Dynamics of electrons in a half-space with cylindrical electro-static field

Abstract

Motion of electrons in a half space with cylindrical electro-static field, which is associated with electron emission devices, is investigated. The equation of motion is given as a nonlinear ordinary differential equation of the second order. Statistical behavior of electrons exhibits a dilatational invariance property of the system. An approximate formula of absorbed points distribution of the electrons is given by the solution of a Fredholm integral equation of the second kind. Since its kernel function is [0, 1) characteristrics function, we give its finite sum expression using the properties of B-spline, which is the iterated kernel function of its Neumann series solution.From the viewpoint of development of cathode-luminescent displays, it is important to study electrons' behavior in a certain electro-static field [4]. This article gives an investigation of electrons' motion in a half space with cylindrical electro-static field. This electric system is related to the surface conduction electron emitter display (SED), which is a novel flat panel cathode-luminescent display [1,7,8,9,10]. The SED is composed of two parallel plates, one with the same number of the surface conduction electron emitters (SCEs) as the pixels of the display and another with phosphors. Since its luminous principle is the same as that of cathode-luminescent tube (CRT) display, it is possible to produce displays with the same brightness and color as CRTs. Moreover simple fabrication process and low driving voltage of the SCEs enable us to realize large size and low power consumption displays.We will consider electrons' absorbed points distribution of isotropically scattered electrons in the system as a model of a situation of the SCE. As shown in [8], by employing an intuitive ansatz for a connection between the absorbed points distribution and the voltage-current characteristics of the SCE, we can easily estimate the characteristics of the SCE with high accuracy. Thus it is very important to evaluate the absorbed points distribution for the design of the SCEs.To evaluate the absorbed points distribution, we should integrate a newtonian equation of motion of an electron. In this system, the equation of motion is given as a non-linear ordinary differential equation of the second order. In general, it is