Hybrid Wave Propagation Research Articles

Relativistic analysis of upper hybrid wave propagation and trapping

We investigate the impact of relativistic effects on upper hybrid (UH) waves in plasmas with thermal electrons, particularly focusing on modifications of the conditions under which UH wave trapping and related low-threshold parametric decay instabilities (PDIs) may occur. A moderately relativistic (MR) dispersion relation for UH waves, valid for electron temperatures up to 25 keV and wave frequencies up to twice the electron cyclotron frequency, is obtained from previous results and shown to reduce to the warm non-relativistic result commonly used for PDI studies at low electron temperatures. The conditions under which MR UH waves propagate are then determined and compared with warm and cold plasma theory, showing a general increase in the electron density and background magnetic field strength at which the UH resonance occurs for finite electron temperatures. We next investigate the impact of the MR corrections on the possibility of UH wave trapping for X-mode electron cyclotron resonance heated (ECRH) plasmas at the ASDEX Upgrade tokamak and scaled versions of the ASDEX Upgrade parameters with core electron temperatures resembling those expected in ITER X-mode ECRH plasmas. The MR UH wave trapping conditions are virtually unchanged for ASDEX Upgrade relative to warm theory, due to the low electron temperatures, while potentially important differences between warm and MR theory exist for ITER-like core electron temperatures; cold theory is found to be insufficient in both cases. Finally, the MR dispersion relation is shown to qualitatively reproduce the PDI thresholds from warm theory for previously studied ASDEX Upgrade cases.

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.

Waves of a Magnetoplasma Solid-State Cylinder Under Quasi-Stationary Conditions

The theory of electromagnetic eigenwaves of a cylindrical plasma waveguide located in a constant coaxial magnetic field is developed. The dispersion equation for a waveguide with high electronic conductivity is obtained. It is shown that the waveguide supports the propagation of bulk and bulk-surface hybrid waves of helicon origin. The nonreciprocity effect of waveguide eigenwaves with the identical field distributions, but differing in the direction of propagation along the azimuthal coordinate and also when the direction of the external magnetic field is reversed, is discovered.

Study of turbulence-induced refraction of lower hybrid waves using synthetic scrape-off layer filaments

Turbulence-induced refraction effects to lower hybrid (LH) wave propagation and current drive are studied using synthetic scrape-off layer (SOL) blob/filament fields. A synthetic 3D, field-following, blob turbulence model is implemented in the ray-tracing/Fokker-Planck (RTFP) codes GENRAY/CQL3D. In Alcator C-Mod, the blob field is shown to significantly affect LH ray-trajectories, leading to increased on-axis damping and smoother current profiles. This effect depends on the average blob size and amplitude. In addition, the diffusion of ray-trajectories in phase-space caused by turbulence increases the robustness of the RTFP model. A modified launch spectrum, acting as a proxy for parametric decay instability (PDI) effects, is included in simulations with the blob model. A synergy between the modified launch spectrum and turbulence-induced refraction results in synthetic hard x-ray profiles that agree with experiment. Lastly, the blob model is used to predict the effect of SOL turbulence on DIII-D high-field side (HFS) LH launch. Assuming low turbulence amplitude in the HFS SOL (∼5%), turbulence-induced refraction is predicted to have little effect on current drive efficiency.

Effects of wave trapping and ducting inside plasma density depletions are studied in a laboratory magnetoplasma

A laboratory experiment creates a pulsed magnetoplasma and demonstrates that oblique propagation of upper hybrid waves is necessary to understand ionospheric heating experiments.

Hybrid Numerical Modeling of Electromagnetic Interference in Train Communication Systems

Electromagnetic interference (EMI) is an important issue that needs to be considered for the safe operation of communication-based train control (CBTC) systems in railway environments. In this paper, two EMI scenarios are considered: the EMI of a wireless local area network (WLAN) at subway stations to CBTC systems and the interference of the CBTC system in tunnels to WLAN devices inside the train. To effectively solve those EMI problems, we introduce two hybrid wave propagation modeling techniques, where ray-tracing and finite-difference time-domain (FDTD) methods are hybridized for the first scenario and vector parabolic equation and FDTD methods are hybridized for the second scenario. The two hybrid models combine advantages of each individual method and achieve a better tradeoff between accuracy and efficiency. Based on our analysis, EMI-aware planning such as the optimization of WLAN antenna placement at subway stations can be pursued. The benefits that this approach can produce are demonstrated.

Electromagnetic Non-Polarized Symmetric Hybrid Wave Propagation in a Plane Waveguide with Nonlinear Anisotropic Permittivity

Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear anisotropic medium. The wave propagation problem is reduced to a transmission eigenvalue problem. Eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using a perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and, therefore, guide waves. Numerical results are presented.

Acoustic tomography based on hybrid wave propagation model for tree decay detection

Acoustic wave technologies have been used in wood defect detection for many years. Various tomographic imaging algorithms have been proposed to construct two dimensional acoustic velocity maps that serve as the scientific evidence of tree’s internal condition. Many previously proposed algorithms were based on the assumption that acoustic waves propagate along straight rays in the cross sections of trees. To simulate the acoustic wave propagation more realistically, this paper proposed a tomographic imaging method based on a hybrid wave propagation model (HWPM) that includes two velocity inversion phases: straight-ray inversion and curved-ray inversion. The straight-ray inversion was first applied to obtain the preliminary velocity distribution, followed by the curved-ray inversion to refine the velocity distribution. A velocity correction factor was determined for each grid cell following each inversion iteration, and then was used to derive a new velocity value for each corresponding cell. The maximum and minimum velocity constraints were imposed on the newly-computed velocities, and some velocity constraints of grid cells were also imposed to address the nonuniqueness problem commonly existed in velocity inversion and generate a more accurate tomographic image. To evaluate the effectiveness of the hybrid inversion method, we conducted multipath acoustic wave testing on three short log sections (one sound and two with artificial defect) in the laboratory and four live trees in Yangzhou Slender West Lake Park, Jiangsu Province, China. Time-of-flight data was collected by PiCUS Tomograph tool and used to generate tomographic images with both Simultaneous iterative reconstruction technique (SIRT) and the proposed hybrid inversion method to make a comparison. Micro-drilling tests were conducted on the live trees to determine the internal condition and served as the basis for evaluating the tomographic images. Our results indicate that the hybrid wave propagation model is effective in constructing acoustic tomographic images that are reasonably accurate in detecting the internal defects of urban trees.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium

Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.

The new type of non-polarized symmetric electromagnetic waves in planar nonlinear waveguide

ABSTRACTPaper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear medium. The wave propagation problem is reduced to a transmission eigenvalue problem. Eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and therefore, guide waves. The found guide regime is novel in the theory of nonlinear waveguides. Numerical results are presented.

Analysis of the Chaotic Behavior of the Lower Hybrid Wave Propagation in Magnetised Plasma by Hamiltonian Theory

The Hamiltonian character of the ray tracing equations describing the propagation of the Lower Hybrid Wave (LHW) in a magnetic confined plasma device (tokamak) is investigated in order to study the evolution of the parallel wave number along the propagation path. The chaotic diffusion of the “time-averaged” parallel wave number at higher values (with respect to that launched by the antenna at the plasma edge) has been evaluated, in order to find an explanation of the filling of the spectral gap (Fisch, 1987) by “Hamiltonian chaos” in the Lower Hybrid Current Drive (LHCD) experiments (Fisch, 1978). The present work shows that the increase of the parallel wave number \(n_{\parallel}\) due to toroidal effects, in the case of the typical plasma parameters of the Frascati Tokamak Upgrade (FTU) experiment, is insufficient to explain the filling of the spectral gap, and the consequent current drive and another mechanism must come into play to justify the wave absorption by Landau damping. Analytical calculations have been supplemented by a numerical algorithm based on the symplectic integration of the ray equations implemented in a ray tracing code, in order to preserve exactly the symplectic character of a Hamiltonian flow.

Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas

In tokamak fusion plasmas, coherent fluctuations in the form of blobs or filaments are routinely observed in the scrape-off layer. Radio frequency (RF) electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the scrape-off layer before reaching the core of the plasma. While the effect of fluctuations on the properties of RF waves has not been quantified experimentally, it is of interest to carry out a theoretical study to determine if fluctuations can affect the propagation characteristics of RF waves. Usually, the difference between the plasma density inside the filament and the background plasma density is sizable, the ratio of the density difference to the background density being of order one. Generally, this precludes the use of geometrical optics in determining the effect of fluctuations, since the relevant ratio has to be much less than one, typically, of the order of 10% or less. In this paper, a full-wave, analytical model is developed for the scattering of a RF plane wave by a cylindrical plasma filament. It is assumed that the plasma inside and outside the filament is cold and uniform and that the major axis of the filament is aligned along the toroidal magnetic field. The ratio of the density inside the filament to the density of the background plasma is not restricted. The theoretical framework applies to the scattering of any cold plasma wave. In order to satisfy the boundary conditions at the interface between the filament and the background plasma, the electromagnetic fields inside and outside the filament need to have the same k∥, the wave vector parallel to the ambient magnetic field, as the incident plane wave. Consequently, in contrast to the scattering of a RF wave by a spherical blob [Ram et al., Phys. Plasmas 20, 056110-1–056110-10 (2013)], the scattering by a field-aligned filament does not broaden the k∥ spectrum. However, the filament induces side-scattering leading to surface waves and can also couple some power to the cold plasma wave different from the incident wave. The changes induced by a filament in the propagation of electron cyclotron waves and lower hybrid waves are illustrated by numerical results displaying the properties of the Poynting vector. The Poynting flux in the wake of the filament, and directed towards the core of the plasma, develops a spatial structure due to diffraction and shadowing. Thus, the fluctuations affect the uniformity of power flow into the plasma.

Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparable to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ∼ 3ωLH, where ωLH represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ∼ 1.3ωLH), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.

A hybrid wave propagation and statistical energy analysis on the mid-frequency vibration of built-up plate systems

Based on the concept of the hybrid finite element (FE) analysis and statistical energy analysis (SEA), a new hybrid method is developed for the mid-frequency vibration of a system comprising rectangular thin plates. The wave propagation method based on symplectic analysis is used to describe the vibration of the deterministic plate component. By enforcing the displacement continuity and equilibrium of force at the connection interface, the dynamic coupling between the deterministic plate component and the statistical plate component described by SEA is established. Furthermore, the hybrid solution formulation for the mid-frequency vibration of the system built up by plates is proposed. The symplectic analytical wave describing the deterministic plate component eliminates the boundary condition limitation of the traditional analytical wave propagation method and overcomes the numerical instability of numerical wave propagation methods. Numerical examples compare results from the proposed method with those from the hybrid FE-SEA method and the Monte Carlo method. The comparison illustrates that the proposed method gives good predictions for the mid-frequency behavior of the system considered here with low computational time. In addition, a constant proportionality coefficient between the system coupling power and the energy difference between the plate components can be found, when external forces are applied at different locations on a line perpendicular to the wave propagation direction. Based on this finding, two fast solution techniques are developed for the energy response of the system, and are validated by numerical examples.

Particle simulation of lower hybrid wave propagation in fusion plasmas

Global particle simulations of the lower hybrid (LH) waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The LH wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a LH wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. This poloidal asymmetry arises from the non-conservation of the poloidal mode number due to the non-uniform magnetic field. In contrast, the poloidal mode number is conserved in the cylindrical geometry with the uniform magnetic field.

The effects of finite electron temperature and diffraction on lower hybrid wave propagation

In this paper we show that the commonly used cold plasma dispersion relation for plasma waves in the lower hybrid range of frequencies (LHRF) produces a wave trajectory that is notably different than when thermal corrections to the Hermitian part of the dielectric tensor are retained. This is in contrast to the common implementation in LH simulation codes in which thermal effects are retained only for the anti-Hermitian part of the dielectric tensor used for damping calculations. We show which term is the critical one to retain in the dielectric tensor and discuss implications for modeling of LHRF waves in present day and future devices. We conclude with some observations on the effects of diffraction that may be isolated once thermal effects are retained in both ray tracing and full-wave approaches.

Detection of lower hybrid waves in the scrape-off layer of tokamak plasmas with microwave backscattering

Microwave backscattering experiments have been performed on the Alcator C-Mod tokamak in order to investigate the propagation of lower hybrid (LH) waves in reactor-relevant, high-density plasmas. When the line-averaged density is raised above 1 × 1020 m–3, lower hybrid current drive efficiency is found to be lower than expected [Wallace et al., Phys. Plasmas 19, 062505 (2012)] and LH power is thought to be dissipated at the plasma edge. Using a single channel (60 GHz) ordinary-mode (O-mode) reflectometer system, we demonstrate radially localized LH wave measurements in the scrape-off layer of high density plasmas (n¯e ≳ 0.9×1020 m−3). Measured backscattered O-mode power varies depending on the magnetic field line mapping, suggesting the resonance cone propagation of LH waves. Backscattered power is also sensitive to variations in plasma density and the launched parallel refractive index of the LH waves. LH ray-tracing simulations have been carried out to interpret the observed variations. To understand the measured LH waves in regions not magnetically connected to the launcher, two hypotheses are examined. One is the weak single pass absorption and the other is scattering of LH waves by non-linear effects.

The effects of the scattering by edge plasma density fluctuations on lower hybrid wave propagation

Scattering effects induced by edge density fluctuations on lower hybrid (LH) wave propagation are investigated. The scattering model used here is based on the work of Bonoli and Ott (1982 Phys. Fluids 25 361). It utilizes an electromagnetic wave kinetic equation solved by a Monte Carlo technique. This scattering model has been implemented in GENRAY, a ray-tracing code which explicitly simulates wave propagation, as well as collisionless and collisional damping processes, over the entire plasma discharge, including the scrape-off layer that extends from the separatrix to the vessel wall. A numerical analysis of the LH wave trajectories and the power deposition profile with and without scattering is presented for Alcator C-Mod discharges. Comparisons between the measured hard x-ray emission on Alcator C-Mod and simulations of the data obtained from the synthetic diagnostic included in the GENRAY/CQL3D package are shown, with and without the combination of scattering and collisional damping. Implications of these results on LH current drive are discussed.

Advances in lower hybrid current drive technology on Alcator C-Mod

Lower hybrid current drive (LHCD) is an attractive option for non-inductive tokamak operation due to its high current drive efficiency and ability to drive current off axis. The parameters of the Alcator C-Mod LHCD system (f0 = 4.6 GHz, Bφ ≃ 5.5 T, ) are similar to the proposed LHCD system on ITER. This paper will describe improvements in LHCD technology on C-Mod designed to increase single-pass absorption at high , extend pulse length (to >3 s), and increase power delivered to the plasma (to ∼2 MW). Modelling of lower hybrid (LH) wave propagation indicates that the observed loss of LHCD efficiency at higher can be mitigated by enhancing the single pass power absorption through use of an off mid-plane launcher. The four rows of the launcher are located above the mid-plane (with Ip and Bφ both clockwise viewing from the top down) in order to exploit the poloidal upshift of n‖ as rays propagate from the antenna into the plasma. The transmitter protection system (TPS) was redesigned to model the coolant temperature in real time and shut off the klystron beam voltage if the coolant is close to boiling. The TPS upgrade has been installed and operated on C-Mod for pulses up to 4.5 s into dummy loads and 1.0 s into the plasma. A new movable local LH launcher protection limiter was designed to reduce reflection coefficients across a wide range of launcher positions. Finally, a high power waveguide double-stub tuner is under development to provide feedback controlled load matching to reduce power reflected from the antenna under poor coupling conditions.