its first and second derivative the
electron optical properties were computed, the electrode geometry was determined from
the solution of Laplace equation.

An analytical model in the form of a hyperbolic function has been suggested for the axial potential distribution of an electrostatic einzel lens. With the aid of this hyperbolic model the relative optical parameters have been computed and investigated in detail as a function of the electrodes voltage ratio for various trajectories of an accelerated charged-particles beam. The electrodes voltage ratio covered a wide range where the lens may be operated at accelerating and decelerating modes. The results have shown that the proposed hyperbolic field has the advantages of producing low aberrations under various magnification conditions and operational modes. The electrodes profile and their three-dimensional diagram have been determined whi

 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

  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

  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

A computational investigation is carried out in the field of charged –particle optics with the aid of numerical analysis method using the personal computer. The work is concerned with the design of electron gun with space-charge effect. The Finite element method (FEM) used in the solution of Poison's equation for determine the axial potential distribution of the two-electrode immersion lens operated under zero magnification condition , and from the solution of the paraxial ray equation the optical properties such as the focal length , spherical and chromatic aberration coefficients are determined, also a calculation of the brightness and perveance for the lens. The electrodes geometry was determined in two and three dimensi

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

In this paper, the path of the extracted and focused ions by the electrostatic lense having three electrodes of the same size and shape have been studied. However, the first and third electrodes had a different potential from the second electrode and the distance between any three electrodes was (d).The beams of the charged particles were controlled by using electrostatic fields which are used for accelerating and focusing. This paper focuses also on the effect of electrodes potentials on ion beam focusing. It is found that the best focusing was achieved when the values of the potential of the first and third electrode are equal to half of the value of the second electrode. Concerning transmiting and acumulating the ions beams, the study sh