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
A computational investigation is carried out in the field of charged particle optics with the aid of the numerical analysis methods. The work is concerned with the design of symmetrical double pole piece magnetic lens. The axial magnetic flux density distribution is determined by using exponential model, from which the paraxial-ray equation is solved to obtain the trajectory of particles that satisfy the suggested exponential model. From the knowledge of the first and second derivatives of axial potential distribution, the optical properties such as the focal length and aberration coefficients (radial distortion coefficient and spiral distortion coefficient) are determined. Finally, the pole piece profiles capable of pr
... Show MoreMany designs have been suggested for unipolar magnetic lenses based on changing the width of the inner bore and fixing the other geometrical parameters of the lens to improve the performance of unipolar magnetic lenses. The investigation of a study of each design included the calculation of its axial magnetic field the magnetization of the lens in addition to the magnetic flux density using the Finite Element Method (FEM) the Magnetic Electron Lenses Operation (MELOP) program version 1 at three different values of current density (6,4,2 A/mm2). As a result, the clearest values and behaviors were obtained at current density (2 A/mm2). it was found that the best magnetizing properties, the high
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Corrosion experiments were carried out to investigate the effect of several operating parameters on the corrosion rate and corrosion potential of carbon steel in turbulent flow conditions in the absence and presence of sodium benzoate inhibitor using electrochemical polarization technique. These parameters were rotational velocity (0 - 1.57 m/s), temperature (30oC – 50oC), and time. The effect of these parameters on the corrosion rate and inhibition efficiency were investigated and discussed. It was found that the corrosion rate represented by limiting current increases considerably with increasing velocity and temperature and that it decreased with time due to the formation of corrosion product layer. The corrosion potential shifted t
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Equation Boizil used to Oatae approximate value of bladder pressure for 25 healthy people compared with Amqas the Alrotinahh ways used an indirect the catheter Bashaddam and found this method is cheap and harmless and easy
The aim of this paper is to introduce the definition of a general fuzzy norned space as a generalization of the notion fuzzy normed space after that some illustrative examples are given then basic properties of this space are investigated and proved.
For example when V and U are two general fuzzy normed spaces then the operator is a general fuzzy continuous at u V if and only if u in V implies S(u) in U.
An analytical expression for the charge density distributions is derived based on the use of occupation numbers of the states and the single particle wave functions of the harmonic oscillator potential with size parameters chosen to reproduce the observed root mean square charge radii for all considered nuclei. The derived expression, which is applicable throughout the whole region of shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- of shell nuclei, such as and nuclei. It is found that introducing an additional parameters, namely and which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkabl
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In this research, an unknown space-dependent force function in the wave equation is studied. This is a natural continuation of [1] and chapter 2 of [2] and [3], where the finite difference method (FDM)/boundary element method (BEM), with the separation of variables method, were considered. Additional data are given by the one end displacement measurement. Moreover, it is a continuation of [3], with exchanging the boundary condition, where are extra data, by the initial condition. This is an ill-posed inverse force problem for linear hyperbolic equation. Therefore, in order to stabilize the solution, a zeroth-order Tikhonov regularization method is provided. To assess the accuracy, the minimum error between
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This study was conducted to provide a detailed description of the osteology features of Alburnus amirkabiri from the Qareh Chai river, markazi province, Iran. For this purpose, eight specimens of A. amirkabiri were collected from the Qareh Chai River by electrofishing and fixed in 4% buffered formalin after anesthesia. The specimens were cleared and stained for osteological examination and its detailed osteological characterizations and differences with available osteological data of other members of the genus Alburnus were provided.