Field emitters can be used as a cathode electrode in a cathodoluminescence device, and single-walled carbon nanotubes (SWCNTs) that are synthesized by arc discharge are expected to exhibit good field emission (FE) properties. However, a cathodoluminescence device that uses field emitters radiates rays whose intensity considerably fluctuates at a low frequency, and the radiant fluctuation is caused by FE current fluctuation. To solve this problem, is very important to obtain a stable output for field emitters in a cathodoluminescence device. The authors consider that the electron-emission fluctuation is caused by Fowler-Nordheim electron tunneling and that the electrons in the Fowler-Nordheim regime pass through an inelastic potential barrier. We attempted to develop a theoretical model to analyze the power spectrum of the FE current fluctuation using metallic SWCNTs as field emitters, owing to their electrical conductivity by determining their FE properties. Field emitters that use metallic SWCNTs with high crystallinity were successfully developed to achieve a fluctuating FE current from field emitters at a low frequency by employing inelastic electron tunneling. This paper is the first report of the successful development of an inelastic-electron-tunneling model with a Wentzel-Kramers-Brillouin approximation for metallic SWCNTs based on the evaluation of FE properties.