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 was represented by a fourth order polynomial function . To measure the optical properties of the lens and to obtain the electrode shape of the electrostatic lens we have solved Poissonequation
This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f
... Show MorePolymeric hollow fiber membrane is produced by a physical process called wet or dry/wet phase inversion; a technique includes many steps and depends on different factors (starting from selecting materials, end with post-treatment of hollow fiber membrane locally manufactured). This review highlights the most significant factors that affect and control the characterization and structure of ultrafiltration hollow fiber membranes used in different applications. Three different types of polymers (polysulfone PSF, polyethersulfone PES or polyvinyl chloride PVC) were considered to study morphology change and structure of hollow fiber membranes in this review. These hollow fiber membranes were manufactured with different proce
... Show MoreThe internet is a basic source of information for many specialities and uses. Such information includes sensitive data whose retrieval has been one of the basic functions of the internet. In order to protect the information from falling into the hands of an intruder, a VPN has been established. Through VPN, data privacy and security can be provided. Two main technologies of VPN are to be discussed; IPSec and Open VPN. The complexity of IPSec makes the OpenVPN the best due to the latter’s portability and flexibility to use in many operating systems. In the LAN, VPN can be implemented through Open VPN to establish a double privacy layer(privacy inside privacy). The specific subnet will be used in this paper. The key and certificate will
... Show MoreCharge multipole Coulomb scattering form factors in 48Ca nucleus have been reproduced utilizing the theory of nuclear shell. The efficient two-body nuclear potential fpbm is considered to construct the-spin orbit term LS vectors with Harmonic Oscillator HO potential as a wave function of single particle in Fp shell. Discarded spaces ( core + higher configuration) are taken into account through the Core polarization effect by model space with accurate two-body potential of Gogny to interact the LS operating particles with the discarded space pair ( particle-hole) with energy of excitation equal to 2ћω. Gogny interaction has been selected as it had succeeded in nuclear shell theory. The computed results were compared with th
... Show MoreA 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 increasing availability of computing power in the past two decades has been use to develop new techniques for optimizing solution of estimation problem. Today's computational capacity and the widespread availability of computers have enabled development of new generation of intelligent computing techniques, such as our interest algorithm, this paper presents one of new class of stochastic search algorithm (known as Canonical Genetic' Algorithm ‘CGA’) for optimizing the maximum likelihood function strategy is composed of three main steps: recombination, mutation, and selection. The experimental design is based on simulating the CGA with different values of are compared with those of moment method. Based on MSE value obtained from bot
... Show MoreA new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.