Simulation of the neutral gas flow within an electric thruster by the kinetic Fokker-Planck method and comparison with force balance measurements

Abstract

Within the German Aerospace Center’s (DLR)Decentralized Energy supplied Electric Propulsion(DEEP) project, amicrowave-heated electric thruster is developed [1]. The plasma is created using an electron-cyclotron-resonance (ECR)discharge and accelerated using a magnetic nozzle. This allows the usage of different propellants such as noble gasesbut will also allow the use of reactive gases like air. Since the power coupling efficiency of the ECR discharge and theconfinement of the plasma depend highly on the local number density, the channel flow and the plume of the thrustershall initially be simulated for neutral gas. This will lead to further understand the influence of the injector geometryand assist in optimization of the neutral flow injection into the discharge channel. Additionally, neutral gas simulationsare computationally less expansive than plasma simulations. The simulation is performed for argon and xenon at threedifferent volume flow rates of ̇V=1,10,45 sccm which are representative for the thruster operation and ignition.The simulations will be performed using the kinetic cubic Fokker-Planck (FP) model [2]. The method is being contin-uously developed at DLR Göttigen as an extension to the open-source DSMC code SPARTA by Sandia National Labs[3]. Unlike Direct-Simulation Monte Carlo (DMSC), the FP method does not resolve the jump process of the Boltzmanncollision operator by calculating interactions between simulated particle pairs. Rather it uses a continous stochastic pro-cess which leads to the computational cost being independent of the Knudsen numberKn. This allows the method to becomputationally more efficient than DSMC in areas of lowKnnumbers like in the inflow structure used in the thrusterunder investigation. The thrust is calculated by integrating over the impulse flux at the end of the channel to considernon-uniformities of the flow that might occur due to an asymmetry of the gas injection.Thrust measurements in the mN-range for neutral and plasma flows of argon and xenon have been performed using athrust balance developed at DLR Göttingen [4], which has previously been tested with a cold gas thruster and a griddedion thruster inside of a vacuum chamber. The thrust measurements of the neutral flows are compared against the simula-tion results. Furthermore, the observed divergence angle of the plume during thruster operation is also compared to thedivergence angle of the plume which results from the neutral gas simulations.The results from the simulation will allow to improve the design of the gas injector and the modelling of the plasmadischarge itself, since the structure of the magnetic field and microwave radiation are known from independent measure-ments and simulations. Therefore, the knowledge of the local number density can directly assist in the improvement ofthe simple discharge models. Additionally, the results for the inflow from the injector can be used as an initial conditionfor particle-in-cell simulations.