Abstract
To obtain the relation between spark discharges and the topography of electrode surfaces, some models, such as a micro-initial model of cone and spherical head cylinder, generated from the scanning of a scanning electron microscope are introduced. Based on the principles of energy conservation and thermal equilibrium, the second-order non-homogeneous differential equation is established. The relationships between the temperature of the cathode surface and the distance from the top of micro-protrusions, the cone angle, and the radius of the ball head are derived from a set of second-order non-homogeneous differential equations. When introduced electron emission theory, the main emission type at the initial stage of the discharge is electron field emission. As the discharge progresses, the Joule heat generated by the emission current will cause thermionic emission. During this progress, the emission current density gradually increases. When the temperature of the cathode surface reaches the melting point of the cathode metal, the current density will increase sharply. Observed from the discharge, the temperature of the cathode surface is inversely proportional to the cone angle and the radius of the ball head maintains a gradually decreasing slope. It is proportional to micro-protrusions maintaining a gradually increasing slope. When the cone angle is less than 12° and the radius of the ball head is less than 0.04 µm, the temperature of the cathode surface changes more dramatically. Through this study, a further understanding of factors that affect the density of cathode current emission can be obtained, which is of great significance to improve the capacity of cathode emission.
Highlights
The International Electrotechnical Commission safety spark test equipment is the most basic experimental equipment for the research of intrinsically safe circuits, and it is the standard equipment for circuit intrinsic safety performance testing, evaluation, and identification.1 When conducting the experiment, there exists a motion between the tungsten wire anode and the cadmium disk cathode on the IEC platform, and these two electrodes can be closed and opened periodically
In order to more intuitively understand the influence of the geometric parameters of the micro-protrusions on the surface temperature of the cathode, the relationship curve between the surface temperature of the cathode, the height of the micro-protrusions, the cone angle, and the radius of the sphere is obtained according to Eqs. (20) and (24)
In order to explore the influence of the geometric parameters of the micro-protrusion on the surface temperature of the cathode, this paper considers Joule heating and the thermal effect of the cathode surface, ignoring the influence of temperature on the electrical conductivity, specific heat capacity, and other physical parameters
Summary
The International Electrotechnical Commission safety spark test equipment is the most basic experimental equipment for the research of intrinsically safe circuits, and it is the standard equipment for circuit intrinsic safety performance testing, evaluation, and identification. When conducting the experiment, there exists a motion between the tungsten wire anode and the cadmium disk cathode on the IEC platform, and these two electrodes can be closed and opened periodically. To find out the influences of the topography of the cathode surface on current emission, a set of second-order non-homogeneous thermal balance equations for cone shape and ball head shape models is formed under a spherical coordinate system based on the conservation of energy This equation considers physical parameters such as the field enhancement factor, electric field strength E, work function φ, thermal conductivity K, and resistivity γ, as well as the upper radius of the micro-protrusion and cone angle. The relationships between the height of the micro-protrusion on the cathode surface, the cone angle, the metal temperature of the cathode surface, and the current density are obtained. When conducting research related to current density, the influence of the field enhancement factor cannot be ignored
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