Full-wave Effects Research Articles

Resolving full-wave through-wall transmission effects in multi-static synthetic aperture radar

Through-wall synthetic aperture radar (SAR) imaging is of significant interest for security purposes, in particular when using multi-static SAR systems consisting of multiple distributed radar transmitters and receivers to improve resolution and the ability to recognise objects. Yet there is a significant challenge in forming focused, useful images due to multiple scattering effects through walls, whereas standard SAR imaging has an inherent single scattering assumption. This may be exacerbated with multi-static collections, since different scattering events will be observed from each angle and the data may not coherently combine well in a naive manner. To overcome this, we propose an image formation method which resolves full-wave effects through an approximately known wall or other arbitrary obstacle, which itself has some unknown ‘nuisance’ parameters that are determined as part of the reconstruction to provide well focused images. The method is more flexible and realistic than existing methods which treat a single wall as a flat layered medium, whilst being significantly computationally cheaper than full-wave methods, strongly motivated by practical considerations for through-wall SAR.

An assessment of full-wave effects on Maxwellian lower-hybrid wave damping

Lower-hybrid current drive (LHCD) actuators are important components of modern day fusion experiments as well as proposed fusion reactors. However, simulations of LHCD often differ substantially from experimental results, and from each other, especially in the inferred power deposition profile shape. Here we investigate some possible causes of this discrepancy; ‘full-wave’ effects such as interference and diffraction, which are omitted from standard raytracing simulations and the breakdown of the raytracing near reflections and caustics. We compare raytracing simulations to state-of-the-art full-wave simulations using matched hot-plasma dielectric tensors in realistic tokamak scenarios for the first time. We show that differences between full-wave simulations and raytracing in previous work were primarily due to numerical and physical inconsistencies in the simulations, and we demonstrate that quantitative agreement between raytracing and converged full-wave simulations can be obtained in reactor relevant-scenarios and qualitative agreement can be obtained in situations with weak damping.

Structure-preserving particle-in-cell simulation of lower hybrid wave propagation and heating in the magnetic mirror

This study presents the first-principle, structure-preserving electromagnetic particle-in-cell simulation of the lower hybrid wave (LHW) in magnetic mirror-confined plasmas. The behavior of LHW propagation and ion heating is studied and compared with the ray-tracing results. Two full-wave effects of LHW propagation in the mirror devices, the rotation of LHW and tunnel effects near the resonance, are revealed and discussed. Meanwhile, the ion heating near the resonance layer is presented. We first provide the spatial profile of energy deposition in 3D space and conduct a long-term simulation that shows an up to 150% ion temperature increment and a maximal ion temperature of over 1.5 keV in the hot spot at the end. In addition, we further discuss the heating mechanism and elucidate the stochastic ion heating behavior in such a regime. The onset and advantages of such a heating mechanism in terms of the magnetic mirror are also discussed. The results proved the reliability and effectiveness of lower hybrid stochastic heating in mirror devices.

A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this work, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

Sensitivity of SK(K)S and ScS phases to heterogeneous anisotropy in the lowermost mantle from global wavefield simulations

SUMMARY Observations of seismic anisotropy at the base of the mantle are abundant. Given recent progress in understanding how deformation relates to anisotropy in lowermost mantle minerals at the relevant pressure and temperature conditions, these observations can be used to test specific geodynamic scenarios, and have the potential to reveal patterns of flow at the base of the mantle. For example, several recent studies have sought to reproduce measurements of shear wave splitting due to D″ anisotropy using models that invoke specific flow and texture development geometries. A major limitation in such studies, however, is that the forward modelling is nearly always carried out using a ray theoretical framework, and finite-frequency wave propagation effects are not considered. Here we present a series of numerical wave propagation simulation experiments that explore the finite-frequency sensitivity of SKS, SKKS and ScS phases to laterally varying anisotropy at the base of the mantle. We build on previous work that developed forward modelling capabilities for anisotropic lowermost mantle models using the AxiSEM3D spectral element solver, which can handle arbitrary anisotropic geometries. This approach enables us to compute seismograms for relatively short periods (∼4 s) for models that include fully 3-D anisotropy at moderate computational cost. We generate synthetic waveforms for a suite of anisotropic models with increasing complexity. We first test a variety of candidate elastic tensors in laterally homogeneous models to understand how different lowermost mantle elasticity scenarios express themselves in shear wave splitting measurements. We then consider a series of laterally heterogeneous models of increasing complexity, exploring how splitting behaviour varies across the edges of anisotropic blocks and investigating the minimum sizes of anisotropic heterogeneities that can be reliably detected using SKS, SKKS and ScS splitting. Finally, we apply our modelling strategy to a previously published observational study of anisotropy at the base of the mantle beneath Iceland. Our results show that while ray theory is often a suitable approximation for predicting splitting, particularly for SK(K)S phases, full-wave effects on splitting due to lowermost mantle anisotropy can be considerable in some circumstances. Our simulations illuminate some of the challenges inherent in reliably detecting deep mantle anisotropy using body wave phases, and point to new strategies for interpreting SKS, SKKS and ScS waveforms that take full advantage of newly available computational techniques in seismology.

Reconstruction of hollow areas in density profiles from frequency swept reflectometry

The standard density profile reconstruction techniques are based on the WKB approximation of the probing wave’s phase, making them unable to properly reconstruct blind areas in the cut-off frequency profile. The reconstruction suffers a significant immediate error that is not rapidly damped. It is demonstrated that even though no reflections occur inside the hollow region causing the blind area, the higher probing frequencies that propagate through it carry information that can be used to estimate its properties. The usually ignored full-wave effects were investigated with the use of full-wave simulations in 1D, with special attention paid to the frequency band where they are dominant. A database of perturbation signals was simulated on five-dimensions of parameters and an application of the database inversion was demonstrated for a magnetic island in a Tore Supra discharge. The new adapted reconstruction scheme improved the description of the density profile inside the hollow region and also along 10 cm after it.

Pre-stack AVA Inversion by Using Propagator Matrix Forward Modeling

Most existing amplitude variation with angle (AVA) inversions are based on the exact Zoeppritz equation or its approximations. These modeling methods, which are ray-tracing-based and describe P-wave primary reflections only, lead to exacting requirements for pre-processing of the input data. Current processing is inadequate to satisfy these demands, especially for removing the effects of transmission losses, P-wave multiples and various converted-wave modes. By using input data with processing errors, inversion results of primary-only methods are predictably not accurate enough. The propagator matrix (PM), like the reflectivity method, uses an analytical solution to the wave equation and considers full-wave propagation effects in horizontal or nearly horizontal multilayered earth models. The numerical examples verify that a PM can effectively estimate transmission losses, multi-reflections and the comprehensive responses of thin interbedded layers, and also has higher reflection sensitivities to P-wave and S-wave velocity and density, as compared with ray-tracing-based AVA modelling. A pre-stack AVA three-parameter inversion by using a PM as the forward engine is proposed. Following a Bayesian approach, the inversion is stabilized by including the correlation of P-wave velocity, S-wave velocity and density. For inversion accuracy, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method is used to solve the augmented function, and the generalized cross-validation (GCV) criterion (Huang et al. in J Geophys Eng 14(1):100–112, 2017) is introduced to adaptively acquire the regularization parameter. Theoretical model inversion analysis shows that the proposed inversion can make use of transmission losses, P-wave multiples and converted wave modes, which not only cost-effectively simplifies the pre-processing, but also generates reasonable inverted results for multilayered conditions. The proposed inversion is then applied to a set of real data, and a comparison with Zoeppritz equation-based inversion demonstrates that PM inversion is clearly superior to Zoeppritz equation-based inversion in terms of stability and accuracy.

Studies of various physics effects on an on-axis LHCD experiment using numerical tools

The lower hybrid current drive (LHCD) plays an important role in the long pulse and high performance experiments on the EAST Tokamak, using LHW systems with frequencies of 2.45 GHz and 4.6 GHz. With the initial parallel refractive index mostly peaking at n∥∼1.8−2.1, it is difficult to have on-axis LHCD due to the accessibility conditions which prevents the LHW from propagating into the plasma core. However, according to the investigation of HXR diagnostics, LHW did provide an on-axis current drive in an EAST experiment. To interpret this on-axis LHCD phenomenon, various physics effects that give rise to variations in parallel wave numbers, thus influencing the propagation and the absorption of the LHW, have been taken into account, such as toroidal effects, full wave effects with focusing and diffraction, and scattering effects due to density fluctuations. Numerical tools including ray-tracing and full wave codes that contain one or two of the above physics effects have been used to model the heating and current drive of the LHW on EAST. Linear Landau damping and quasi-linear Landau damping have been compared by using the coupling between ray-tracing and the Fokker-Planck codes. Convergence studies have been performed for the full wave modeling, the maximum poloidal modes in the full wave have been scanned, and the results are compared with each other. The factors that characterize the amplitude, the radial thickness, and the location of the density fluctuations have been studied and scanned. The measurement of HXR diagnostics has been compared with synthetic diagnostics by reconstructing the HXR data from both the standard GENRAY/CQL3D LHCD modelling and the modeling taking the scattering effects into account.

Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation.

Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles. This causes unusual phase-space dynamics that is typically not captured by the WKE. We demonstrate how to correctly model this dynamics with the WME instead. Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations. We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii) we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies. We also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.

Calculating a sensitivity kernel for the final cutoff of received energy in a broadband channel impulse response

The final cutoff of a deep-water ocean acoustic tomography reception is often interpreted through a modal analysis. An alternative approach is presented here. First, a stable travel-time is generated by using an estimator-correlator to account for the statistical variability of the final low-angle arrival with the assumption of an appropriate coherent bandwidth and depth coherence. A time-series of these travel-times can then be tracked using the Viterbi algorithm. Then, the resolvable, trackable peaks are interpreted using the travel-time sensitivity kernel (TSK). The TSK has been previously used to account for the full-wave effects of ray-like arrivals. But the TSK machinery can be adapted to any processing strategy with the application of the chain-rule. The question of how to interpret an arrival produced by an Estimator-Correlator vs. an arrival produced by standard processing is examined. The feasibility of this approach is first analytically determined with the Pekeris waveguide and then an example...

Self-Optimizing Photoelectrochemical Growth of Nanopatterned Se-Te Films in Response to the Spectral Distribution of Incident Illumination.

Photoelectrochemical growth of Se-Te films spontaneously produces highly ordered, nanoscale lamellar morphologies with periodicities that can be tuned by varying the illumination wavelength during deposition. This phenomenon has been characterized further herein by determining the morphologies of photoelectrodeposited Se-Te films in response to tailored spectral illumination profiles. Se-Te films grown under illumination from four different sources, having similar average wavelengths but having spectral bandwidths that spanned several orders of magnitude, all nevertheless produced similar structures which had a single, common periodicity as quantitatively identified via Fourier analysis. Film deposition using simultaneous illumination from two narrowband sources, which differed in average wavelength by several hundred nanometers, resulted in a structure with only a single periodicity intermediate between the periods observed when either source alone was used. This single periodicity could be varied by manipulating the relative intensity of the two sources. An iterative model that combined full-wave electromagnetic effects with Monte Carlo growth simulations, and that considered only the fundamental light-material interactions during deposition, was in accord with the morphologies observed experimentally. Simulations of light absorption and concentration in idealized lamellar arrays, in conjunction with all of the available data, additionally indicated that a self-optimization of the periodicity of the nanoscale pattern, resulting in the maximization of the anisotropy of interfacial light absorption in the three-dimensional structure, is consistent with the observed growth process of such films.

Modelling of the EAST lower-hybrid current drive experiment using GENRAY/CQL3D and TORLH/CQL3D

The coupled GENRAY-CQL3D code has been used to do systematic ray-tracing and Fokker–Planck analysis for EAST Lower Hybrid wave Current Drive (LHCD) experiments. Despite being in the weak absorption regime, the experimental level of LH current drive is successfully simulated, by taking into account the variations in the parallel wavenumber due to the toroidal effect. The effect of radial transport of the fast LH electrons in EAST has also been studied, which shows that a modest amount of radial transport diffusion can redistribute the fast LH current significantly. Taking advantage of the new capability in GENRAY, the actual Scrape Off Layer (SOL) model with magnetic field, density, temperature, and geometry is included in the simulation for both the lower and the higher density cases, so that the collisional losses of Lower Hybrid Wave (LHW) power in the SOL has been accounted for, which together with fast electron losses can reproduce the LHCD experimental observations in different discharges of EAST. We have also analyzed EAST discharges where there is a significant ohmic contribution to the total current, and good agreement with experiment in terms of total current has been obtained. Also, the full-wave code TORLH has been used for the simulation of the LH physics in the EAST, including full-wave effects such as diffraction and focusing which may also play an important role in bridging the spectral gap. The comparisons between the GENRAY and the TORLH codes are done for both the Maxwellian and the quasi-linear electron Landau damping cases. These simulations represent an important addition to the validation studies of the GENRAY-CQL3D and TORLH models being used in weak absorption scenarios of tokamaks with large aspect ratio.

Solution of the Electric Field Integral Equation When It Breaks Down

With a method developed in this work, we find the solution of the original electric field integral equation (EFIE) at an arbitrary frequency where the EFIE breaks down due to low frequencies and/or dense discretizations. This solution is equally rigorous at frequencies where the EFIE does not break down and is independent of the basis functions used. We also demonstrate, both theoretically and numerically, the fact that although the problem is commonly termed low-frequency breakdown, the solution at the EFIE breakdown can be dominated by fullwave effects instead of just static or quasi-static physics. The accuracy and efficiency of the proposed method is demonstrated by numerical experiments involving inductance, capacitance, RCS extraction, and a multiscale example with a seven-orders-of-magnitude ratio in geometrical scales, at all breakdown frequencies of an EFIE. In addition to the EFIE, the proposed method is also applicable to other integral equations and numerical methods for solving Maxwell's equations.

Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters

Progress in experiment and simulation capability in the lower hybrid range of frequencies at ITER relevant parameters is reviewed. Use of LH power in reactor devices is motivated in terms of its potential for efficient off-axis current profile control. Recent improvements in simulation capability including the development of full-wave field solvers, inclusion of the scrape off layer (SOL) in wave propagation codes, the use of coupled ray tracing/full-wave/3D (r v⊥, v//) Fokker Planck models, and the inclusion of wave scattering as well as nonlinear broadening effects in ray tracing / Fokker Planck codes are discussed. Experimental and modeling results are reviewed which are aimed at understanding the spectral gap problem in LH current drive (LHCD) and the density limit that has been observed and mitigated in LHCD experiments. Physics mechanisms that could be operative in these experiments are discussed, including toroidally induced variations in the parallel wavenumber, nonlinear broadening of the pump wave, scattering of LH waves from density fluctuations in the SOL, and spectral broadening at the plasma edge via full-wave effects.

Progress towards steady-state regimes in Alcator C-Mod

Recent progress on lower hybrid current drive (LHCD) experiment and simulation towards steady-state (t ⩾ 3–5 × τr, where τr is the current relaxation time) regimes on Alcator C-Mod is presented. Highly non-inductive reversed shear plasmas are obtained with spontaneous generation of internal transport barriers at the density close to what is expected on ITER steady-state scenarios. Progress has been made to better understand and mitigate the unexpected degradation of LHCD efficiency at high densities, which poses an issue both for extending the non-inductive plasmas to advanced tokamak regimes (with a high bootstrap current fraction, fBS) on C-Mod and for predicting the performance of LHCD on future devices such as ITER. Several physics mechanisms that potentially contribute anomalous losses of LHCD power have been studied extensively. Numerical modelling of collisional absorption in cold scrape-off layer plasmas has been integrated into a ray-tracing code. The LHEAF full-wave code clarifies that full-wave effects move the power deposition profile closer to the separatrix than a calculation based on the WKB approximation, leading to a lower efficiency. Non-linear wave interactions were studied experimentally by LH wave spectral measurements using Langmuir probes, suggesting parametric decay instabilities to explain the remaining difference between experiments and simulations. An experimental demonstration of recovery of good LHCD efficiency at high densities is also reported. Improving the single pass absorption is proposed as a key to recover LHCD efficiency. A wave physics design of additional launcher (LH3) has been developed in order to demonstrate an improved LHCD performance by realizing high (∼80%) single pass absorption, in which the synergistic interaction in the velocity space with the existing launcher is maximized.

DR OMUX for Satellite Communications: A Complete Step-by-Step Design Procedure for the C-Band Dielectric Resonator Output Multiplexer

Although the behavior of dielectric materials has been known since 1939 when R.D. Richtmyer showed that unmetalized dielectrics can operate as microwave resonators [1], it was only in the 1970s when real breakthroughs occurred in ceramic technology, and low loss and temperature stable ceramics were developed. In 1975 the first practical dielectric resonator (DR) loaded microwave filter was reported at the IEEE MTT-S International Microwave Symposium [2]. Significant advancements in ceramic technology and the progress in satellite and mobile communications in the 1990s revived interest in DR applications for a wide variety of microwave components. A number of new materials such as zirconium-tin titanate, ZST ((Zr ? Sn)TiO4), barium zinc tantalate, BZT (Ba(Zn,Ta)O3), and barium magnesium tantalate, BMT (Ba(Mg,Ta)O3), with high-dielectric constant, high-quality factor and low-temperature coefficient were developed [3]. These new materials, along with the application of rigorous full-wave modeling and analysis methods, fueled the development of new DR filter configurations such as single and dual mode filters with elliptic transfer function. Today, DR filters and output multiplexers (OMUXs) are widely used in satellite communications because of their superior characteristics, such as smaller size, better temperature stability, and higher unloaded Q compared to conventional cavity-based OMUXs. A number of papers have been published on DR filters and OMUXs [4]?[6], [8], [9], but no comprehensive paper on the design of a DR-based OMUX has been reported. The large interchannel interaction (due to contiguity of channel filter frequencies, performance of one channel filter is effected by the presence of other channel filters), wide spurious free frequency band, and stringent in-band and out-of-band (OOB) specifications (such as large near band and far band rejections, small passband group delay and flatness), along with the requirement of high Q, low frequency drift with temperature, and high power handling capability, make the design of DR OMUXs extremely challenging. This article presents a practical approach to the design of C-band high power OMUXs based on single mode DR filters for space application (Figures 1 and 2), making extensive use of present day simulation capabilities. All the major steps involved in the design of a DR OMUX such as the concept of a singly terminated filter, conversion of doubly terminated filters to singly terminated filters using a series L-C circuit, modeling of the DR OMUX in a circuit simulator incorporating full wave effects, and the OMUX optimization sequence are explained in detail. A successful design of the DR filter is crucial to the eventual design of the DR OMUX.

Efficient DC Analysis of Power Planes Using Contour Integral Method With Circular Elements

Contour integral method, well-known for the analysis of 2-D full-wave effects on power planes, is extended here for the computation of DC resistances of power planes. In particular, circular elements, e.g., vias and antipad holes, are treated using cylindrical modal expansion functions, which leads to a more efficient and accurate calculation than the conventional implementation by the linear discretization. For individual power planes, the method produces a resistor network consisting of only the nodes that are associated with power or ground vias, which can be further employed to formulate solutions for complete multilayer structures. The method is applied to several power plane configurations and results are validated by a 3-D finite element method solver. The efficiency of the extended method is analyzed and a reduction of the number of unknowns by a factor of four for the circular elements can be expected by the modal expansion. Good accuracy can be achieved by including up to the second higher order mode for dense clusters of antipad holes.

Signal integrity: Efficient, physics-based via modeling: Integration of striplines

In the first article of this series, principles and methods of physics-based via modeling were discussed. It was shown how the electromagnetic behavior of vias can be captured by an equivalent circuit based modeling approach that describes all relevant full-wave effects. In this follow-up article, the authors present an approach to integrate striplines into the physics-based via model. The striplines can be located at any layer of the stackup and they may constitute both single and multiconductor transmission lines. The integration of striplines extends the via representation to a full, efficient interconnect model of, for instance, printed circuit board signal links. An intuitive integration approach at a circuit simulator level and application examples are discussed in this article as well.

A Rigorous Solution to the Low-Frequency Breakdown in Full-Wave Finite-Element-Based Analysis of General Problems Involving Inhomogeneous Lossless/Lossy Dielectrics and Nonideal Conductors

Existing methods for solving the low-frequency breakdown problem associated with full-wave solvers rely on low-frequency approximations, which has left a number of research questions to be answered. The conductors are also generally treated as perfect conductors and the dielectric loss is not considered. In this work, a rigorous method that does not utilize low-frequency approximations is developed to eliminate the low frequency breakdown problem for the full-wave finite-element based analysis of general 3-D problems involving inhomogeneous lossless and/or lossy dielectrics and nonideal conductors. This method has been validated by the analysis of realistic on-chip circuits at frequencies as low as dc. Furthermore, it is applicable to both low and high frequencies. In this method, the frequency dependence of the solution to Maxwell's equations is explicitly and rigorously derived from dc to high frequencies. In addition to eliminating the low-frequency breakdown, such a theoretical model of the frequency dependence can be used to understand how the field solution, in a complicated 3-D problem with both lossless/lossy inhomogeneous dielectrics and nonideal conductors, should scale with frequency and at which frequency full-wave effects become important.

Full wave effects on the lower hybrid wave spectrum and driven current profile in tokamak plasmas

A numerical modeling of current profile modification by lower hybrid current drive (LHCD) using a fullwave/Fokker-Planck simulation code is presented. A MHD stable LHCD discharge on Alcator C-Mod was analyzed, and the current profile from full wave simulations was found to show better agreement with the experiment than a ray-tracing code. Comparison of full wave and ray-tracing simulation shows that, although ray-tracing can reproduce the stochastic wave spectrum broadening, the full wave calculation predicts even wider spectrum broadening, and the wave spectrum fills all of the kinematically allowed domain. This is the first demonstration of LHCD current profile modeling using a full wave simulation code in a multi-pass absorption regime, showing the clear impact of full wave effects on the LHCD driven current profile.