Nonuniform Plasma Research Articles

Thomson scattering in inhomogeneous plasmas: The Role of the Fluctuation-Dissipation Theorem

A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a non-uniform plasma is derived. We draw the readers’ attention to the inconsistency in recent results on the Thomson scattering in inhomogeneous plasma, which leads to violation of the Fluctuation-Dissipation Theorem. We show, that not only the imaginary part, but also the derivatives of the real part of the dielectric susceptibility determine the amplitude and the width of the Thomson scattering spectral lines. As a result of inhomogeneity, these properties become asymmetric with respect to inversion of the sign of the frequency. A method is proposed for measuring local gradients of the electron density with the aid of Thomson scattering.Arising from: P. Kozlowski, et al. Sci. Rep. 6, 24283 (2016); https://doi.org/10.1038/srep24283.

Evolution of ion–ion acoustic instability in multi-ion plasma sheaths

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.

Sausage oscillations in a plasma cylinder with a surface current

Linear sausage oscillations of a cylinder embedded in a plasma with an azimuthal magnetic field, created by a current on the surface of the cylinder, are studied. Such a plasma configuration could be applied to modelling flaring loops, and magnetic ropes in coronal mass ejections. The plasma is assumed to be cold everywhere. Dispersion relations demonstrate that the lowest radial harmonic of the sausage mode is in the trapped regime for all values of the parallel wave number. In the long-wavelength limit, phase and group speeds of this mode are equal to the Alfvén speed in the external medium. It makes the oscillation period to be determined by the ratio of the parallel wavelength, e.g. double the length of an oscillating loop, to the external Alfvén speed, allowing for its seismological estimations. The application of the results obtained to the interpretation of long-period (longer than a minute) oscillations of emission intensity detected in solar coronal structures, gives reasonable estimations of the external Alfvén speed. Cutoff values of the parallel wavenumber for higher radial harmonics are determined analytically. Implications of this finding to the observational signatures of fast magnetoacoustic wave trains guided by cylindrical plasma non-uniformities are discussed.

Theory of Thomson scattering in inhomogeneous plasmas.

A self-consistent kinetic theory of Thomson scattering of an electromagnetic field by a nonuniform plasma is derived. We show that not only the imaginary part, but also the time and space derivatives of the real part of the dielectric susceptibility determine the amplitude and the width of the Thomson scattering spectral lines. As a result of inhomogeneity, these properties become asymmetric with respect to inversion of the sign of the frequency. Our theory provides a method of a remote probing and measurement of electron density gradients in plasma; this is based on the demonstrated asymmetry of the Thomson scattering lines.

Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source

It is well known that the plasma non-uniformity caused by the standing wave effect has brought about great challenges for plasma material processing. To improve the plasma uniformity, a low-frequency (LF) power source is introduced into a 100 MHz very-high-frequency (VHF) capacitively coupled argon plasma reactor. The effect of the LF parameters (LF voltage amplitude ϕL and LF source fL) on the radial profile of plasma density has been investigated by utilizing a hairpin probe. The result at a low pressure (1 Pa) is compared to the one obtained by a 2D fluid-analytical capacitively coupled plasma model, showing good agreement in the plasma density radial profile. The experimental results show that the plasma density profile exhibits different dependences on ϕL and fL at different gas pressures/electrode driven types (i.e., the two rf sources are applied on one electrode (case I) and separate electrodes (case II)). At low pressures (e.g., 8 Pa), the pronounced standing wave effect revealed in a VHF discharge can be suppressed at a relatively high ϕL or a low fL in case I, because the HF sheath heating is largely weakened due to strong modulation by the LF source. By contrast, ϕL and fL play insignificant roles in suppressing the standing wave effect in case II. At high pressures (e.g., 20 Pa), the opposite is true. The plasma density radial profile is more sensitive to ϕL and fL in case II than in case I. In case II, the standing wave effect is surprisingly enhanced with increasing ϕL at higher pressures; however, the center-high density profile caused by the standing wave effect can be compensated by increasing fL due to the enhanced electrostatic edge effect dominated by the LF source. In contrast, the density radial profile shows a much weaker dependence on ϕL and fL in case I at higher pressures. To understand the different roles of ϕL and fL, the electron excitation dynamics in each case are analyzed based on the measured spatio-temporal distributions of the electron-impact excitation rate by phase resolved optical emission spectroscopy.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Cylindrical Plasma Antenna with Large Longitudinal Density Irregularity

The efficiency of operation of a cylindrical plasma antenna as a function of the degree of longitudinal nonuniformity of the plasma density is examined. The study is based on the method of spectral field expansion into a complete set of functions comprising surface and pseudosurface waves of the plasma column. The system of integrodifferential equations for expansion coefficients determining radiation patterns and the amplitudes of transmitted, reflected, and scattered waves is solved in the case of rapid variation in the plasma density. Dependences of the coefficients of conversion of the surface-wave energy on the plasma-density gradient, the electric length of the section of plasma nonuniformity, and the electric radius of the plasma cylinder are calculated. It is demonstrated by examples that the portion of energy of the surface wave converted into radiation may exceed 50%. It has been found that the radiation patterns are narrow with a single lobe whose maximum is at an angle of several degrees to the direction of propagation of the surface wave. As the plasma-density gradient increases, the lobe width decreases and the lobe itself shifts toward 0°.

Study of plasma-based stable and ultra-wideband electromagnetic wave absorption for stealth application

A plasma-based stable, ultra-wideband electromagnetic (EM) wave absorber structure is studied in this paper for stealth applications. The stability is maintained by a multi-layer structure with several plasma layers and dielectric layers distributed alternately. The plasma in each plasma layer is designed to be uniform, whereas it has a discrete nonuniform distribution from the overall view of the structure. The nonuniform distribution of the plasma is the key to obtaining ultra-wideband wave absorption. A discrete Epstein distribution model is put forward to constrain the nonuniform electron density of the plasma layers, by which the wave absorption range is extended to the ultra-wideband. Then, the scattering matrix method (SMM) is employed to analyze the electromagnetic reflection and absorption of the absorber structure. In the simulation, the validation of the proposed structure and model in ultra-wideband EM wave absorption is first illustrated by comparing the nonuniform plasma model with the uniform case. Then, the influence of various parameters on the EM wave reflection of the plasma are simulated and analyzed in detail, verifying the EM wave absorption performance of the absorber. The proposed structure and model are expected to be superior in some realistic applications, such as supersonic aircraft.

Compressive and rarefactive double layers in non-uniform plasma with q $q$ -nonextensive distributed electrons

Electrostatic solitary waves and double layers (DLs) formed by the coupled ion acoustic (IA) and drift waves have been investigated in non-uniform plasma using \(q\)-nonextensive distribution function for the electrons and assuming ions to be cold \(T_{i}< T_{e}\). It is found that both compressive and rarefactive nonlinear structures (solitary waves and DLs) are possible in such a system. The steeper gradients are supportive for compressive solitary (and double layers) and destructive for rarefactive ones. The \(q\)-nonextensivity parameter \(q\) and the magnitudes of gradient scale lengths of density and temperature have significant effects on the amplitude of the double layers (and double layers) as well as on the speed of these structures. This theoretical model is general which has been applied here to the \(F\)-region ionosphere for illustration.

Existence regimes for shocks in inhomogeneous magneto-plasmas having entropy

The finding of connection of plasma density and temperature with entropy gives an incitement to study different plasma models with respect to entropy. Nonlinear dissipative one- and two-dimensional structures (shocks) are investigated in nonuniform magnetized plasma with respect to entropy. The dissipation comes in the medium through ion-neutral collisions. The linear dispersion relation is derived. The Korteweg–deVries-Burgers and Kadomtsev-Petviashvili-Burgers equations are derived for nonlinear drift waves in 1-D and 2-D by employing the drift approximation. It is found that vd/u (vd is the diamagnetic drift velocity and u is the velocity of nonlinear structure) plays a significant role in the shock formation. It is also found that entropy has a significant effect on the strength of shocks. It is noticed that vd/u determines the rarefactive and compressive nature of the shocks. It is observed that upper and lower bounds exist for the shock velocity. It is also observed that the existing regimes for both one- and two-dimensional shocks for kappa distributed electrons are different from shocks with Cairns distributed electrons. Both rarefactive and compressive shocks are found for the 1-D drift waves with kappa distributed electrons. Interestingly, it is noticed that entropy enhances the strength of one- and two-dimensional shocks.

Numerical calculation of the reflection, absorption and transmission of a nonuniform plasma slab based on FDTD

In this paper, reflection, absorption and transmission characteristics of nonuniform plasma layer with varying electron number density are analyzed. The plasma number density profile is parabolic. Finite-difference time-domain (FDTD) and subslabs approximation methods are utilized and the results are validated. In FDTD, we use auxiliary differential equation (ADE) to simulate the plasma dispersive characteristics. In subslabs method, the plasma layer is divided into several thin subslabs with constant electron number density in each subslab. Partial reflection coefficients at each subslab boundary with different electromagnetic parameters are calculated. The total reflected and transmitted coefficients are then deduced using transmission line method. The reflected, transmitted and absorption power ratio with respect to the incident power is acquired. Their functional dependence on the number density, collision frequency and the distribution of number density, collision frequency is studied.

Relationship between the velocity of hypersonic vehicles and the transmission efficiency of radio waves

ABSTRACTAnalyzing the flow field distributions around a near-space blunt-cone vehicle at different flight speeds, we observe that, when the flight speed exceeds a certain threshold, the relationship between the flow field density and the vehicle speed presents a characteristic opposite to that at the flight condition of the speed lower than the threshold. On this basis, the Runge–Kutta method is applied to solve the ray equations in non-uniform plasma, in which the electron density at any computing point is obtained by the Lagrange interpolation based on the discrete data of the flow field. Then the EM wave attenuation in the sheath is determined by the subsection integral method combining with the electromagnetic theory. The numerical results also show that when the flight velocity is lower than the threshold, the energy transfer efficiency of the EM waves decreases with the increase of the vehicle velocity. However, when the flight speed is greater than the threshold, the energy transfer efficiency increases as the vehicle speed increases. This conclusion will be helpful to further understand the EM wave propagation characteristics for hypersonic vehicles, and to provide a reference for the channel selection of antennas.

Study on the attenuation characteristic of terahertz wave through a non-uniform magnetized plasma

In this paper, the interaction between terahertz wave and a non-uniform magnetized plasma slab is investigated. The electric field distribution in non-uniform plasma is presented and used to calculate the attenuation of the electromagnetic wave through plasma. Several types of electron density profiles are proposed and discussed. Effects of different plasma parameters (electron density, collision frequency, plasma thickness) and magnetic field amplitudes on THz wave attenuation characteristic are investigated. The transmission ratios at several typical THz signal frequencies in both unmagnetized and magnetized plasma are presented as well. These simulation results are meaningful for the flight communication.

Plasma non-uniformity in a symmetric radiofrequency capacitively-coupled reactor with dielectric side-wall: a two dimensional particle-in-cell/Monte Carlo collision simulation

A Cartesian-coordinate two-dimensional electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) plasma simulation code is presented, including a new treatment of charge balance at dielectric boundaries. It is used to simulate an Ar plasma in a symmetric radiofrequency capacitively-coupled parallel-plate reactor with a thick (3.5 cm) dielectric side-wall. The reactor size (12 cm electrode width, 2.5 cm electrode spacing) and frequency (15 MHz) are such that electromagnetic effects can be ignored. The dielectric side-wall effectively shields the plasma from the enhanced electric field at the powered-grounded electrode junction, which has previously been shown to produce locally enhanced plasma density (Dalvie et al 1993 Appl. Phys. Lett. 62 3207–9; Overzet and Hopkins 1993 Appl. Phys. Lett. 63 2484–6; Boeuf and Pitchford 1995 Phys. Rev. E 51 1376–90). Nevertheless, enhanced electron heating is observed in a region adjacent to the dielectric boundary, leading to maxima in ionization rate, plasma density and ion flux to the electrodes in this region, and not at the reactor centre as would otherwise be expected. The axially-integrated electron power deposition peaks closer to the dielectric edge than the electron density. The electron heating components are derived from the PIC/MCC simulations and show that this enhanced electron heating results from increased Ohmic heating in the axial direction as the electron density decreases towards the side-wall. We investigated the validity of different analytical formulas to estimate the Ohmic heating by comparing them to the PIC results. The widespread assumption that a time-averaged momentum transfer frequency, vm, can be used to estimate the momentum change can cause large errors, since it neglects both phase and amplitude information. Furthermore, the classical relationship between the total electron current and the electric field must be used with caution, particularly close to the dielectric edge where the (neglected) pressure gradient term becomes significant.

Multi‐level model of radiation transport in inhomogeneous plasma

Radiation transport in plasma can be important for a number of problems, for example, first wall‐shielding effects or influence of hydrogen isotope radiation on tokamak edge plasma. Existing calculations in the field employ many simplifying assumptions. For example, the model of radiation transport in one of the most used codes, SOLPS, suggests that photoexcitation can be ignored for all transitions, not including the ground level. We develop a collisional radiative model of radiation transport in a multi‐level system, fully accounting for all transitions between levels. The role of the Stark effect in line shape is taken into account. The validity of some of the approximations made in SOLPS is analysed for detached divertor plasma in DIII‐D‐like tokamak geometry. It is shown that total radiation flux is directed away from the divertor target due to nonuniform plasma temperature and density.

Phase transitions in local equation-of-state approximation and anomalies of spatial charge profiles in non-uniform plasma

Impressive appearance of discontinuities in equilibrium spatial charge profiles in non-uniform Coulomb systems is under discussions in wide number of thermoelectrostatics problems. Such discontinuities are considered as peculiar micro-level manifestation of phase transitions and intrinsic macro-level non-ideality effects in local equation of state (EOS), which should be used for description of non-ideal ionic subsystem in frames of local-density (or “pseudofluid”, or “jellium” etc) approximation. Such discontinuities were discussed already by the authors for electronic subsystems. Special emphasis is made in present paper on the mentioned above non-ideality effects in non-uniform ionic subsystems, such as micro-ions profile within screening “cloud” around macro-ion in complex (dusty, colloid etc) plasmas, equilibrium charge profile in ionic traps or (and) in the neighborhood vicinity of “charged wall” etc). Multiphase EOS for simplified ionic model of classical charged hard spheres on uniformly compressible electrostatic compensating background was constructed and several illustrative examples of discussed discontinuous ionic profiles were calculated.

On drift wave instabilities excited by strong plasma gradients in toroidal plasmas

Motivated by the recent global gyrokinetic simulations of electrostatic drift-wave instabilities in the strong plasma gradient region of toroidal plasmas [Fulton et al., Phys. Plasmas 21, 042110 (2014); Xie et al., Phys. Rev. Lett. 118, 095001 (2017); Xie and Xiao, Phys. Plasmas 22, 090703 (2015)], we have carried out the corresponding analytical and numerical investigations in the case of ion temperature gradient driven modes. It is shown that, for sufficiently strong plasma gradients, the eigenmodes are slab-like and predominantly bounded by the plasma non-uniformities. Our results are qualitatively consistent with the simulation observations.

Propagation of microwave radiation through an inhomogeneous plasma layer in a magnetic field

The problem of reliable microwave communication through a plasma sheath has its origin from the beginning of space flights. During reentry of spacecraft, the plasma layer can interrupt the communication. At sufficiently high plasma density, the plasma layer either reflects or attenuates radio wave communications to and from the vehicle. In this work, we present a simple analytical one-dimensional algorithm to study the propagation of electromagnetic (EM) waves through a nonuniform plasma layer in a static nonuniform magnetic field. The experimental study of the EM wave transmission and reflection through plasma layer was carried out on the (i) microwave set and (ii) on the unit using a high-voltage pulsed discharge.

Effects of magnetized plasma on the propagation properties of obliquely incident THz waves

In this paper, the propagation of obliquely incident terahertz (THz) wave in a non-uniform magnetized plasma slab is investigated. The electron density and the collision frequency across the plasma are assumed to have a Gaussian profile. To deal with the non-uniform profile, the plasma slab is divided into a series of subslabs. For more accuracy, twice reflection between the interfaces of each subslab is considered, and the corresponding transmitted and reflected power are derived. Effects of collision frequency, magnetic field amplitude and incident angle on THz wave propagation characteristics are investigated. Specifically, the refraction angles in each subslab are presented. These simulation results are meaningful for the hypersonic flight communication.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

In this paper, we address the theoretical resolution of the Vlasov–Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov–Arnold–Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.