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基于已有的一维虚拟阴极理论模型，本研究进一步建立了虚拟阴极的绝对误差理论，并系统分析了热阴极温度、饱和电子发射电流、电子收集电流、杜师曼常数以及电子逸出功等参数对虚拟阴极测量的误差贡献。研究结果表明，影响虚拟阴极势阱深度测量的主要因素与虚拟阴极的强弱密切相关，当热阴极产生的虚拟阴极较强时，阴极加热温度的不确定性约有61%的概率成为势阱深度测量的主要误差源，而当虚拟阴极较弱时，电子电流测量的不确定约有39%的概率成为主要误差源。此外，在虚拟阴极的空间宽度测量方面，对于常见的热阴极材料，其测量结果的主要误差大概率（至少90%）是由热阴极温度和电子逸出功的不确定造成的，只有当虚拟阴极非常微弱时，电子电流的不确定是主要误差源。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.
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Keywords:
- virtual cathode /
- absolute error /
- hot-cathode temperature /
- thermionic emission
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