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The Vlasov–Poisson equation is one of the most fundamental models in plasma physics. It has been widely used in areas such as confined plasmas in thermonuclear research and space plasmas in planetary magnetospheres. In this study, we explore the feasibility of the physics-informed neural networks for solving forward and inverse Vlasov–Poisson equation (PINN-Vlasov). The PINN-Vlasov method employs a multilayer perceptron (MLP) to represent the solution of the Vlasov–Poisson equation. The training dataset comprises the randomly sampled time, space, and velocity coordinates and the corresponding distribution function. We generate training data using the fully kinetic PIC simulation rather than the analytical solution to the Vlasov–Poisson equation to eliminate the correlation between data and equations. The Vlasov equation and Poisson equation are concurrently integrated into the PINN-Vlasov framework using automatic differentiation and the trapezoidal rule, respectively. By minimizing the residuals between the reconstructed distribution function and labeled data, and the physically constrained residuals of the Vlasov–Poisson equation, the PINN-Vlasov method is capable of dealing with both forward and inverse problems. For forward problems, the PINN-Vlasov method can solve the Vlasov–Poisson equation with given initial and boundary conditions. For inverse problems, the completely unknown electric field and equation coefficients can be predicted with the PINN-Vlasov method using little particle distribution data.

Chemical and electrical thrusters are generally utilized to control the attitude and orbit of spacecraft in aerospace. When they are firing, the exhaust expands into the vacuum environment, known as the vacuum plume. The plume flow can collide with spacecraft surfaces due to sufficient expansion, exerting adverse effects on the spacecraft, such as heating load, force/torque, contamination, and sputtering. Therefore, it is vital to investigate the vacuum plume to ensure the function and safety of the spacecraft. This review introduces the ground test and numerical simulation methods of the vacuum plume for chemical and electrical thrusters. The vacuum environment, invasive, and non-invasive (optical) measurements of the ground test are concluded. Numerical simulation of plume flow and its effects is exampled. The hybrid CFD-DSMC (computational fluid dynamics and direct simulation Monte Carlo) algorithm is employed to simulate the gas plume flow spanning continuum and transitional and free molecular flow regimes for chemical thrusters. By contrast, the PIC-DSMC (particle-in-cell plus direct simulation Monte Carlo) algorithm is used for the plasma plume flow containing charged particles exhausted by electrical thrusters. Moreover, the topics of fast prediction of the vacuum plume, plume–surface interaction, and plume–Lunar/Mars regolith interaction are proposed for future research.

A momentum flux measuring instrument (MFMI), which ranges from 1 mN∼300 N, is designed to measure the parameters related to the momentum flux of exhaust plume of attitude and orbit control thrusters covered electric and chemical thrusters. A MFMI with the variable-range provides an efficient and economy way to study the exhaust plume of both electric and chemical thrusters. The flexural pivots, replaceable strain gauge, replaceable target plate, and force arm with the variable length make it possible. The designed MFMI with the non-displacement measurement can reduce the influence of pipelines and test lines, especially the elastic force and friction due to displacement. The designed MFMI system with the range of 0∼100 mN and 0∼15 N was calibrated separately. The target indirect measurement method is a simple and economical option for measuring the thrust of electric thrusters, and is employed to measure the thrust of the LIPS-200 ion thruster using the designed MFMI. Research indicates that the sputtering contributes to the momentum transfer of plasma-surface interactions. In addition, the high-speed charged ions from the thruster will experience a charge-exchange (CEX) collision with the slow neutral background. Therefore, the influence of the sputtering and CEX on target indirect measurement method is derived in detail, and then the measured thrust is corrected. The measured average thrust, which is 40.1 mN, demonstrates that the designed MFMI is effective. The designed MFMI can also be employed as a thrust stand by directly mounting the thrusters on torsional arm, and a maximum of three thrusters can be installed on the MFMI at the same time.