Breakdown voltage of high pressure helium parallel plates and effect of field emission
Authors: Yang Chu-Ping , Geng Yi-Nan , Wang Jie , Liu Xing-Nan , Shi Zhen-Gang ,   Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
Published: June 2021

In this paper, a helium discharge model under high pressure is established. To qualitatively verify the validity of the model, we compare the results obtained from the previous experiments with those acquired from our model under similar operational conditions. In the simulation model, the electron temperature is obtained according to its relationship with the local electric field. According to the principle of electrical neutrality, the number density of He	<sup>+</sup> and the number density of	<inline-formula>	<tex-math id="Z-20210629213600">\begin{document}${\rm{He}}_2^+$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_Z-20210629213600.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_Z-20210629213600.png"/>	</alternatives>	</inline-formula> are also equal to the initial electron density, and we can assume that the He	<sup>+</sup> and the	<inline-formula>	<tex-math id="Z-20210629213630">\begin{document}${\rm{He}}_2^+$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_Z-20210629213630.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_Z-20210629213630.png"/>	</alternatives>	</inline-formula> account for 30% and 70%, respectively. For helium and copper electrodes, the secondary electron emission coefficient is 0.19 and the secondary electron average energy is15.3 eV. The Fowler-Nordheim equation is used to calculate the field-emission current density, and the electron flux is calculated according to the “charge conservation condition”. The electron flux is added to COMSOL's corresponding wall boundary, which can play the role of field emission. Finally, the analysis is carried out at a macro level (breakdown voltage) and micro level (spatial electron density). It is found that the field-emission current density is determined by the electric field intensity, the field enhancement factor, and the metal escaping work. The effect of field emission can be ignored when	<inline-formula>	<tex-math id="M4">\begin{document}$\beta = 300$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M4.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M4.png"/>	</alternatives>	</inline-formula>. However, if	<inline-formula>	<tex-math id="M5">\begin{document}$\beta = 400$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M5.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M5.png"/>	</alternatives>	</inline-formula>, the influence of field emission on the breakdown is significant when the electric field intensity is above	<inline-formula>	<tex-math id="M6">\begin{document}$10\;{\rm{ MV}}/{\rm{m}}$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M6.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M6.png"/>	</alternatives>	</inline-formula>. For the breakdown of helium gas with copper serving as a parallel plate electrode, the effect of field emission can be ignored when the electric field intensity is lower than	<inline-formula>	<tex-math id="M7">\begin{document}$8\;{\rm{ MV}}/{\rm{m}}$\end{document}</tex-math>	<alternatives>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M7.jpg"/>	<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20210086_M7.png"/>	</alternatives>	</inline-formula>. At a micro level, the field emission can provide new "seed electrons" for the discharge space, which can increase the electron density of the whole space and intensify the particle collision reaction, finally leading to the breakdown.