## 2 Simulation Methodology, Material, and the Experiments
### CNCs as Electron Emitting Nanomaterial  
The unique properties of carbon nanomaterials, such as their high thermal conductivity, low work function, and excellent electron migration rate, make them promising FE emitters. CNTs have received much attention since their discovery by [PERSON] [26, 27, 28, 29, 30, 31, 32]. An advantage of CNTs in FE is that they are natural field-enhancing objects because of their high aspect ratio.  
CNCs [13, 14, 15, 33, 34, 35, 36, 37] are nanocarbon materials with a coiled structure and are composed of nanometer-scale fibers. Compared with CNTs, CNCs have considerably more electron emission sites--not only at the tips but also at the numerous nanocrystallites embedded in the amorphous carbon body. Additionally, CNCs are more robust than CNTs because the former are much thicker and thus can withstand a higher current density. Owing to their much larger diameter and higher FE site density, CNCs exhibit better long-term current emission stability, current density, FE efficiency, and lifetime than CNTs [18, 19], and so they have already found application in FE lighting [38, 39, 40, 41]. Consequently, CNCs are used as the emitter material in the X-ray tube in this work.  
CNCs are generally synthesized by catalytic thermal chemical vapor deposition (TCVD) or arc discharge. Since CVD can be used in the low-cost, large-scale commercial synthesis of CNCs, it was utilized to synthesize the CNCs herein.  
The substrates that were used herein for the synthesis of CNC cathodes were 304 stainless steel circular disks with a diameter of 15 mm. Each substrate was firstly cleaned with acetone, ultrasonicated for 10 min, and subsequently washed in deionized water. To expose the bare metal surface, each stainless steel substrate was then immersed in 10%-37% HCl for 3-10 min and rinsed again with deionized water. Before TCVD, Pd catalysts were deposited onto the substrates through chemical displacement in a 100-800 ppm PdCl\({}_{2}\) solution of pH 1.6-1.8 at 80 \({}^{\circ}\)C for 10 min. After the reaction was complete, the cathodes were rinsed with deionized water and dried with N\({}_{2}\) gas. The prepared cathodes were placed in a TCVD furnace and the pressure was pumped down to 10\({}^{-2}\) Torr. The temperature was gradually increased to 600 \({}^{\circ}\)C at a rate of 20 \({}^{\circ}\)C/min in an atmosphere of H\({}_{2}\) and Ar. The flow rates for H\({}_{2}\) and Ar were 10 and 100 sccm, respectively. When the temperature reached 600 \({}^{\circ}\)C, the Ar gas was evacuated and the H\({}_{2}\) flow rate was increased to 20 sccm to pretreat the Pd catalysts for 5 min. Next, to grow the CNCs, C\({}_{2}\)H\({}_{2}\) gas was fed at a flow rate of 5 sccm for 20 min while the furnace temperature was maintained at 600 \({}^{\circ}\)C.  
The morphologies of the CNCs were examined using a transmission electron microscope (TEM, model: Tecnai F30, FEI, Hillsboro, OR, USA) and a field emission scanning electron microscope (FE-SEM, model: JEOL JSM-7600F, Japan Electron Optic Laboratory Co., Ltd., Tokyo, Japan). Their graphite crystallinity was analyzed using Raman spectroscopy.