Investigation of Quantitative Relation Between the Π Cathode Structure of Cylindrical Diode and Current of Cathode

Abstract

The anode and the cathode of the cylindrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> cathode diode are not coaxial, and the quantitative calculation of its space charge limited current (SCLC) has not been reported. In this article, we propose the SCLC quantitative expression of cylindrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> cathode diode through improving the theory model of Japanese distinguished scholar Y. Koike ( <fig orientation="portrait" position="float" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <graphic orientation="portrait" position="float" xlink:href="wu14-3105975.eps"/> </fig> ) based on the 3/2 power law of SCLC of the coaxial cylindrical diode and study the relationship between current and cathode structure of cylindrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> cathode diode by using the numerical simulation method based on the CST Particle Studio (CST-PS). This improved model is more suitable than previous empirical formulas when the radius of a single cathode is greater than or equal to 1.0 mm and can be used in combination with the theory model of Y. Koike to estimate quantitatively the SCLC of cylindrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> cathode diode. Moreover, it also provides an effective basis for the design and optimization of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> cathode structure of the high-power vacuum transmitting tube.