# The Effect of Non-Transferred Plasma Torch Electrodes on Plasma Jet: A Computational Study
## 4 Conclusions  
This study presented a computational investigation of cathode and anode geometries in non-transferred plasma torches using steady-state MHD modeling on a 2D axisymmetric domain in COMSOL Multiphysics (v6.1). The impact of electrode shape on flow structure, temperature, velocity, and current density in the plasma jet was systematically analyzed.  
Three cathode configurations were evaluated: conical, tapered, and flat. The results showed that while the arc length remained largely unchanged across cathode types, the intensity of the arc varied depending on the shape. Cathode geometry significantly influenced local plasma temperature at the cathode tip, though outlet conditions (temperature and velocity) were similar among all cathodes. Further, flat-shaped cathodes exhibited flow separation near the tip, and an in-depth investigation of the phenomenon is explained in our previous work [41].  
The analysis of cylindrical and stepped anode nozzles demonstrated that stepped anodes introduce flow separation, resulting in reduced plasma velocity and arc current. In contrast, cylindrical nozzles produced more stable plasma jets and higher axial velocities.  
One interesting finding of this work is that the cathode shape can cause a difference in the thermal efficiencies by 10%. Efficiency analysis revealed that flat cathodes offered slightly better thermal efficiency compared to other geometries, highlighting that cathode e can be used for further studies related to the upscaling. However, anode geometry had a minimal effect on efficiency. Overall, input power and gas flow rate were found to be the dominant factors influencing the thermal efficiency of non-transferred plasma torches, with electrode shapes playing a secondary role.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Geometry**} & **Input Power** & **Inlet Velocity** & **Efficiency** \\  & **(kW)** & **(m/s)** & **(\%)** \\ \hline Cathode a & 14 & 11.06 & 76 \\ Cathode b & 14 & 11.06 & 75.9 \\ Cathode c & 14 & 11.06 & 75.4 \\ Cathode d & 14 & 11.06 & 73 \\ Cathode e & 14 & 11.06 & 81 \\ Cathode f & 14 & 11.06 & 72 \\ Stepped nozzle & 6.2 & 11.06 & 54.5 \\ Stepped nozzle & 18.4 & 11.06 & 80.8 \\ Cylindrical nozzle & 6.2 & 11.06 & 54.5 \\ Cylindrical nozzle & 18.4 & 11.06 & 81 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Thermal efficiencies of non-transferred plasma torch with different cathode shapes and anodes.  
**Author Contributions:** Conceptualization, S.L.S., L.-G.W. and H.O.A.; Methodology, S.L.S., L.-G.W., H.O.A., H.W. and A.S.; Software, S.L.S.; Validation, S.L.S.; Formal analysis, S.L.S.; Investigation, S.L.S., L.-G.W., H.O.A., H.W., and A.S.; Resources, L.-G.W. and H.W.; Data curation, S.L.S., H.O.A., H.W. and A.S.; Writing--original draft, S.L.S.; Writing--review & editing, L.-G.W., H.O.A., H.W. and A.S.; Visualization, S.L.S., H.O.A. and L.-G.W.; Supervision, L.-G.W., H.O.A., H.W. and A.S.; Project administration, L.-G.W.; Funding acquisition, L.-G.W. and H.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The project is funded by Swedish Energy Agency, Project grant no.49609-1.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.