Numerical Modeling of Electromagnetic Wave Transmission Through a 2-D Magnetized Plasma Sheath

“Communication blackout” is such a consequence that the attenuation of electro-magnetic (EM) waves becomes drastic when the frequency of EM waves is near or below the oscillation frequency of plasmas. Deep comprehension on the propagation characteristics of EM waves in the plasma sheath plays an important role in solving this issue. However, relevant works in the literature are almost based on the cold plasma sheath model, neglecting the temperature of the plasmas as well as the spatial dispersion effect. We apply COMSOL Multiphysics software to simulate and study the spatial dispersion effect in the warm plasma sheath in this paper. The mode conversion between EM waves and Langmuir waves in the warm plasmas is observed. The characteristics of field distributions in the warm plasma sheath are different from the cold plasma sheath distinctly, when the resonance between EM waves and the plasmas happens. The reflection and absorption coefficients are also influenced accordingly. The research in this paper gives an insight into EM waves propagation in the warm re-entry plasma sheath and supplies a better comprehension on the interaction between EM waves and the plasma sheath.

There have been many studies on the sub-terahertz (sub-THz) wave transmission in reentry plasma sheaths. However, only some of them have paid attention to the transmission of sub-THz waves in magnetized plasma sheaths. In this paper, the transmission of sub-THz waves in both unmagnetized and magnetized reentry plasma sheaths was investigated. The impacts of temporal evolution of the plasma sheath on the wave transmission were studied. The transmission of “atmospheric window” frequencies in a magnetized plasma sheath was discussed in detail. According to the study, the power transmission rates (Tp) for the left hand circular (LHC) and the right hand circular modes in the magnetized plasma sheath are obviously higher and lower than those in the unmagnetized plasma sheath, respectively. The Tp of LHC mode increases with both wave frequency and external magnetic field strength. Also, the Tp of LHC mode in both magnetized and unmagnetized plasma sheaths varies with time due to the temporal evolution of the plasma sheath. Moreover, the performance of sub-THz waves in magnetized plasma sheath hints at a new approach to the “blackout” problem. The new approach, which is in the capability of modern technology, is to utilize the communication system operating at 140 GHz with an onboard magnet installed near the antenna.

Based on the complex Snell's law of lossy media, a ray tracing method is proposed to study the propagation attenuation characteristics of electromagnetic (EM) waves in plasma sheaths. The plasma sheath is modelled as layered media. This method considers the complex ray characteristics of inhomogeneous plane EM waves, tracks the propagation rays of EM waves in each layer of media, and calculates the propagation attenuation of EM waves in each layer of media according to the propagation direction of the complex rays. The attenuation during numerical cumulative propagation is the total attenuation of EM waves through the plasma sheath. By comparing the results with that obtained from the WKB method, the accuracy of the ray tracing algorithm is proved. The results of the propagation attenuation of a blunt cone model are calculated by the proposed method, and the effects of different parameters on the EM wave propagation attenuation in the plasma sheath are analysed at different heights, velocities, incident angles, and incident positions. Studying the propagation characteristics of EM waves in the plasma sheath is of importance in application for radar target tracking, blackout communication, and other issues.

The effects of ion–neutral collision on the characteristics of a magnetized plasma sheath which consists of two species of positive ions are investigated. It is assumed that the ions have different masses. In contrast to our previous work, the effects of ion–neutral collision frequency are added to the magnetized plasma sheath. Using a three-fluid hydrodynamic model and some dimensionless variables, the dimensionless equations are obtained and solved numerically. By taking into account the ion–neutral collision effects on a magnetized three-component plasma sheath, it is shown that apart from the presence of the second ion species, by increasing the collision frequency of two ions with neutrals, the amplitude of fluctuations of ion species density distributions increases and the position of these fluctuations is shifted towards the plasma sheath edge. Also, by increasing the ion–neutral collision frequency these fluctuations turn off faster than those in a collisionless case. It is shown that in the collisional magnetized plasma sheath, the effects of the presence of the heavier ion species on the lighter ion density turn off much faster in comparison with what happens in a collisionless magnetized plasma sheath. Furthermore, it is found that in a collisionless plasma sheath by increasing the density of the heavier ion species, the normalized electrostatic potential decreases while in a collisional plasma sheath the presence of the heavier ion species does not have any considerable effect on the normalized electrostatic potential. In addition, it is shown that when the distance of each ion species from the plasma sheath boundary becomes larger than five times the electron Debye length (x > 5λDe) the fluctuations of the ion species velocities disappear by increasing the ion–neutral collision frequency. Also, it is found that the electron density distribution decreases by increasing the ion–neutral collision frequency.

The “magnetic window” is considered a promising means to eliminate reentry communication blackout. However, the turbulence of plasma sheath results in phase jitter and amplitude turbulence of electromagnetic (EM) wave and may influence the eliminating effect. Therefore, the effect of fluctuating property of reentry plasma sheath on EM wave propagation when a magnetic field is used for eliminating blackout is investigated. For this purpose, a time-varying electron density model, which includes both temporal variation and spatial turbulence, is proposed. Hybrid matrix method is also employed to investigate the interaction between time-varying magnetized plasma and EM wave. The EM wave transmission coefficients in time-varying magnetized and unmagnetized plasmas are likewise compared. Simulation results show that amplitude variation and phase jitter also exist on transmitted EM wave, and the turbulent deviation increases as the degree of plasma fluctuates. Meanwhile, the fluctuation of transmitted EM wave attenuates at low-frequency passband and increases at high-frequency passband with the increasing magnetic field. That is, comparing with unmagnetized time-varying plasma, the fluctuation effect can be mitigated by using a magnetic field when the EM wave frequency is at low-frequency passband. However, the mitigating effect can be influenced by the nonuniformity of magnetic field.

A high-speed vehicle flying through the atmosphere between 100 and 20 km may suffer from a “communication blackout.” In this paper, a low frequency system with an on-board loop antenna to receive signals is presented as a potential blackout mitigation method. Because the plasma sheath is in the near-field region of the loop antenna, the traditional scattering matrix method that is developed for the far-field region may overestimate the electromagnetic (EM) wave's attenuation. To estimate the EM wave's attenuation in the near-field region, EM interference (EMI) shielding theory is introduced. Experiments are conducted, and the results verify the EMI shielding theory's effectiveness. Simulations are also conducted with different plasma parameters, and the results obtained show that the EM wave's attenuation in the near-field region is far below than that in the far-field region. The EM wave's attenuation increases with the increase in electron density and decreases with the increase in collision frequency. The higher the frequency, the larger is the EM wave's attenuation. During the entire re-entry phase of a RAM-C module, the EM wave's attenuations are below 10 dB for EM waves with a frequency of 1 MHz and below 1 dB for EM waves with a frequency of 100 kHz. Therefore, the low frequency systems (e.g., Loran-C) may provide a way to transmit some key information to high-speed vehicles even during the communication “blackout” period.

The plasma sheath is produced by high-temperature heating during the reentry of a hypersonic vehicle to the Earth atmosphere. Temperature around the vehicle rises rapidly because of severe friction with air. The vehicle temperature behind friction is high enough to excite various real gas effects including chemical reactions of air, which contains ablation particles of vehicle, free electrons, and ions. The plasma sheath greatly affects the transmission of electromagnetic waves and has very strong interference on the communication signals, which results in interrupt between the target and the ground station, namely, blackout. The electron density of plasma sheath surrounding the aircraft is inhomogeneous and varies with time. Temperature and pressure will also change at different altitudes. Therefore, it is meaningful to investigate the propagation characteristics of electromagnetic waves in temporally and spatially inhomogeneous plasma sheath. The temporally and spatially inhomogeneous plasma sheath model is introduced and the electron density data of the National Aeronautics and Space Administration (NASA) reentry vehicle is employed. The relationships among temperature, pressure, and collision frequency are obtained with the empirical formula of collision frequency. Then, the reflection coefficient and transmission coefficient of time-varying single layer plasma are calculated with the shift operator finite-difference time-domain (SO-FDTD) method. These results are compared to verify the correctness of the proposed method. Finally, the LTJEC-FDTD method is used to calculate the reflection coefficient, transmission coefficient and absorptivity at different relaxation time, temperature, and pressure in the terahertz (THz) band. The results show that the higher temperature and pressure will enable the electromagnetic wave to penetrate the plasma sheath at high relaxation time of electron density. If the incident wave frequency is lower than the cut-off frequency of plasma, the reflection of electromagnetic wave will be more obvious. However, when the incident wave frequency is in the THz band, the effects of temperature and pressure on the propagation of electromagnetic wave are obviously weakened. The absorption of electromagnetic wave by plasma will be more obvious when the relaxation time, temperature, and pressure decrease. If the relaxation time of electron density is shorter than or equal to the period of THz wave, more energy of electromagnetic wave will be absorbed by the plasma sheath. Contrarily, if the relaxation time of electron density is much longer than the period of THz wave, the absorption of electromagnetic energy will decrease. This study gives some insight into the temporally and spatially inhomogeneous plasma sheath, and provides a theoretical basis for solving the blackout problem.

Ultra-high frequency (UHF) partial discharge (PD) measurement, i.e., detecting electromagnetic (EM) waves in the UHF range radiated from PD, is an attractive method for diagnoses of power transformers and has recently received much attention. However, the EM waves tend to suffer attenuation while propagating within a transformer to UHF sensors, which in some cases results in decreasing detection sensitivity of PD signals. In order to understand the propagation and attenuation characteristics of the EM waves within transformers, simulation technique of the EM wave propagation is essential. Although many previous researches on the EM wave simulation have been published, validations of those simulated results by comparing with the experimental ones are insufficient. In this research, at first, the attenuation characteristics of signal amplitudes, cumulative energies as well as frequency components of the EM waves while propagating through transformer windings were investigated both by time- and frequency-domain measurement. The EM wave propagation was simulated based on time-domain finite integration technique (FIT), then the simulated results were compared with the experimental ones. Consequently, the simulated EM waveforms, their signal attenuation level and S-parameter showed good agreement with the experimental results. Therefore, the validation of this EM wave simulation was successfully confirmed.

It is important for reliable diagnosis technique to clarify electromagnetic (EM) wave propagation characteristics at the impedance discontinuity part in gas insulated switchgear (GIS) like spacer, disconnecting part, L branch, and T branch. In this paper the influence of the existence of the insulating spacer on the partial discharge (PD) induced EM wave propagating through T-Branch of 154 kV GIS tank model was examined by the UHF PD measurement. It is observed that PD induced EM wave was attenuated with the distance even in the absence of the spacer. The existence of the spacer decreases the transmission rate of PD induced EM wave. The transmission rate of high frequency component of EM wave (TE mode) was almost the same with the transmission rate of raw EM wave, while the transmission rate of low frequency component of EM wave (TEM mode) was higher than the transmission rate of high frequency component with and without spacer. The transmission rate of PD induced EM wave is influenced mainly by propagation of high frequency component (TE mode) of PD induced EM wave. The existence of the spacer has less influence on the propagation characteristics before and after T branch. The transmission rate through straight direction is higher than the transmission rate through turn direction for the raw wave and the high frequency component of PD induced EM wave.

The plasma sheath surrounding a hypersonic vehicle will cause severe interference to the wireless communications and even interrupt the communications, threatening the flight safety. To better understand and mitigate the interference of the plasma sheath to electromagnetic (EM) wave propagation, the interaction mechanisms between them are studied in this paper. First, using the COMSOL multiphysics software, the flow field of the plasma sheath is simulated, from which the EM parameters are obtained. The plasma sheath is then separated into three zones with different behaviors of the electron density profile. Finally, combining the theory of the EM wave propagation in the plasma, ray tracing equations are solved numerically to observe the EM wave propagation characteristics in the plasma sheath. On this basis, some special propagation characteristics result, such as the directional characteristic of the wave propagation and the “waveguide” behavior of the plasma sheath, which are then explained using the geometrical optics theory. The results obtained in this paper are expected to be able to provide some new applications for wireless communications during hypersonic flight, and to further advance the research related to this subjects.

The shock tube generates a near real hypersonic plasma sheath environment with high temperature and high pressure for investigating the propagation characteristics of the electromagnetic (EM) waves in a hypersonic plasma fluid. With existing methods, it is difficult to measure the propagation characteristics from the transmitted component of low-frequency (LF) EM waves due to large-size LF focusing antennas and LF shielding structure. In this paper, a novel experimental apparatus is proposed to measure the propagation characteristics of the LF EM waves in a shock-tube-generated hypersonic plasma fluid. The tested plasma is utilized as a dynamic fluid EM shield of a receiver during the experiment. This individual receiver is placed in the center of the experimental segment tube of the shock tube so that it is enveloped completely by the hypersonic plasma fluid during the shock, thereby only allows the transmitted component of the LF EM waves to reach the receiver. The proposed method guarantees good measurement accuracy without requiring large LF focusing antennas, and the complex LF shielding structure extends to the shock tube. Both experiments and simulations were performed to evaluate its performance. The results indicated that the propagation characteristics of the transmitted magnetic field component meet that of the numerical simulations faithfully, where the shock wave velocity reached approximately 5 km/s, the plasma layer thickness was 80 mm, the electron density was 1012-1013/cm3, and the collision frequency was approximately 36 GHz. The proposed experimental apparatus is also suitable in studying the EM wave propagation, testing communication system performances, and testing the properties of transmitting and receiving antennas in the hypersonic plasma fluid.

Fluctuations in the signal of optical coefficients of propagative electromagnetic (EM) waves in plasma, can cause problems in phase analysis, especially in microwave diagnostic systems which are based on the reflection, and transmission of EM waves in the vicinity of cut‐off layer of the plasma. In this study, optical properties of EM wave propagation in a single layer, homogeneous, and partially ionized plasma slab are investigated. For realistic analysis of propagation characteristics of the EM wave in the plasma slab, multiple reflections of the EM wave from plasma‐vacuum boundaries, known as incoherent internal reflections (IIR) are considered. Optical coefficients of the EM wave are numerically simulated in terms of the plasma parameters and wave frequency, with and without consideration of the incoherent internal reflections effect. It was found that in the low‐loss collision regime, the cut‐off fluctuations of the optical coefficients can be filtered considering the incoherent internal reflections of the EM wave. Such analysis of the EM wave propagation in plasma slab can be considered the primary physical design of diagnostic facilities and EM wave absorbing structures operating in the cut‐off frequency ranges.

Propagation of electromagnetic wave through an inhomogeneous magnetized nonextensive plasma sheath is numerically examined for a realistic density profile of a reentry problem around a hypersonic vehicle. The effect of nonextensivity and inhomogeneity on radio wave communication is studied parametrically. Variation of reflection and transmission coefficients, total attenuation, and total phase shift over the plasma sheath with respect to the strength of applied magnetic field are derived and compared for different values of q-nonextensive parameter. The obtained results for inhomogeneous plasma sheath are compared with previously obtained results of authors for homogeneous plasma sheath. The comparison shows that radio communication in the inhomogeneous plasma sheath is more advantageous than that in the homogeneous case. The transmission coefficient of a plasma sheath with superthermal electrons (13<q<1) has larger value compared to that with q > 1. Moreover, for ωce>ω, the minimum value of total attenuation corresponds to the range 13<q<1. An interesting result is that nonextensivity effect on wave propagation in plasma sheath depends on the strength of the ambient magnetic field. The effect of nonextensivity on attenuation coefficient is found to be negligible for ωce<ω while it is significant for ωce>ω.

Diagnoses of power transformers by partial discharge (PD) measurement are effective to prevent dielectric failures of the apparatus. Ultra-high frequency (UHF) method has recently received attention due to its various advantages, such as the robustness against external noise and the capability of PD localization. However, electromagnetic (EM) waves radiated from PD tend to suffer attenuation before arriving at UHF sensors, because active part of the transformer disturbs the EM wave propagation. In some cases, that results in poor detection sensitivity. To understand propagation and attenuation characteristics of EM waves and to evaluate the detection sensitivity quantitatively, a computational approach to simulate the EM wave propagation is important. Although many previous researches have dealt with EM wave simulation for transformers, validations of those simulations by comparing with the experimental ones have seldom been reported. In this paper, cumulative energies, signal amplitudes and propagation times of EM waves were measured using a 630 kVA transformer. EM wave propagation was computed using the time-domain finite integration technique and the results were compared with the experimentally obtained ones. These simulation results showed good agreement with the experimental ones. The results can serve as guidelines to improve the efficiency of UHF PD detection and offer the possibility to achieve optimal placement of UHF sensors in power transformers.

Degradation of the electrical insulation within power transformers by partial discharge (PD) may lead to catastrophic failure of the apparatus, hence PD should be detected at an early stage. Ultra‐high frequency (UHF) measurement method, i.e. detecting electromagnetic (EM) waves in the UHF range radiated from PD, has recently received attention for its various advantages, such as the robustness against external noises and its capability of localisation of the PD position. However, the EM waves suffer attenuation while propagating within transformers, in some cases, which results in undesirable low detection sensitivity. To evaluate the propagation and attenuation characteristics of the EM waves quantitatively, the simulation technique of the EM wave propagation is of importance. In this study, at first, the EM waveforms as well as attenuation properties of their amplitudes and cumulative energies while propagating through transformer windings in an oil‐filled tank were experimentally investigated. Next, the detailed conditions for simulating the EM wave propagation based on time‐domain finite integration technique were described. Then, the simulated results were compared with the experimentally obtained ones. These simulation and measurement results showed good agreement with each other, therefore the authors have successfully validated the newly developed simulation of the EM wave propagation.