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This work addresses one-dimensional evolution of a collisionless plasma next to a solid surface that is immersed into the plasma instantaneously. In particular, we consider how the self-similar rarefaction wave (Allen & Andrews, J. Plasma Phys., vol. 4, 1970, pp. 187–194) establishes dynamically and how the electron reflection from the surface modifies the structure of the rarefaction wave and the Debye sheath. We demonstrate that a sufficiently strong reflection eliminates the Debye sheath and changes the wall potential and the plasma flow parameters significantly. The paper presents numerical results that illustrate the developed analytical theory.

Enhancing the frequency band of the electromagnetic wave is regarded as an efficient way to solve the communication blackout problem. In this paper, frequency of incident wave is raised to Terahertz (THz) band and the radar cross section (RCS) of the three-dimensional conductive model is calculated and simulated based on the Runge&ndash, Kutta Exponential Time Differencing&ndash, Finite Difference Time Domain method (RKETD-FDTD). Interaction of THz wave and magnetized plasma sheath is discussed. Attenuations in incident wave frequencies of 0.34 THz and 3 GHz and different plasma densities are analyzed. The monostatic RCS is used to compare the penetration in different incident wave frequencies while the bistatic RCS is fixed on 0.34 THz to study its characteristics. The simulation result has almost the same RCS as that of the model without coating plasma when the frequency of incident wave reaches 0.34 THz. The advantages of THz wave at 0.34 THz on increasing RCS and reducing the attenuation are demonstrated from different aspects including polarizations, incident angles, magnetization and anisotropy of plasma, thickness of plasma, scan planes and inhomogeneous distribution of plasma. It can be concluded that 0.34 THz has unique advantages in increasing the radar cross section and can be applied to solve the problem of communication interruption.

The propagation characteristics of terahertz (THz) waves incident vertically into inhomogeneous and collisional dusty plasma with a ceramic substrate are studied using the scattering matrix method (SMM). The effects of the incident wave frequency and plasma parameters, such as the maximal electron density, dust particle density, dust particle radius and collision frequency, on the reflectance and transmittance of THz waves in the dusty plasma are discussed. In addition, the differences of the propagation properties in the dusty plasma, with and without ceramic substrate, are analyzed. Meanwhile, the differences of the propagation properties in dusty plasma and common plasma, respectively, with ceramic substrate are also compared. Simulation results show that the substrate and dust particles have significant influence on the propagation characteristics of THz wave in plasma sheath. Finally, the transmission increases with the increase of electron density, dust density, dust particle radius and collision frequency.

We provide a formulation that describes the propagation of solitons in a nondissipative, nonmagnetic plasma, which does not depend on the particular electron density distribution considered. The Poisson equation in the plasma sheath is expressed in terms of the Mach number for ions entering the sheath from the plasma and of a natural scale for the electrostatic potential. We find a class of reference frames with respect to which certain functions become stationary after arbitrary small variations of the Mach number and potential scale, that is, by determining the critical values of those quantities based on a variational method. It is shown that the critical Mach number defines the limits for the applicability of the reductive perturbation technique to a given electron density distribution. Based on our provided potential scale, we show that the Taylor expansion of the suprathermal electron distribution around equilibrium converges for all possible values of the spectral κ-index. In addition, owing to the admissible range for the critical Mach number, it is found that the reductive perturbation technique ceases to be valid for 3/2

The structure of the sheath and the current exchange of two-dimensional electron-emitting objects with elliptic cross section immersed at rest in Maxwellian plasmas are investigated with an energy-conserving stationary Vlasov-Poisson solver free of statistical noise. The parameter domains for current collection within the orbital-motion-limited (OML) regime and current emission in space-charge-limited (SCL) conditions were studied by varying the characteristic dimension of the ellipse, its eccentricity, and the emission level. The analysis reveals the correlations between the onset of the non-OML and SCL regimes and the local curvature of the ellipse. As compared to nonemitting ellipses, electron emission broadens the parameter domain for OML current collection for ions and reduces considerably the current drop for non-OML conditions. Under identical plasma environments, elliptic bodies are more prone to operate under non-OML and SCL conditions than cylinders. Their emitted current in SCL conditions can be computed accurately from well-known results for cylinders if appropriate dimensionless variables and an equivalent radius are used. The role of the eccentricity, which acts as an integrability-breaking parameter, on the filamentation of the distribution function of the attracted species is studied. This work was supported by the Europen Union's Horizon 2020 FET Open project with Grant Number 828902 (E.T.PACK project).

Effects of nonuniform weakly ionized dusty plasma on the polarization properties of obliquely incident electromagnetic (EM) waves were theoretically investigated in this paper. The dielectric coefficient of magnetized dusty plasma is obtained based on the Bhatnagar–Gross–Krook collision model. Then, the effects of external magnetic field, dust radii, and density on the polarization mismatch loss of obliquely incident EM waves in the L-band were analyzed using the equivalent impedance method. Results indicate that the larger the external magnetic field, the greater the polarization mismatch loss. In addition, we also found that dusty particles alleviate the deterioration of the polarization state significantly; regulating and controlling dust radius and density can avoid polarization reversal and reduce the polarization mismatch loss. We further analyzed the variation of the polarization state under different reentry heights. Our analysis reveals interesting features concerning polarization properties of obliquely incident EM waves, which provide an important theoretical basis for information reception in the plasma sheath containing ablative particles.

In recent years, EUV lithography scanner systems have entered high-volume manufacturing for state-of-the-art integrated circuits, with critical dimensions down to 10 nm. This technology uses 13.5-nm EUV radiation, which is shaped and transmitted through a near-vacuum H2 background gas. This gas is excited into a low-density H2 plasma by the EUV radiation, as generated in pulsed mode operation by the laser-produced plasma in the EUV source. Thus, in the confinement created by the walls and mirrors within the scanner system, a reductive plasma environment is created that must be understood in detail to maximize mirror transmission over the lifetime and to minimize molecular and particle contamination in the scanner. In addition to the irradiated mirrors, reticle, and wafer, the plasma and radical load to the surrounding construction materials also must be considered. We provide an overview of the EUV-induced plasma in the scanner context. Special attention is given to the plasma parameters in a confined geometry, such as that found in the scanner area near the reticle. It is shown that plasma confinement and resulting contributions from secondary electron emission delay the formation of the plasma sheath and thereby reduce the peak ion energies to below the sputtering threshold for mirrors and construction materials. Furthermore, for a confined pulsed plasma with a pulse period shorter than the decay time of the plasma, the plasma consists of a quasi-steady-state cold background plasma and periodic transient peaks in ion energy and ion flux. In terms of modeling, this means that no assumptions can be made on the electron distribution functions and a (Monte-Carlo) particle-in-cell (PIC) model is needed. We present an extension of the PIC model approach to complex three-dimensional geometries and to multiple pulses using a hybrid PIC-diffusion approach. Also, the translation of these specific plasma parameters to off-line setups and the aspects that must be included to make a meaningful translation from off-line laboratory EUV setups to the scanner plasma are discussed.

In this paper, the finite-difference time-domain method based on the Runge-Kutta exponential time differencing formulation (RKETD-FDTD) is used to analyze the radiation characteristics of the plasma-covered Beidou antenna. Simulation results show that the plasma sheath will seriously hinder the propagation of electromagnetic waves, which may cause communication interruption. Specially, adding a “magnetic window”, the influence of plasma on electromagnetic waves can be weakened, which is expected to alleviate the problem of communication interruption. Therefore, our research has an extensive application prospect.

The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves. Based on the calculation of the flow field of a conical cylindrical, this work studies the propagation of electromagnetic waves in plasma sheath at L-band and Ku-band, and discusses the propagation characteristics in the head, side and tail of the sheath. The dielectric properties of plasma sheath are related to flight speed and altitude. A flight condition corresponds to a unique distribution of dielectric properties. For the conical cylindrical, the results show that flight speed is generally negatively correlated with the transmissivity of the plasma sheath. The reflection characteristics of electromagnetic waves at the L-band and Ku-band when obliquely incident to the plasma sheath show a downward trend. When the frequency is increased to Ku-band, the propagation characteristics of electromagnetic waves in the plasma sheath are related to the position of the sheath.

The plasma sheath can induce radar signal modulation, causing not only ineffective target detection, but also defocusing in inverse synthetic aperture radar (ISAR) imaging. In this paper, through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath, we simulated the defocusing of ISAR images in typical environment. Simulation results suggested that the ISAR defocusing is caused by false scatterings, upon which the false scatterings’ formation mechanism and distribution property are analyzed and studied. The range of false scattering correlates with the electron density fluctuation frequency. The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering. Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.

A one-dimensional fluid model of an unmagnetized collisional plasma sheath consisting of q-non-extensive electrons and singly charged positive ions with finite temperature is developed and presented. The ions are described by the fluid model, which is based on the continuity and momentum equations of ions, while the electrons are considered obeying non-extensive distribution according to the Tsallis statistics. In this work, different ion source terms are used in order to compare their contribution. The modified Bohm sheath criterion is determined for different source terms to specify the ion velocity at sheath entrance. The model equations are solved numerically in the plasma-wall transition region. The effect of ion source terms on the collisional electropositive plasma sheath characteristics such as ion and electron density, electric potential, ion velocity, sheath width and space charge is investigated. The influence of the ionization frequency parameter on the sheath behavior has also been studied. The results obtained show a strong impact of ion source terms on the plasma sheath structure. It is also shown that the ion source terms effect increases significantly when the ionization frequency parameter increases.

RCS modeling of a typical hypersonic vehicle and its plasma sheath was investigated. The plasma parameters were analyzed to determine which were most dominant for accurate RCS prediction. HF was determined to provide BLOS detection and good conductivity of the plasma, for optimum RCS.

In this paper, we present a finite-volume direct kinetic method, the so-called discrete unified gas kinetic scheme (DUGKS), for electrostatic plasma. One key feature of this method is the semi-implicit unsplitting treatment of particle transport and collision, and thus the time step in current DUGKS is not limited by the particle collision time. In addition, a fourth-order compact MUSCL scheme with a positivity preserving limiter is implemented in the interface reconstruction, which enables present DUGKS to preserve the favorable conservative property and positivity of distribution function. Combined with this MUSCL method, the semi-Lagrangian scheme is used for the particle transport in velocity space to remove Courant-Friedricks-Lewy restriction induced by the large electric force. As a result, the proposed DUGKS becomes an efficient and stable multiscale scheme. Several numerical experiments, including plasma sheath, linear Landau damping, collisional nonlinear Landau damping, and plasma ion acceleration, are performed to validate current DUGKS. A comparative study of current DUGKS with a general particle in cell (PIC) method which could handle particle collision in a conservative way is also presented. Theory and numerical experiments demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes, while the PIC method is desired for the field- dominated plasma flows involving a wide range of velocities.

International audience; Plasma sheaths in front of six different materials samples (BN, BNSiO 2 , Al 2 O 3 , SiO 2 , stainless steel and silicon) used in various experiments and devices (Hall thrusters, plasma discharge, microelectronics) are studied using the Laser Induced Fluorescence diagnostic. The specific Secondary Electron Emission (SEE) yield of each material is expected to induce differences in the sheath structure from one sample to another. The experiments are carried out in two different plasma discharges (multipolar device and ECR device), exhibiting distinct electron distribution functions: bi-maxwellian and maxwellian. The agreement between the two experiments is good and allow to classify the materials in a consistent way regarding their SEE yields. The multipolar experiments results are compared to a 1D kinetic sheath model and a 1D-1V kinetic sheath simulation code. The predictions of the model are discussed and are in good agreement with previous theory. The influence of the low energy impinging electrons on the SEE yield and emissive sheaths is investigated with the code.

The effects of the electron energy distribution function (EEDF) on the structure of a dusty plasma sheath are investigated. Here, it is assumed that the electrons obey a Druyvesteyn-type distribution with a parameter $x$ controlling the shape of the EEDF. The Druyvesteyn-like distribution tends to a Maxwellian distribution as $x$ varies from 2 to 1. Using the orbital motion limited theory, the incident electron current on the dust is evaluated for a given $x$ . The results of numerical simulations are compared with those of a Maxwellian distribution. It was found that the sheath dynamics depends strongly on the magnitude of $x$ . The sheath thickness increases monotonically with increasing $x$ . However, the absolute dust charge decreases and, as a result, the accelerating ion drag force is weakened and thus the dust number density is enhanced. For a plasma with a Druyvesteyn-like distribution, the Bohm speed is a function of $x$ and increases with increasing $x$ .

Complex plasmas are interesting systems as the charged dust can self-assemble into different types of ordered structures. To understand the mechanisms which govern the transitions from one type of structure to another, it is necessary to know both the dust charge and the confining electric fields within the environment, parameters which are difficult to measure independently. As dust is usually confined in a plasma sheath where the ions stream from the bulk plasma to the negative lower electrode, the problem is further complicated by the ion wake field, which develops downstream of the dust grains in a flowing plasma. The differences in local ion density caused by the wake field change the equilibrium dust charge and shielding distance of the dust grains, and thus affect the interaction between grains. Here we use a molecular dynamics simulation of ion flow past dust grains to investigate the interaction between the dust particles and ions. We consider a long vertical chain of particles confined within a glass box placed on the lower electrode of a Gaseous Electronics Conference rf reference cell. We apply the model iteratively to self-consistently determine the dust charge, electric field, and ion density along the length of the chain as well as the ion flow speed. Simulation results indicate that the ion flow speed within the box is subsonic.

The sheath formation in a weakly magnetized collisionless electronegative plasma consisting of electrons and negative and positive ions has been numerically investigated using the hydrodynamic equations. The electrons and negative ions are assumed to follow the Boltzmann relation. A sheath formation criterion has been analytically derived. This paper focuses on studying the sheath structure by varying the electronegativity. It has been observed that the presence of negative ions has a substantial effect on the sheath structure. The observations made in the present work have profound significance on processing plasmas, specifically in the semiconductor industry as well as in fusion studies.

A plasma sheath inside an ion source has a strong focusing effect on the formation of an ion beam from the plasma. Properties of the beam depend on the shape and location of the plasma sheath inside the source. The most accessible experimental data dependent on the plasma sheath are the beam phase space distribution. Variation of beam emittance is a reflection of the properties of the plasma sheath, with minimum emittance for the optimal shape of the plasma sheath. The location and shape of the plasma sheath are governed by complex physics and can be understood by simulations using plasma models in particle tracking codes like IBSimu. In the current study, a model of the D-Pace’s TRIUMF licensed filament powered volume-cusp negative ion source is made using the IBSimu code. Beam emittance trends are compared between experiments and simulations. peerReviewed

An analytic solution of the time-dependent Boltzmann kinetic equation is found for the first time. The plasma-wall transition (PWT) layer is analyzed using time-dependent velocity distribution functions for electrons and ions. The process of wall charging by electrons is described and estimated. For states close to the time-independent (stationary) state, for which the time dependence of the PWT parameters is weak, (i) the potential shapes in the pre-sheath (PS) and the Debye sheath (DS) are analyzed and (ii) the intermediate region, which bridges the PS and DS sublayers, is defined and its characteristic length is determined. The ion kinetics are dominated by charge exchange with cold neutrals and electron-impact ionization collisions of neutrals. The charge-exchange mean free path λcx is assumed to be constant and much larger than the electron Debye length λDe. The detailed time dependence of the PS sublayer's approach of the stationary state is found. It is proved that the stationary state can be realized only if the floating-potential condition is fulfilled.

During the reentry process, the plasma sheath covering the surface of the hypersonic aircraft will cause the amplitude attenuation and phase jitter of the communication electromagnetic waves. Channel parameters such as the electron density and collision frequency of the plasma sheath reflect the changing trend of the plasma sheath, and these parameters can be measured by physical means. However, these parameters cannot directly reflect the change of the channel communication ability and cannot directly serve the design of communication methods in the plasma sheath. Due to the particularity of the plasma sheath, the traditional channel estimation method for Additive White Gaussian Noise channels will no longer be applicable. This paper presents a channel capacity estimation method for dynamic plasma sheath. First, the plasma sheath is equivalent to a discrete input continuous output memoryless channel, and then the channel capacity expression is derived according to Shannon formula. Finally, the channel capacity of the dynamic plasma sheath is estimated by calculating the transition probability density function. The simulation results show that the channel capacity of the dynamic plasma sheath is affected by both the signal-to-noise ratio (SNR) and the dynamic parameters of the plasma sheath. When the electron density is small, the channel capacity is mainly affected by the SNR. As the electron density increases, the dynamic parameters of the plasma sheath gradually become the main factor affecting the channel capacity. This method is a theoretical analysis of the channel capacity when the channel parameters of the plasma channel are known, and it is meaningful for conducting the work of communication methods design.

Plasma sheaths characterized by electrons with relativistic energies and far from thermodynamic equilibrium are governed by a rich and largely unexplored physics. A reliable kinetic description of relativistic non-equilibrium plasma sheaths—besides its interest from a fundamental point of view—is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Sheath models proposed in the literature adopt either relativistic equilibrium distribution functions or non-relativistic non-equilibrium distribution functions, making it impossible to properly capture the physics involved when both relativistic and non-equilibrium effects are important. Here we tackle this issue by solving the electrostatic Vlasov–Poisson equations with a new class of fully-relativistic distribution functions that can describe non-equilibrium features via a real scalar parameter. After having discussed the general properties of the distribution functions and the resulting plasma sheath model, we establish an approach to investigate the effect of non-equilibrium solely. Then, we apply our approach to describe laser–plasma ion acceleration in the target normal sheath acceleration scheme. Results show how different degrees of non-equilibrium lead to the formation of sheaths with significantly different features, thereby having a relevant impact on the ion acceleration process. We believe that this approach can offer a deeper understanding of relativistic plasma sheaths, opening new perspectives in view of their applications.

The simulation of the electromagnetic wave propagation as well as the antenna performance plays an important role in solving the communication blackout issue. Finite element analysis software package COMSOL multiphysics facilitates the simulation of the electromagnetic wave propagation in the presence of the non-uniform reentry plasma sheath. The 3D simulation model including the realistic antenna structure is established in this paper. The propagation characteristics of electromagnetic waves are analyzed by the observation of the field distributions. The antenna performance is analyzed and evaluated based on the simulation results, such as the S parameter and the Gain of the antenna. The relevant research in this paper can be the foundation to employ the COMSOL to study the interactions between the electromagnetic wave and the reentry plasma sheath.

For the high power pulsed magnetron sputtering (HPPMS), several investigations regarding correlations between plasma and coating properties and the process parameters have been carried out, especially with respect to the HPPMS pulse parameters frequency f and pulse-on-time ton, the power density at the target and the process gas pressure. Another important aspect with respect to industrial coating processes is the substrate bias UB, which is used to accelerate ionized coating forming species to the substrate in order to obtain homogeneous fine columnar coatings. In order to understand this mechanism, the correlation of substrate-oriented plasma properties and the resulting coating properties is important to investigate. For this purpose, the present work focuses on strategies to provide a contribution to quantifiable investigations on the HPPMS plasma properties using substrate bias. These investigations were conducted for a reactive HPPMS (Cr,Al)N process, which was chosen due to the applicability as protective coating for many tool applications. The strategies were developed for the plasma diagnostics optical emission spectroscopy, Langmuir probe and energy resolved mass spectroscopy in an industrial scale coating unit. Using a varying direct current substrate bias with values from UB = 0 V to UB = −250 V, the methods were validated. For example an increasing Debye sheath thickness sD, ion energy distributions and metal-to-ion-flux ratio JM/JG were observed for higher values of UB. These results were correlated with the corresponding coating properties regarding the coating thickness distribution on complex surfaces, the Al/Cr ratio in the coatings, the phase composition, the residual stress and the mechanical properties as well as the coating adhesion to the substrate. Generally, with these correlations it was proven that the methods for the usage of substrate bias during plasma diagnostics are meaningful for an industry-related coating development.

There is a variety of cases in nature when the action–reaction symmetry is broken. In particular, suitable conditions for this are realized in colloidal suspensions and complex plasmas. Since the first theories and simulations of the nonreciprocal effective interactions between microparticles in complex plasmas were published in 1995–1996, there have been hundreds of studies in the theoretical development of this theme. However, despite such a rich theoretical background, one of the important unsolved problems is a direct experimental determination of the nonreciprocal interparticle interaction forces. Here, we studied experimentally in detail the forces of the nonreciprocal effective interaction between microparticles suspended a radio-frequency produced plasma sheath. For this purpose, an experimental method based on an analysis of the spectral density of random processes in an open dissipative two-particle system was developed. In contrast to previous investigations, the proposed method takes into account random and dissipative processes in the system, does not require a special design of the experimental setup and any external perturbations, pre-measurements of external fields and any assumptions about the type of interaction. We found that even small charge changes of one particle, caused by its thermal motion in a wake field of another particle, can lead to a significant change in the effective (measurable) interaction between the particles.

After entering the near space, a layer of plasma sheath is formed outside the hypersonic vehicles due to the hightemperature and high-pressure environment. The plasma sheath, which characteristic frequency is similar to microwave, will cause serious impediment to communication signal. This phenomenon is known as the blackout problem. With the rapid development of aerospace industry, plasma sheath blackout has become an urgent problem to be solved. Current research shows that increasing the frequency of electromagnetic wave higher than the plasma characteristic frequency can effectively reduce the shielding effect of plasma. The frequency of terahertz (THz) wave is much higher than microwave, it can propagate through plasma sheath, which provides an effective method to solve the problem of plasma sheath. In this paper, a theoretical model of plasma is established, and the transmission properties of THz wave in plasma is simulated using scattering matrix method. Then a kind of plasma jet is produced in laboratory environment according to dielectric barrier discharge. And the experiments of a broadband THz source and THz time-domain spectrum transmission in this kind of plasma and a 2.52 THz wave reflection imaging of target under plasma shelter are carried out respectively. The transmittance increases with frequency under 0.5 THz and becomes stable at 100% over 0.5 THz, and the result of experiments and simulation are in good agreement. Both theory and experiments show that THz wave has good penetration in plasma jet and can detect targets behind plasma, and this study will lay a theoretical foundation for solving the plasma blackout problem of hypersonic vehicle in near space.

International audience

Air ionization and heat shield ablation generate a plasma sheath around vehicles during hypersonic reentry or entry. Terahertz (THz) waves (0.1–10 THz) are much easier than millimeter waves to propagate through plasma with electron density up to 1024 m–3. The Finite Difference Time Domain (FDTD) methods have been successfully applied to many electromagnetic (EM) problems, including issues in plasma for its accuracy. In this paper, FDTD method is used to analyze the terahertz wave propagation in time-varying plasma. The current density in plasma is assumed to be located at the center of the Yee cube. Finally, the FDTD equations for the current density are derived from Maxwell's equations and constitutive relation. In the simulation, a time-varying and spatially inhomogeneous plasma is considered. The electron number density profile of the plasma is assumed to be the linear profile. The plasma is divided into a series of layers. The electron density in each layer varies with time in different forms. The power attenuation characteristic of different time-varying forms are calculated with FDTD method. The overall power attenuation with time are analyzed for different plasma and signal parameters, such as the electron density, the collision frequency, the signal frequency and so on. Using FDTD method, other kinds of plasma, such as magnetized plasma and thermal plasma. Therefore, simulations of scattering characteristics of complex equipment in dynamic and inhomogeneous plasma will be meaningful work in the future.

Three dimensional high-order discontinuous Galerkin time domain (DGTD) method is proposed to solve electromagnetic problems of dispersive media, which utilizes hierarchical basis function in space domain and Rung-Kutta iteration in time domain. The presented method is applied into the analysis of scattering problems of hypersonic aircraft which is coated with plasma. The hypersonic aircraft includes blunt cone model, missile model and metal warhead model. It is observed that high-order DGTD method reduces the number of unknowns greatly and accelerates the convergence against low-order DGTD. Numerical results are given to demonstrate the accuracy, efficiency, and compatibility of the presented method.

A constant mean free path collisional plasma sheath model is investigated in the presence of two-temperature q-nonextensive electrons and fluid ions. By using Sagdeev potential technique, a modified Bohm sheath criterion is derived and also verified. It is shown that the density distribution of positive ions reduces monotonically when the Bohm velocity lies between the derived limits. The effect of collision on the plasma sheath profiles viz. density, potential, net space charge density and positive ion velocity in the sheath in presence of the proposed plasma configuration is investigated. It is also shown that the increasing values of ion-neutral collisionality leads to a decrease of sheath thickness, increase of sheath potential and net space charge density in the sheath region.

During hypersonic flights of a space vehicle, shock heating ionizes the molecules of the surrounding air, which will create a plasma sheath that covers all or part of the vehicle. The plasma sheath absorbs and reflects electromagnetic (EM) waves, resulting in communication blackout of the installed electronic devices or systems. Moreover, when a high-power microwave (HPM) illuminates the moving vehicle, the constituent parameters of the plasma sheath will be altered since the plasma covering absorbs part of the energy of the HPM. In consequence, the transmission and scattering properties of the high-speed vehicle to the EM communication signals are changed. In order to investigate the complicated interactions among the plasma sheath, the HPM, and the low-power communication EM signals, a multiphysics model based on the computational fluid dynamics and the computational EMs is proposed, and the corresponding numerical solution is provided as well. Since the primary aim of the paper is to reveal the multiphysics method and relevant phenomenon, both the theoretical derivations and numerical examples are only presented in the 2-D space.

The effects of plasma sheath on communication signals are not only power attenuation but also multiplicative noise addition because of the sheath's instability. The fluctuation properties of time-varying electron density are crucial to comprehensively understand the blackout problem. In this paper, the fluctuation laws of time-varying electron density are first comprehensively revealed in space–time–frequency domain. A layered fluctuation model of time-varying electron density is then proposed based on these fluctuation laws. The effects of dynamic plasma sheath on electromagnetic (EM) waves at Ka band are calculated by Monte Carlo quasistatic EM numerical method. Results show that the amplitude and phase of time-varying transmission coefficient both follow Gaussian distribution, whereas the spectrum curves follow a bi-Gauss function because of the effect of second mode instability in the hypersonic boundary layer. Furthermore, the means of amplitudes increase with the increasing of the incident EM wave frequency and the decreasing of the peak electron density, while the standard deviations decrease with the increasing of incident EM wave frequency, the decreasing of the peak electron density and the decreasing of electron density standard deviation.

Dynamic plasma sheath can lead to the communication interruption because of its severe impact on the electromagnetic waves. Existing studies mainly focused on the numerical analysis, either regarding the specific experimental results or regarding the computational modeling of the plasma sheath channel, without theoretical and quantitative analysis of the communication performance. In this paper, the bit error rate and the outage probability with $m$ -ary frequency shift keying modulation are derived theoretically based on the hidden Markov model of plasma sheath channels. Specifically, since the outage probability can be viewed as the probability of an interruption in the communication system, it can reflect the intensity of the channel dynamics. Therefore, we analyze the effect of channel model parameters on the outage probability and propose a dynamic criterion calculation formula to model the dynamic of the plasma sheath channel. Finally, simulation results are carried out to reveal a positive correlation between the dynamic criterion and the outage probability, which shows that the dynamic criterion calculation formula can accurately illustrate the dynamic of the plasma sheath channel and the communication performance.

The generation of ion-acoustic solitary waves is investigated in a nonuniform multicomponent collisional plasma sheath containing cold ions and Boltzmann electrons to probe the formation and physics of modulation of nonlinear ion-acoustic waves. The new model for the plasma is adapted to include the effects of ion production-loss and momentum loss terms due to ion-neutral collisions, and implementation related to space and laboratory plasma applications are discussed. The discrete modes, the instability conditions and the growth rate of the streaming instability with the effect of the present plasma parameters are calculated based on the approximate but yet precise complex dispersion relation. The marginal stability curve, characterized by mode bifurcation, cutoff, and complex fold point, indicates a growth rate of a few percents of effective plasma frequency. The damping of ion-acoustic is affected by heavy neutrals, and its maximum rate found near the ion-neutral collision frequency. The variable-coefficient Korteweg-de Vries equation is derived via reductive perturbation method to govern the dynamics of small- as well as large-amplitude solitons. It is found that the propagating nonlinear coherent structures through the created ion phase-space vortices lead to ion trapping and acceleration, and the modulation of ion-acoustic instabilities in the turbulent region. The effect of ion streaming motion on the driven solitons and modulation instability for the variable-coefficient Korteweg-de Vries equation is numerically investigated in detail. The theoretical results can be applied to the observation of electrostatic waves in space plasmas, in industrial pair-ion plasmas as well as in laboratory dusty plasmas.

In this paper, we propose an improved scattering-matrix method (ISMM) to deal with the propagation of electromagnetic (EM) wave in plasma. As a stratification-based method, the ISMM is based on the scattering-matrix method (SMM) and thus inherits the advantages of the SMM in accuracy and high efficiency. But different from the SMM, the ISMM improves the scattering matrices by adjusting the reference point for each layer interface, making the matrices more robust in calculation. This improvement enhances the robustness of the method in dealing with various media situations, especially for the case of a metal as the floor layer and that of extreme plasmas, which is a weakness for the SMM. After presenting the ISMM, we use it to analyze the EM wave reflected by a reentry plasma sheath, which is an important field but with few new results. With the study of various plasma parameters of the reentry plasma sheath, the ISMM is applied to reveal the characteristics of the sheath. In simulations, the validity of the ISMM is first demonstrated, and then the reflection, transmission, and absorption properties of the EM wave propagating in the plasma sheath are studied by the ISMM. The phenomena of “sunken regions” and “phase jumps” of the plasma sheath are revealed in simulations, which may cause energy loss and distortion of the EM wave.

The blackout problem caused by plasma sheath is a serious obstacle to the communication system of hypersonic vehicles. The uplink relay transmission method is an effective means of mitigating serious attenuation caused by plasma sheath. This paper proposes a Ka-band $2\times2$ dual-polarization multiple-input multiple-output (MIMO) scheme by adopting a left-/right-hand circular polarized antenna to increase channel capacity and signal quality. The relay dual-polarized MIMO channel model between the hypersonic vehicle and satellite is established by emphasizing the plasma sheath effect, especially the cross-polar coupling and polar correlation under plasma sheath. Useful numerical results on the relay dual-polarized MIMO ergodic channel capacity are analyzed. Thus, significant capacity gains with respect to the conventional single-input single-output case are illustrated based on this analysis. Simulation results show that the relay dual-polarized MIMO method can increase the channel ergodic capacity by 1.9–2 times under most circumstances, and the angle between the selected relay satellite and the vehicle normal direction should be minimal. This statistical channel model can be applied to the wireless communication system design and evaluation for hypersonic vehicles.

The effects of polarized Debye sheath (i.e., polarization force) and trapped ions on the nonlinear propagation of dust-acoustic (DA) waves are investigated, including the dust inhomogeneity in the strongly coupled dusty plasma. Dispersion relation and propagation of possible modes are calculated from the underlying usual hydrodynamic model. Then, a variable coefficient’s modified Korteweg-de Vries equation describing the dynamics of DA solitary waves is derived from a weakly nonlinear analysis, and is solved to get the stationary solutions using a sine–cosine method. It is found that for experimental conditions under which the interaction of resonant ions and highly negatively charged dust grains is important, only soliton with negative potential can propagate in such a strongly coupled inhomogeneous dusty plasma. In the presence of trapped ions, the amplitude of solitary waves is found to be smaller compared with that for the Boltzmann distribution. Moreover, it is argued that the soliton profile is highly sensitive to the effects of modified strength of the polarization force, dust temperature, and dust density inhomogeneity.

A plasma sheath is formed on the surface of high speed spacecrafts when they return to atmosphere, which leads to electromagnetic waves be reflected, absorbed, and finally the intensity decreases. In this paper, the hyperbolic electron number density distribution model is established firstly. Then, the power reflection coefficient, power absorption coefficient and the power transmission coefficient of this model is derived by the analytic method. Finally, this study mainly focuses on the comparison of the analytic method and Wentzel-Kramer-Brillouin (WKB) method about their applicability and limitations, by discussing the electromagnetic wave power transmission coefficient of one-dimensional case. In short, the related research can provide a theoretical reference for the spacecraft to overcome the “blackout” effect of communication.

The characteristics of sheath in a plasma system containing q-nonextensive electrons, cold fluid ions, and Boltzmann-distributed negative ions are investigated. A modified Bohm sheath criterion is derived by using the Sagdeev pseudopotential technique. It is found that the proposed Bohm velocity depends on the degree of nonextensivity (q), negative ion temperature to nonextensive electron temperature ratio (σ), and negative ion density (B). Using the modified Bohm sheath criterion, the sheath characteristics, such as the spatial distribution of the potential, positive ion velocity, and density profile, have been numerically investigated, which clearly shows the effect of negative ions, as well as the nonextensive distribution of electrons. It is found that, as the nonextensivity parameter and the electronegativity increases, the electrostatic sheath potential increases sharply and the sheath width decreases.

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert., Comment: 59 pages, 17 figures

Physical vapor deposited (PVD) coatings are widely-used in tool and component applications, where the predominant aims are the enhancement of the lifetime and an improvement of the economic efficiency. The achievement of these aims amongst others strongly depends on a homogeneous distribution of the coating properties with respect to the entire functional surface, in particular on complex-shaped tools. In order to obtain a sufficient coating homogeneity, pulsed high power plasma processes such as the high power pulsed magnetron sputtering (HPPMS) or the pulsed cathodic arc evaporation (PCAE) has to be chosen. In order to characterize the influence of both technologies on the coating homogeneity, the Debye sheath thickness sD at the substrate side was determined, which is expected to strongly correlate with the coating homogeneity on complex surfaces, since it is a measure for the shielding of charged coating atoms. Measurements with varying pulse parameters were performed. In addition, as reference a direct current magnetron sputtering (dcMS) and cathodic arc evaporation (CAE) process were conducted, respectively. As it is widely used as protective coating for tools in many applications, the coating system (Cr,Al)N was chosen. In the first step, the Debye sheath thickness was determined by means of Langmuir probe. A Debye sheath thickness from sD = 430 μm to sD = 48 μm was found for the different processes and parameters. In the second step, the (Cr,Al)N coatings were deposited with selected process parameters on structured tungsten carbide substrates. The coating morphology, coating thickness, surface roughness and chemical composition were observed to be more homogeneous for processes with a lower Debye sheath thickness. The best results were obtained for the HPPMS and PCAE technology. In summary, processes and parameters were identified which can be used for the coating of complex structured tools.

The time-varying plasma sheath surrounding a reentry spacecraft (or object) can influence the radar detection of the spacecraft seriously, causing detection error or even track loss. To study the influence of plasma sheath on radar detection, a time-varying plasma sheath model based on scattering matrix method is constructed. In the model, the surface media of reentry object is considered, together with some algorithm adjustments to avoid computational singularity, and the time-varying characteristics of plasma sheath are taken into account based on available measured data. By the model, the reflection coefficient of plasma sheath and the radar echo reflected by plasma-covered object are both calculated. And then a processing method of time-varying echo signal based on ambiguity function are put forward, by which the time delay and Doppler frequency of echo signal are analyzed. In the simulation, the rules of a series of time-varying parameters of plasma affecting the reflection coefficient are analyzed. Then, by ambiguity function analysis, the influence rules of plasma sheath on radar echo are revealed, accompanied by some qualitative and quantitative results. The proposed model, method, and simulation results are thought to be helpful for the radar detection of plasma-covered reentry objects.

Time-varying plasma sheath likely causes parasitic amplitude and phase modulation effects on communication signals. It can increase the carrier tracking error of tracking telemetry and command systems for hypersonic vehicles flying in near space, and it may lead to loss of lock under serious conditions. This paper comprehensively analyzes the influence mechanism of the amplitude modulation effects on the loss threshold of Type3-phase-locked loop (PLL) in phase-locked receivers. Analysis result shows that amplitude fading in time-varying plasma sheaths is similar to the Gaussian distribution unrelated to the fluctuant densities. The standard deviation of amplitude fading increases with the fluctuant intensity. The 8% fluctuant intensity of electron density begins to have a significant impact on the lock probability of Type3-PLL. On the basis of the analysis results and the amplitude modulation effects, Type3-PLL with a prefiltering (PF-Type3-PLL) method is proposed to mitigate the amplitude modulation effects. PF is placed before the discriminators of Type3-PLL to restrict the amplitude variation within a reasonable range. The tracking loop PF-Type3-PLL is tested with spatial–temporal fluctuant plasma sheath model and compared with the traditional Type3-PLL. Tracking results show that PF-Type3-PLL is more robust than the traditional Type3-PLL. The phase error jitter is significantly reduced when the fluctuant intensity is 8%, and the loss threshold is reduced by 4 dB. The robustness is also enhanced under different loop noise bandwidths (5–15 Hz).

In this work a two-dimensional, axisymmetric plasma sheath model is presented that is used to predict ion trajectory deviations in the plasma-wafer interface for a given set of physical etch conditions and chamber geometries. The model successfully predicts the plasma sheath deformation and the associated ion tilt in the vicinity of the wafer edge due to electrical discontinuities. We couple the predictive power of the plasma sheath model with a feature-scale kinetic Monte Carlo etch model to determine the asymmetries in post-etched structures and hence on-product overlay. The feature-scale model serves as a tool to translate the ion tilt within plasma sheath to the sidewall angle asymmetries in the etched trenches and the resulting overlay errors in two adjacent layers of a semiconductor device that could ultimately affect the device yield.

Reentry plasma sheath diagnostic plays extremely important roles in the research of the blackout problem. In this paper, a broadband microwave reflectometer based on the invariant point of reflection data has been designed and developed for the reentry plasma sheath diagnostic. The invariant point Y(ωp, 1) is derivable from the broadband reflection data. The electron density and collision frequency are measured simultaneously. The diagnostic algorithm was verified by the simulation analysis and diagnostic experiment. The algorithm has low computational complexity and relatively high precision. This algorithm offers a certain reference value for the plasma sheath diagnostic of reentry vehicles or hypersonic vehicles in the future. Especially, the design of broadband VVD antenna with heat-resistant wave-transparent composites has certain practical values.

Terahertz waves have long been considered as the most efficient of many solutions to solve the blackout problem for the reason that terahertz waves have much stronger penetration than microwaves. In this paper, we will raise the incident wave band to terahertz band to discuss the application of terahertz technology in solving blackout problem. The plasma sheath attached to the reentry is considered as steady-state parabolic distribution. The back scattering radar cross section is used as an index to illustrate the strong penetration of terahertz wave, which is calculated with the Runge-Kutta Exponential Time Differencing-Finite Difference Time Domain method. The attenuation of electromagnetic wave in uniform plasma is analyzed with Wentzel-Kramer-Brillouin method. Moreover, the variation of different parameters of homogeneous and inhomogeneous plasma including the plasma density, the thickness of plasma and collision frequency, is also studied in this paper. It can be concluded that all the calculations of back scattering radar cross section reveals that terahertz wave have a powerful potential to cope with blackout problem and can be widely applied in the field of communication.

In a high power pulsed magnetron sputtering (HPPMS) process a substrate bias is applied to affect the ions in the coating chamber and therefore the coating properties. For this reason the present experiments on an industrial scale coating unit are focusing on the identification of correlations between plasma and coating properties for a CrAlN process while using a pulsed substrate bias. The measurements regarding the plasma properties were carried out on the substrate side for a better understanding of the interaction of plasma and coating properties. These investigations should point out the significant potential of plasma diagnostics for measuring plasma properties to contribute to improved coating processes using pulsed substrate bias UB,p. For this purpose a substrate bias synchronized to the HPPMS pulse is used since the pulsed bias can influence ions of a specific species. It was found that the even low values of a pulsed substrate bias lead to high values of the Debye sheath thickness and thus to a shielding of opposite surfaces. For complex shaped substrates like cemented carbide cutting inserts a better coatability for pulsed substrate bias up to UB,p = -150 V was reached. Also increased values of the mean ion energy and the ion flux density were found compared to the use of a continuous substrate bias. Regarding the chemical composition a significant higher nitrogen content of the coatings was found when using a pulsed substrate bias compared to the use of a continuous substrate bias. Comparing the indentation hardness of a process using a pulsed substrate bias increased hardness values were found compared to the use of a continuous substrate bias. Generally, a significant change of both, plasma and coating properties was found when changing the mode of substrate bias.

In this paper, a linear distribution model, a double exponential distribution model and a hyperbolic number distribution model are developed, and the effect of dust particle size distribution on its attenuation coefficient is considered. On this basis, the transmission characteristics of electromagnetic waves in dusty plasma under different electron density distribution models are investigated. The attenuation coefficients of electromagnetic waves are derived in detail using analytical methods, and the effects of electromagnetic wave frequency, particle collision frequency and dust particle density on the transmission characteristics of electromagnetic waves are discussed. The results show that the choice of terahertz wave as the carrier wave and the appropriate change of particle collision frequency can improve the attenuation of electromagnetic waves. In summary, the relevant research can provide some theoretical references for propagation science.

Dust particles generated from the thermal protection layer greatly influence the propagation of electromagnetic (EM) waves in the plasma sheath. This paper presents the first calculation of the effects of these dust particles on microstrip antenna radiation. On the basis of an integrated model of the ablation plasma sheath and C-band microstrip antenna, the ray tracing method is used to obtain the disturbed electric field in a traditional plasma and a dusty plasma (with different dust parameters). The results show that the dust particles cause greater attenuation of incident waves, and different dust parameters have different effects on the penetrating electric field. This study reveals that the ablation of the thermal protection layer changes the electromagnetic properties of the plasma sheath, and the generated dust particles should not be ignored in the electromagnetic computation.

We have studied the effects of the magnetic field on the active electronegative plasma sheath properties and dust charging process in the sheath region for two different collisional models: constant ion mean free path and constant ion mobility using 1d3v fluid hydrodynamics model. It is found that the magnetic field strength and choice of collisional models have a significant effect on the active plasma sheath characteristics and charging of an isolated dust grain. The sheath criterion for an active electronegative magnetized plasma for both collisional models has been extended, and the effects of neutral gas pressure, source frequency, obliqueness of magnetic field, and initial electric field at sheath edge are graphically illustrated. There are two distinct regions observed in the sheath region: magnetic field and electric field dominant regions. The spatial distribution of plasma sheath parameters is systematically presented. It is found that the evolution of dust surface potential is affected by the magnitude of the magnetic field and collisional models. The stable levitation of dust grains in the sheath region is close to the sheath entrance. Moreover, the total force experienced by an isolated dust grain in the sheath region rapidly increases close to the material surface, and the magnitude of force is higher for larger dust grain.