In this paper, a discrete Boltzmann method (DBM) for plasma kinetics is proposed and further used to investigate the non-equilibrium characteristics in Orszag–Tang (OT) vortex and Richtmyer–Meshkov instability (RMI) problems. The construction of DBM mainly considers two aspects. The first is to build a physical model with sufficient capability to capture underlying physics. The second is to devise schemes for extracting more valuable information from massive data. For the first aspect, the generated model is equivalent to a magnetohydrodynamic model, and a coarse-grained model for extracting the most relevant thermodynamic non-equilibrium (TNE) behaviors including the entropy production rate. For the second aspect, the DBM uses non-conserved kinetic moments of (f−feq) to describe the non-equilibrium states and behaviors of complex systems. It is found that (i) for OT vortex, the entropy production rate and compression difficulty first increase and then decrease with time. (ii) For RMI with interface inversion and re-shock process, the influence of magnetic field on TNE effects shows stages: before the interface inversion, the TNE strength is enhanced by delaying the interface inversion; while after the interface inversion, the TNE strength is significantly reduced. Both the global average TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inversion. In general, this paper proposes a generalized physical modeling and analysis scheme that has the potential for investigating the kinetic physics in plasma.

The Kelvin–Helmholtz Instability (KHI) with and without external magnetic fields is computationally investigated based on the Discrete Boltzmann Method (DBM). The maximum local Knudsen number in the system is up to more than 0.06. Simultaneously, the density correction induced by the second-order Knudsen number effects near some interfaces is up to more than 10% . This work aims at the kinetic physics that occurs on the length and time scales of particle collisions, which leads to discrete/non-equilibrium effects and may contribute to the observed differences between hydrodynamic predictions and experiments. Through selecting appropriate kinetic moments, the DBM has the capability to describe flow systems ranging from continuum to early transition flow regime. The first- and second-order DBMs with different physical capabilities are constructed. The results of the two DBMs are compared, including the hydrodynamic non-equilibrium and the most relevant thermodynamic non-equilibrium behaviors. It is found that: (i) In KHI, without an external magnetic field, two competing energy transport mechanisms influence the saturation moment of the vortex. (ii) In the presence of an external magnetic field, viscous shear stress and heat flux are enhanced, while the magnetic field suppresses the KHI evolution by inhibiting vorticity transport and inducing secondary vortex structures. This results in an increased local Knudsen number and density difference. (iii) The Atwood number At further amplifies the local Knudsen number and density difference. The maximum density difference first increases and then decreases with At as it suppresses the formation of rotational discontinuities near the saturation moment.

This study investigates the low-frequency ionization instability, high-frequency ion acoustic turbulence, and the energy distributions of energetic ions in ampere-level hollow cathodes. The effects of discharge currents and gas flow rates on discharge instabilities and energetic ion distributions are systematically analyzed, focusing on the mechanisms of ion-acoustic waves at both low- and high-frequency. Key factors influencing the power-law ‘ η ’ ( ϕ 2 ∝ ω η , η < 0 ) of high-frequency ion acoustic waves are identified, including electron trapping, ion resonance broadening, and the nonlinear Landau damping effect. Furthermore, the generation mechanisms of energetic ions are illustrated at the micro (e.g. anomalous collision frequency ‘ ν an IAT ’ induced by IAT) and macro (e.g. discharge voltage) levels. Correlation analysis reveals the relationships between energetic ions, low-frequency ionization instabilities, and high-frequency ion acoustic turbulence. These findings offer valuable insight into the unstable discharge oscillations of ampere-level hollow cathodes and the generation of energetic ions. It provides guidance for optimizing the discharge parameters of hollow cathodes, thus improving the endurance and stability of the cathode.

In this work, the direct kinetic method is employed to investigate the anomalous transport process of current-driven instability in the hollow cathode plume. The influences of electron Mach number, gas species, and gas flow rate on the evolution of both the electron/ion velocity distribution functions and the corresponding macroscopic quantities (bulk velocity and temperature) are carefully examined. The spatial distribution of neutral particles is determined under a conical diffusion assumption, and the role of electron–neutral classical collisions in the anomalous transport process is quantitatively evaluated. The results reveal that: (i) increasing the electron Mach number enhances particle–wave interactions, thereby accelerating the formation of electron holes, high-energy ion tails, and stronger macroscopic oscillations; (ii) lighter gas species intensify particle–wave coupling, leading to a faster and stronger non-equilibrium evolution of both electrons and ions; and (iii) a higher gas flow rate suppresses nonlinear evolution by strengthening electron–neutral classical collisions, which stabilizes the velocity distributions and reduces anomalous energy transfer from electrons to ions. These findings provide new theoretical insight into the particle–wave anomalous transport mechanism and offer valuable guidance for the design and optimization of high-performance hollow cathodes.

Plume oscillations in ampere-level hollow cathodes significantly impact the performance and stability of electric thrusters. In this study, a dimensionless perturbation analysis is applied to the zero-dimensional fluid equations for predicting the oscillation frequency and growth rate of discharge current. The correlation between the predicted and measured frequency of discharge current, as well as the theoretical growth rate and measured total spectral power, is calculated for an ampere-level hollow cathode. Based on the theoretical growth rate, the onset criterion for the electron temperature is used to characterize the ionization instability and describe the physical mechanisms behind ampere-scale hollow cathode plume oscillations. The validity of the critical electron temperature is confirmed by comparing it with the classical instability criterion. Given the strong correlation between the electron temperature instability criterion and oscillation intensity, this criterion is considered more reasonable for predicting the ionization instability. The effect of structural (anode distance, keeper to cathode orifice distance, cathode orifice diameter) and working parameters (keeper current), on the applicability and reliability of this method is systematically evaluated through a detailed analysis of instability phenomena. It should be noted that this paper is an expanded experimental validation of the critical electron temperature theory originally proposed by Georgin [6]. Besides that, the critical electron temperature is not straightforward to apply, since it does not rely directly on macroscopic discharge parameters, such as discharge current, anode voltage, and gas flow rate. One must have access to plasma measurements in the cathode plume in order to apply this criterion, which may make it hard to use in a laboratory testing setting without plasma diagnostics. Despite this, the critical electron temperature could enhance our understanding of ionization instability and offer valuable insights for optimizing high-performance hollow cathodes.

In the present work, the turbulent mixing process of a polydisperse quartz particle flow with a plasma stream generated by a radio-frequency (RF) inductively coupled plasma torch was numerically studied. The thermobaric stress in the quartz particles under dynamic heating in a heterogeneous plasma flow was determined by a two-stage approximation approach. The effect of the presence of vacuoles in natural quartz on the particle thermobaric destruction conditions was studied. It was found that the equivalent thermal and baric stresses in quartz particles may significantly increase in the presence of vacuoles within a small gas volume fraction. The influence of the regime and energetic working conditions of an RF inductively coupled plasma torch system on the particle thermobaric destruction conditions was examined, and a recommendation was given to promote the degree of thermobaric destruction of quartz particles, which is of substantial importance for improving the overall enrichment efficiency of quartz concentrates.