## 1 Introduction  
Gas-insulated transmission lines (GILs) are extensively employed in electric energy transmission systems due to their exceptional reliability and substantial power transfer capacity [1]. As an innovative reserve technology, direct current (DC) GIL efficiently utilizes limited spatial resources while playing a pivotal role in the development of future power transmission networks characterized by large capacity and long-distance capabilities [2]. Under DC voltage, charge accumulation in high-voltage direct current (HVDC) cables and gas-insulated systems markedly distorts electric field distributions, compromising insulation performance and increasing the risk of dielectric breakdown [3; 4]. Similarly, this charge-induced distortion influences the electric field distribution of GIL, which gradually transitions from an initial capacitive field to a resistive field, with surface charge accumulation on the insulator further exacerbating electric field distortion [5]. When voltage polarity reversal occurs, the local electric field distortion caused by surface charge accumulation becomes particularly pronounced [6]. Furthermore, under high-voltage and high-current operating conditions of DC GIL, the combined influence of electric and thermal fields exacerbates surface charge accumulation, consequently intensifying local electric field distortion [7; 8]. Therefore, investigating the characteristics of insulator surface charge accumulation and electric field distribution under multi-physical field coupling is crucial for improving the insulation performance of DC GIL and enhancing overall system stability. In recent years, with the continual advancement of high-voltage DC transmission capacity and voltage levels, the gas-solid insulation systems of DC GIL have encountered increasingly severe challenges [9]. Charge accumulation on insulator surfaces is widely recognized as a key factor affecting electric field distribution and subsequently elevating the risk of insulation failure [10]. Particularly under polarity-reversal voltage, residual charge preceding the reversal can trigger local electric field distortion, thereby significantly compromising the safe and reliable operation of power equipment [11]. Consequently, researchers have conducted extensive and rigorous investigations to improve the insulation performance of DC GIL. Studies have demonstrated that charge accumulation on insulator surfaces is primarily influenced by material conductivity, gas conductivity, and interfacial charge transport [5; 12]. In actual operation, the distribution of electric and thermal fields significantly alters the conductivity characteristics of insulator materials and the migration and diffusion behavior of charged particles in the gas medium, thereby exacerbating surface charge accumulation and resulting in distortion of the electric field along the surface [13; 14]. [PERSON] et al. experimentally measured the surface charge distribution using a scaled-down insulator model under an electro-thermal coupling field [15]. However, due to limitations in measurement techniques, conducting accurate measurements of insulator surface charge accumulation under real operating conditions remains a significant challenge [16]. In contrast, numerical simulation methods offer superior flexibility. With advancements in computational science, simulation techniques have become increasingly mature and reliable, providing significant advantages for investigating transient characteristics of insulator surface charge accumulation and electric field distributions that are difficult to capture experimentally [17; 18]. [PERSON] et al. investigated the effect of volumetric conductivity on surface charge distribution and transient potential changes using finite element method (FEM) simulations [19]. [PERSON] et al.