Calculation of Geometric Dimensions of Cold Cathode Surface in High-Voltage Glow Discharge Electron Sources

Abstract: The paper proposes a new iterative algorithm for finding the transverse dimension of the cold cathode of high-voltage glow discharge electron guns, based on formulation of a nonlinear equation for the functional dependence of the cathode size on the discharge current and solving this equation using the Steffenson iterative method. A distinctive feature of the proposed calculation method is taking into account the dependence of high-voltage glow discharge current on the plasma boundary position. To obtain the corresponding nonlinear equation, we use the approximate theory of one-dimensional discharge gap and well-known statement of the discharge theory that the anode plasma occupies a definite volume, which is determined by concentration of charged particles, regardless of the geometry of the electrode system. There are specified the geometric parameters of the electronic system of the high-voltage glow discharge with a spherical cathode and a hollow anode, and also well as restrictions on the system of parameters that satisfy the requirements of completeness, consistency, and closure are introduced. On a basis of the numerical analysis of the proposed iterative algorithm convergence process, we show that in case of the restrictions on the introduced parameters system are satisfied, the method convergence is usually ensured. We compare the calculations results of the transverse dimension of the cathode of high-voltage glow discharge guns with correspondent experimental data. The comparative analysis results showed that proposed iterative algorithm application results in the difference between calculations and experimental data does not exceed a few percent. The research results and proposed iterative method for calculating the transverse dimension of the cold cathode of high-voltage glow discharge guns are of great practical value and can be directly used at the initial stage of designing gas discharge guns to assess their technological possibilities. © Allerton Press, Inc. 2023.