Calculation and error analysis of virtual cathode caused by a thermionic cathode

The relative errors of virtual cathodes calculated by using the one-dimensional virtual cathode theory are analyzed and discussed. The studies of the error analysis show that the cathode temperature is the major factor affecting the calculated results of virtual cathodes, especially for calculations of the virtual cathode width. The smaller the virtual cathode produced by a hot cathode, the more significant the relative error of the virtual cathode caused by the uncertainties of electron emission parameters. Using the accurate cathode temperature, the potential barrier and the spatial width of virtual cathodes generated by a tungsten filament are calculated with experimental and theoretical electron emission parameters. The calculated results show that there is a strong linear correlation between the potential barrier of the virtual cathode and the heating current of the tungsten filament, which is independent of the electron collection current. With the increase in the heating current, the variation of the virtual cathode width is very sensitive to the relation between the electron collection current and the heating current.