###### Abstract  
This paper examines the modeling approaches used to analyze the electric field distribution in high-voltage direct-current gas-insulated systems (HVDC-GISs) used for the acceleration grid power supply (AGPS) of neutral beam injectors (NBIs). A key challenge in this context is the degradation of dielectric performance due to radiation-induced conductivity (RIC), a phenomenon specific to the harsh radioactive environments near fusion reactors. Traditional models for gas conductivity in HVDC-GISs often rely on constant or nonlinear conductivity formulations, which are based on experimental data but fail to capture the effects of external ionizing radiation that triggers RIC. To address this limitation, a more advanced approach, the drift-diffusion recombination (DDR) model, is used, as it more accurately represents gas ionization and the influence of radiation fields. However, this increased accuracy comes at the cost of higher computational complexity. This paper compares the different modeling strategies, discussing their strengths and weaknesses, with a focus on the capabilities in evaluating the charge accumulation and the RIC phenomenon.  
HVDC; gas-insulated systems; transmission line; AGPS; neutral beam injector (NBI); radiation-induced conductivity (RIC) +
Footnote †: journal: Physics Letters B  
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Footnote 1: email: _applied_  
Footnote †: journal: Physics Letters B  
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Footnote 1: email: _et al._  
Footnote †: journal: Physics Letters B  
ITER and fusion demonstration power plants. The NNBI of DTT accelerates ions up to an energy of 510 keV [8; 9], while that of CFETR reaches 1 MeV [10].  
Differently from the commercial HVDC gas-insulated lines (GILs), the TL of the AGPS is multi-conductor, indeed all the voltage levels of the ion acceleration grids are transmitted within the same line. The design of the TL requires particular attention to what concerns both the conductors' mutual positioning and the cross-section diameter selection. Indeed, conflicting demands must be met. From one side, reducing the overall volume of the TL is advantageous to reduce the amount of insulating gas. However, the selected geometry must satisfy the insulation requirements to avoid partial discharges and breakdowns.  
Usually, commercial HVDC-GILs are placed underground [11]; however, this is not true for HVDC-GSs of NNBI AGPS. Due to the harsh radioactive environment in which HVDC-GISs will be forced to operate when placed in the proximity of MCF devices, the dielectric performances of the insulating gas can degrade quickly given radiation-induced conductivity (RIC) effects [12].  
Advanced numerical tools tailored for specific applications are required to address these issues and sustain the engineering and operational phases. In the literature, different approaches are proposed to analyze the electric field distribution within HVDC-GISs, each characterized by pros and cons. This paper aims to compare the different modeling approaches for HVDC-GISs used in fusion technology and their capability to capture fundamental phenomena affecting the dielectric performances of the systems.  
This paper is organized as follows. Section 2 briefly recalls the surface charge accumulation phenomenon within HVDC-GIS equipment. In Section 3, the RIC phenomenon is described. The electric field modeling approaches are described in Section 4. The conduction mechanism within the gas is explained in Section 5; in particular, an equivalent gas conductivity model accounting for the RIC phenomenon is introduced in Section 6. Numerical results are shown in Section 7. A discussion about the outcomes of the research is given in Section 8. Finally, Section 9 summarizes the main outcomes of this work.