Concentric Spherical System Research Articles

Imaging Electron Optics of Electrostatic Focusing Concentric Spherical System Part C: Electron Optics of Concentric Spherical System Composed of Multiple Electrodes

Imaging Electron Optics of Electrostatic Focusing Concentric Spherical System Part C: Electron Optics of Concentric Spherical System Composed of Multiple Electrodes

Imaging Electron Optics of Electrostatic Focusing Concentric Spherical System Part B: Paraxial Lateral Chromatic Aberration and Geometrical Lateral Spherical Aberration

Imaging Electron Optics of Electrostatic Focusing Concentric Spherical System Part B: Paraxial Lateral Chromatic Aberration and Geometrical Lateral Spherical Aberration

复合电磁同心球系统的成像电子光学. D章：近轴方程渐近解

复合电磁同心球系统的成像电子光学. D章：近轴方程渐近解

复合电磁同心球系统的成像电子光学. C章：近轴方程近似解

复合电磁同心球系统的成像电子光学. C章：近轴方程近似解

Paraxial imaging electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

The paraxial solutions play an important role in studying electron optical imaging system and its spatial-temporal aberrations, as was discussed in previous paper [1], but investigation of a bi-electrode concentric spherical system with electrostatic focusing directly from paraxial electron ray equation and paraxial electron motion equation has not been done before. In this paper, we shall use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing. In the present paper, start from the paraxial ray equation and paraxial motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the photocathode has been solved for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the general regularity of imaging in paraxial optical system has been explored. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced, that are classified by the order of ( ɛ z / ϕ ac ) 1/2 and ( ɛ T / ϕ ac ) 1/2. Thus we get same conclusions about paraxial spatial and temporal aberrations as we have given in the previous paper and it completely shows that the paraxial spatial-temporal aberrations can be investigated directly from the paraxial ray equation and paraxial motion equation.

Static and dynamic imaging electron optics and spatial–temporal aberrations in a bi-electrode spherical concentric system with electrostatic focusing

In imaging electron optics, for a concentric spherical system composed of two spherical electrodes with electrostatic focusing, the electrostatic potential distribution and the spatial–temporal trajectory of electron motion can be expressed by analytical forms. It is naturally to take such system as an ideal model to investigate the imaging properties, as well as the spatial–temporal aberrations, to analyze its particularity and to find the clue of universalities and regularities. Research on this problem has important significance, which can afford theoretical foundation not only in studying static electron optics for the night vision devices, but also in studying dynamic electron optics for high-speed image converter tubes. In the present paper, based on the practical electron ray equation and electron motion equation for a bi-electrode concentric spherical system with electrostatic focusing, the spatial–temporal trajectories of moving electrons emitted from the photocathode have been solved, the exact and approximate formulae for image position and flight time of electrons, have been deduced. Start from solutions of spatial–temporal trajectories, the electron optical spatial–temporal properties of this system are then discussed. According to the definitions of spatial–temporal aberrations, the paraxial and geometrical lateral aberrations, as well as the paraxial and geometrical temporal aberrations, have been deduced, that are classified by the order of ε z / ϕ a c and ε r / ϕ a c .

Imaging electron-optics and spatial-temporal aberrations for a bi-electrode spherical concentric system with electrostatic focusing

In the present paper, based on the practical electron ray equation and the electron motion equation,for a bi-electrode concentric spherical system with electrostatic focusing, the spatial-temporal trajectories of moving electrons emitted from the photocathode are obtained, the exact and the approximate formulae for image position and flight time of electrons are deduced. Starting from the solutions of spatial-temporal trajectories, the electron optical spatial-temporal properties of this system are then discussed. A unified definition of spatial-temporal aberrations is given, in which the lateral aberration can be regarded as a combination of paraxial lateral aberration and geometrical lateral aberration; and the temporal aberration can be regarded as a comibination of paraxial temporal aberration and geometrical temporal aberration. All expressions of these corresponding aberrations are deduced.

Paraxial electron optics and its spatial-temporal aberrations for a bi-electrode concentric spherical system with electrostatic focusing

In this paper, we use the paraxial equations to study the spatial-temporal trajectories and their aberrations for a bi-electrode concentric spherical system with electrostatic focusing. In the present paper, starting from the paraxial ray equation and the paraxial motion equation, the paraxial spatial-temporal trajectory of moving electron emitted from the photocathode is obtained for a bi-electrode concentric spherical system with electrostatic focusing. The paraxial static and dynamic electron optics, as well as the paraxial spatial-temporal aberrations in this system are then discussed, the general regularity of imaging in paraxial optical system has been explored. The paraxial spatial aberrations, as well as the paraxial temporal aberrations with different orders, have been defined and deduced. Thus we get same conclusions about paraxial spatial and temporal aberrations as it has been given in paper[1], and it completely shows that the paraxial spatial-temporal aberrations can be investigated directly from the paraxial ray equation and paraxial motion equation.

On the theory of temporal aberrations for dynamic electron optics

A new theory for temporal aberrations of dynamic optics by applying the direct integral method is put forward in the present paper. A new definition of temporal aberration is given, in which a certain initial energy of electron emission emitted from a photocathode along the axial direction √ɛz1(0⩽√ɛz1⩽√ɛ0max) was taken as a criterion. New expressions of the temporary aberration coefficients in integral forms for the electron optical imaging systems have been deduced. An electrostatic concentric spherical system model is used to test and verify expressions of the coefficients given by the “direct integral method” and “τ variation method”. The analytical solutions prove that both methods are correct and equivalent. Compared to the “τ variation method”, the direct integral method only needs to carry out the integral calculation for the three geometrical temporal aberration coefficients of the second order, which is more convenient and suitable for computation in the practical design. Finally, results of the study for the theory of temporal aberrations of electron optical imaging systems, from the point of view of methodology, have been elaborated.

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε z 1 ( 0 ⩽ ε z 1 ⩽ ε 0 max ) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “ τ-variation method” is that the “ τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order. All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “ τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.

Test and verification of temporal aberration theory for electron optical imaging systems by an electrostatic concentric spherical system model

On theory of temporal aberration of dynamic electron optical imaging systems, we have put forward two methods: “τ-variation method" and “direct integral method" to calculate the temporal aberration coefficients. The difference betwe en them is that the “τ-variation method"needs to solve the differential eq uations for geometrical temporal aberration coefficients of second order, while the “direct integral method" needs only to carry out the integral calculations. The aim of the present paper is to test and verify the correctness of the two m ethods using an electrostatic concentric spherical system model. Results show th at these two methods can obtain identical solutions and the solutions of tempora l aberration coefficients of dynamic electron optical imaging systems are the sa me with the analytical solutions. Thus it can be concluded that these two method s are equivalent and correct, but the “direct integral method" is more convenie nt for computation and it could be suggested to use in the practical design.

RADIATION FROM A SPHERICAL ANTENNA WITH AN ANISOTROPIC PLASMA SHEATH

The boundary-value problem for a concentric spherical system consisting of an infinitesimally thin shell of magnetoplasma surrounding a source-excited slotted sphere is solved. The solution is carried out in some detail under the assumption that the properties of the sheath do not vary with the angular coordinates. It is indicated that the anisotropy of the sheath introduces a cross-polarized component of the radiated field. The extension to a sheath, with a spatial variation of its properties, is outlined briefly.

Cavity resonances for a spherical earth with a concentric anisotropic shell

A boundary-value problem of a concentric spherical system involving anisotropic media is considered. Rather gross simplifications are made in order to achieve tractability and yield physical insight. The principal idealization is the representation of the concentric plasma layer by a thin shell of ionization. The derived results have some relevance to the phenomenon of resonance in the concentric cavity formed by the earth and the ionosphere. For example, it is shown that the earth's magnetic field and the electron collisions both contribute to the damping of the cavity resonances.