## 1 Introduction  
With the expansion of Mars exploration, the utilization of local resources on Mars to produce mission-critical consumables for Mars exploration, such as propellants and life-support consumables, has gained widespread attention [1; 2; 3]. Carbon dioxide (CO\({}_{2}\)), the most abundant component of the Martian atmosphere (96%), can be used as the prime source for in situ resource utilization (ISRU) to produce carbon monoxide (CO) and oxygen (O\({}_{2}\)). The carbon monoxide can be collected to manufacture rocket vehicles, and the oxygen can be made available for breathing [4; 5]. In addition, CO\({}_{2}\) is a major source of carbon and oxygen and can be used for the in situ manufacturing of plastics and other organic compounds. However, the thermodynamic stability of CO\({}_{2}\) molecules is the major challenge to the ISRU of CO\({}_{2}\) on Mars. In recent years, non-thermal plasmas (NTTPs) have become a widely discussed topic in many fields due to their unique advantages [6; 7; 8]. NTP is an efficient gas-activation approach maintained by electrical discharges, which allow the energetic electrons to coexist with relatively cold gas molecules. The energy stored in energetic electrons can offer a unique way to break the strong C=O bond [9; 10]. More significantly, the low pressure (\(\sim\)600 Pa) and low temperature (\(\sim\)210 K) of the Martian atmosphere are considered to be the ideal conditions for the local splitting of CO\({}_{2}\) using NTTPs [11; 12]. Currently, extensive numerical and experimental investigations are performed to achieve the splitting of CO\({}_{2}\) using dielectric barrier discharges [13; 14], gliding arc discharges [15; 16], microwave discharges [17; 18], and radio-frequency (RF) discharges [19; 20; 21]. Among the plasma sources mentioned above, RF discharges are distinguished by higher electron density, especially operating in the low-pressure and low-temperature environment on Mars [22]. RF discharge, therefore, offers a promising avenue for the ISRU of CO\({}_{2}\) on Mars. However, as the input power increases, the homogenous RF plasma may transform into a radially contracting plasma with a high gas temperature, with the possible risk of damaging the electrodes. Previous research has demonstrated that RF discharges could exhibit higher stability with increasing driving frequency [23; 24]. As a complementary method to experimental diagnosis, numerical simulations can overcome the experimental limitations and provide insight into the discharge properties and plasma chemistry of RF CO\({}_{2}\) plasma. The zero-dimensional kinetic model is widely used to describe the behaviors of various plasmas due to its high computational efficiency, but the spatial properties, such as the distributions of the electric field and the profiles of the product particles, are not available [25; 26]. The fluid model is able to obtain the spatial distributions of plasma species and the electric field with relatively high computational efficiency, which has received more attention in simulating CO\({}_{2}\) conversion [27; 28; 29]. Unfortunately, on the one hand, CO\({}_{2}\) plasma is a multi-scale system with significant differences in the lifetimes of different plasma species; on the other hand, plasma species under Martian pressure are characterized by large transport rates. To accurately describe the behaviors of different species, the fluid model should adopt fine time steps and spatial meshes, which significantly increases the computational load of the fluid model. In addition, in order to accurately describe the driving frequency effect in RF CO\({}_{2}\) plasma, a given power density should be chosen to eliminate the influence of other discharge parameters [30]. However, it is challenging to precisely meet the given power density at all driving frequencies in the numerical simulation.