In this paper, a methodology is presented to compute the plasma properties (e.g.,, density and temperature) accounting for the dynamics of the excited states. The proposed strategy applies to both zero-dimensional (0D) models and multidimensional fluid and hybrid codes handling low-pressure (<50 mTorr) plasma discharges filled with argon, neon, krypton, and xenon gases. The paper focuses on two main aspects: (i) a lumping methodology is proposed to reduce the number of reactions and species considered in order to keep at bay the computational cost without a major loss of accuracy; (ii) the influence that different datasets of cross sections have on the results has been assessed. First, the lumping methodology has been implemented in a 0D model accounting for singly charged ions, neutrals, along with 1s and 2p excited states (Paschen notation). Metastable and resonant are treated as two separate species within the 1s energy level ($1s_M$ and $1s_R$ , respectively). The results have been benchmarked against those obtained treating each energy level of the excited states as an individual species. Differences lower than 1% have been obtained. Second, the results of the 0D model have been compared against measurements of electron density and temperature performed on an inductively coupled plasma. Numerical predictions and experiments present a disagreement up to 20%–30%, which is comparable to the uncertainty band of the measurements. Finally, the lumping strategy has been implemented in a 2D fluid code to assess its computational affordability, and the results have been compared against the experiments as well. A variance up to 30% in electron density and temperature is registered adopting different datasets of cross sections.

The accurate simulation of the plasma transport in helicon sources is a key aspect to improve the design of Helicon Plasma Thrusters (HPTs). Specifically, the 3D-VIRTUS code was proven to provide satisfactory estimations of the propulsive performance of realistic HPTs (difference between measures and numerical estimations of the thrust <30%). Nonetheless, further investigations are needed to deepen the influence that the plasma chemistry model, the formulation of the energy equation, and the definition of the diffusion coefficients have on the results of the simulation. First, a quantitative analysis has been conducted on a simplified configuration of HPT to study each phenomenon separately. Second, the generalized fluid model has been benchmarked against measures of plasma density performed on a helicon source. The radiative decay reactions affect the estimation of the performance (e.g., thrust) up to 40%. The quasi-isotherm formulation of the energy equation affects results (e.g., electron density) up to 30%. Accounting for anomalous transport or defining diffusion coefficients classically does not have a major effect on the simulation (e.g., thrust varies less than 20%). The generalized formulation of the fluid model provides estimations of the plasma density, which are within the uncertainty band of the measures (i.e., differences <20%).