Absolute error analysis of virtual cathode measurement in a vacuum

The virtual cathode is an important phenomenon in the process of thermionic emission, and it is widely present in a variety of electronic devices and systems such as vacuum tubes, electron guns, high-power microscopes, x-ray tubes, concentrated solar thermionic converters, and emissive probes. Given that the virtual cathode can directly affect the performance level of these devices, it is of great significance to study the characteristics of the virtual cathode and conduct experimental measurements on it. In our recent research, a one-dimensional model of thermionic emission was established, and the analytical expressions for the potential barrier and the spatial width of the virtual cathode were derived. With the development of virtual cathode theories, measuring the virtual cathode experimentally has become a reality. In this study, based on the one-dimensional theoretical model developed by us, the absolute error theory of the virtual cathode is established, and the contributions of different parameters such as the hot-cathode temperature, the saturated electron emission current, the electron collection current, Dushman constant, and the work function of hot cathodes to the absolute errors in the virtual cathode measurement are systematically analyzed. The research results show that the main factors affecting the measurement of the virtual cathode potential are closely related to the size of the virtual cathode. When the virtual cathode generated by hot-cathodes is strong, the uncertainty of the hot-cathode temperature is the main error source with a probability of about 61% for the potential barrier measurement, while when the virtual cathode is weak, the main factor now becomes the uncertainty of the electron current measurement with a probability of about 39%. Besides, in the measurement of the virtual cathode width, for common hot-cathodes such as oxide (BaO) cathode, tungsten cathode and molybdenum cathode, the main factors affecting the measurement results are respectively approximately 94%, 96% and 97% to be the uncertainties of the hotcathode temperature and the work function. Only when the virtual cathode is very weak, the uncertainty of the electron current is the main error source for the measurement of the virtual cathode width.