This paper presents a fully kinetic particle-in-cell simulation of collisionless mesothermal plasma expansion with a focus on the macroscopic electron properties. The results show that the electron thermal properties are anisotropic and nonuniform. In the beam core region, the electrons are thermalized due to interactions between the trapped electrons and the potential well between the beam exit and the beam front. The electron expansion inside the beam is equilibrium and significant cooling occurs associated with the expansion. Immediately out of the beam boundary, the electrons undergo an isothermal expansion. In the outer expansion region, the electrons transition into a nonequilibrium expansion and again exhibit significant cooling. We find that the commonly used assumption of Boltzmann electron simplification is not valid for modeling electrons in mesothermal plasma expansion. An analysis of the electron temperature and density correlation along each individual ion streamlines suggests that simplified models for electron dynamics may be constructed using multiple polytropic laws in different plume regions.

This paper presents a fully kinetic particle particle-in-cell simulation study on the emission of a collisionless plasma plume consisting of cold beam ions and thermal electrons. Results are presented for both the two-dimensional macroscopic plume structure and the microscopic electron kinetic characteristics. We find that the macroscopic plume structure exhibits several distinctive regions, including an undisturbed core region, an electron cooling expansion region, and an electron isothermal expansion region. The properties of each region are determined by microscopic electron kinetic characteristics. The division between the undisturbed region and the cooling expansion region approximately matches the Mach line generated at the edge of the emission surface, and that between the cooling expansion region and the isothermal expansion region approximately matches the potential well established in the beam. The interactions between electrons and the potential well lead to a new, near-equilibrium state different from the initial distribution for the electrons in the isothermal expansion region. The electron kinetic characteristics in the plume are also very anisotropic. As the electron expansion process is mostly non-equilibrium and anisotropic, the commonly used assumption that the electrons in a collisionless, mesothermal plasma plume may be treated as a single equilibrium fluid in general is not valid.

Both fully kinetic and hybrid particle-in-cell (PIC) simulations are performed to investigate the two-dimensional (2D) expansion of a collisionless, hypersonic plasma plume into a vacuum. The fully kinetic PIC simulations are carried out using the real ion-to-electron mass ratios of ${\text{H}}^{+}$, ${\text{Ar}}^{+}$, and ${\text{Xe}}^{+}$, while the hybrid PIC model assumes the electrons to be a massless, isothermal fluid. We find that the hypersonic plasma plume exhibits four distinct regions, the unperturbed, quasisteady expansion, self-similar expansion and electron front regions. The behavior of electrons is strongly anisotropic, causing considerably different expansion characteristics between the plume direction and the transverse direction. Along the plume direction, the expansion dynamics is similar to that of the classical one-dimensional (1D) semi-infinite plasma expansion and the electrons are almost isothermal. In the transverse direction, the expansion process can be considered analogous to the 1D expansion of a finite plasma where the effect of electron cooling is important. This anisotropic characteristic is attributed to the amount of electron thermal energy available from the source in different directions. A direct comparison between the hybrid and full PIC simulations shows that the widely used equilibrium isothermal electron fluid model is in general not valid for modeling the expansion of a collisionless plasma plume.

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O₂, including the distributions of species mole fractions and vibrational temperature of the first excited state of O₂ molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

A commonly used approach to simulate ion thruster plumes is a hybrid particle-in-cell (PIC) with the Boltzmann relation to model electrons. The limitations of such an approach are investigated by benchmarking hybrid PIC against fully kinetic PIC simulations using the real Xe⁺ to electron mass ratio (m_i/m_e = 241073). The results show that both full PIC and hybrid PIC lead to similar plume density structures but very different plume potentials. If one could ignore the ion beam neutralization region near the thruster exit, the main physics missing from a hybrid PIC plume model is that from the anisotropic electron characteristics. Including the beam neutralization region leads to further changes in electron temperature and plume potential. Compared to full PIC simulations, the hybrid PIC model results in an overestimation of the plume potential by about 30%–40% in the transverse direction for the simulations considered. Since the electrons in the plume are nonequilibrium and anisotropic, simply replacing the Boltzmann relation with the more general polytropic thermodynamic relation for electrons in a hybrid PIC plume model will not lead to a significant improvement in accuracy.