## 4 Conclusions  
In this paper, a 2D3V IFE-PIC numerical model was established to simulate a portion of the radial-azimuthal plane near the exit of the HETs. The effect of the magnetic field line curvature on the sheath formation and dielectric wall erosion was analyzed under different tilt angles of the magnetic field. When the electric field \(E\) is perpendicular to the magnetic field \(B\), the erosion rate caused by ion sputtering on the dielectric wall remains constant after simulation convergence with a value of 2.9 \(\times\) 10\({}^{-10}\) m/s. If the magnetic field line is convex to the anode, the number of electrons that can hit the wall increases, which causes the wall potential to decrease. The increased potential gradient between the wall and the quasi-neutral region accelerates the ions towards the wall, leading to a more intense degree of wall erosion compared to the case where the electric field \(E\) is perpendicular to the magnetic field \(B\). Furthermore, as \(\alpha\) increases, the erosion rate becomes larger, and the value of the erosion rate increased by 4.9%, 31%, 70%, and 171% as \(\alpha\) changed from 0\({}^{\circ}\) to 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\), respectively. If the magnetic field line is convex to the exit plane of HETs, the number of electrons that can reach the wall decreases, resulting in an increase in the wall potential. The decreased potential drop along the radial direction reduces the energy of the ions hitting the wall. Therefore, the wall sputtering erosion rate is smaller than that with orthogonal electromagnetic fields. As \(\alpha\) varies from 0\({}^{\circ}\) to \(-\)15\({}^{\circ}\), \(-\)30\({}^{\circ}\), \(-\)45\({}^{\circ}\), and \(-\)60\({}^{\circ}\), the value of the erosion rate decreases by 5.5%, 59%, 83%, and 90%, respectively. Figure 14: The averaged erosion rate of the dielectric wall corresponding to different values of the negative \(\alpha\). Although the influence of the magnetic field line curvature on the channel wall erosion in HETs has been investigated in the present work, it is necessary to discuss the limitations of our model, and it should be improved in the future. Firstly, the wall surface variation caused by sputtering erosion is ignored in this paper, and in future work, we expect to achieve a more accurate study by realizing a self-consistent plasma-wall interaction. Secondly, the secondary electron emission is not considered in our PIC model. This will influence the thickness of the sheath and leads to the variation of the wall potential. Therefore, the role that secondary electron emission plays in the erosion process needs to be further discussed in future work. Finally, a detailed theoretical analysis of the influence of the curved magnetic field configuration on the mechanism of channel wall erosion is necessary to implement in future work. Conceptualization, L.Q. ; Methodology, Y.C. ; Validation, B.T. ; Formal analysis, L.Q. ; Investigation, K.G. ; Data curation, K.G. ; Writing--original draft, L.Q. ; Writing--review & editing, Y.C. and B.T. ; Supervision, Y.C. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (No. 51907039), the China Postdoctoral Science Foundation (No. 2022M720949), the Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515011368 and 2023A1515010137), and the Shenzhen Technology Project (No. JCYJ20190806142603534, No. ZDSYS201707280904031). Not applicable. This work was supported by the National Natural Science Foundation of China (No. 51907039), the China Postdoctoral Science Foundation (No. 2022M720949), the Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515011368 and 2023A1515010137), and the Shenzhen Technology Project (No. JCYJ20190806142603534, No. ZDSYS201707280904031). Not applicable. This work was supported by the National Natural Science Foundation of China (No. 51907039), the China Postdoctoral Science Foundation (No.