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At least 1,477 records · Page 82

Gas-driven permeation of deuterium through tungsten and tungsten alloys

Here, to address the transport and trapping of hydrogen isotopes, several permeation experiments are being pursued at both Sandia National Laboratories (deuterium gas-driven permeation) and Idaho National Laboratories (tritium gas- and plasma-driven tritium permeation). These experiments are in part a collaboration between the US and Japan to study the performance of tungsten at divertor relevant temperatures (PHENIX). Here we report on the development of a high temperature (≤1150 °C) gas-driven permeation cell and initial measurements of deuterium permeation in several types of tungsten: high purity tungsten foil, ITER-grade tungsten (grains oriented through the membrane), and dispersoid-strengthened ultra-fine grain (UFG) tungsten being developed in the US. Experiments were performed at 500–1000 °C and 0.1–1.0 atm D 2 pressure. Permeation through ITER-grade tungsten was similar to earlier W experiments by Frauenfelder (1968–69) and Zaharakov (1973). Data from the UFG alloy indicates marginally higher permeability (< 10×) at lower temperatures, but the permeability converges to that of the ITER tungsten at 1000 °C. The permeation cell uses only ceramic and graphite materials in the hot zone to reduce the possibility for oxidation of the sample membrane. Sealing pressure is applied externally, thereby allowing for elevation of the temperature for brittle membranes above the ductile-to-brittle transition temperature.

36 MATERIALS SCIENCE↗

Multigrid in energy preconditioner for Krylov solvers

We have added a new multigrid in energy (MGE) preconditioner to the Denovo discrete-ordinates radiation transport code. This preconditioner takes advantage of a new multilevel parallel decomposition. A multigroup Krylov subspace iterative solver that is decomposed in energy as well as space-angle forms the backbone of the transport solves in Denovo. The space-angle-energy decomposition facilitates scaling to hundreds of thousands of cores. The multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of Krylov iterations required for convergence. This preconditioner is well-suited for use with advanced eigenvalue solvers such as Rayleigh Quotient Iteration and Arnoldi.

97 MATHEMATICS AND COMPUTING↗

A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spatially adaptive stochastic methods for fluid–structure interactions subject to thermal fluctuations in domains with complex geometries

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid–structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation–dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs–Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with O(N) computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An algorithm for computing the 2D structure of fast rotating stars

Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditioner of the Jacobian matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Compression of tokamak boundary plasma simulation data using a maximum volume algorithm for matrix skeleton decomposition

This report demonstrates satisfactory data compression of SOLPS-ITER simulation output ranging from 2D fields, 1D profiles, and 0D scalar variables with a novel matrix decomposition approach. The singular value decomposition (SVD) scales poorly for large matrix sizes and is unsuited to the application on high dimensional data common to fusion plasma physics simulation. In this work, we employ the columns-submatrix-rows (CUR) matrix factorization technique in order to compute a low-rank approximation up to two orders of magnitude faster than the SVD, but within a nominal L2-norm relative error of ε = 10 –2 . In addition, the CUR approach maintains the original format of the data, in its extracted columns and rows, allowing for interpretable data storage at the original resolution of the simulation. We utilize an iterative algorithm to compute the CUR decomposition of simulation output by maximizing the volume, or linearly independent information content, of a low-rank submatrix contained within the data. Experiments over $\textit{n} × \textit{n}$ randomized test matrices with embedded rank-deficient features show that this maximum volume implementation of CUR matrix approximation has reduced asymptotic computational complexity on the order of n compared to the SVD, which scales approximately as $n^3$. These results show that the CUR technique can be used to effectively select time step snapshots (columns) of over 140 SOLPS-ITER output variables and the associated discretized coordinate timeseries (rows) allowing for reconstruction of the complete simulation dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling the asynchronous Jacobi method without communication delays

Asynchronous iterative methods for solving linear systems are gaining renewed interest due to the high cost of synchronization points in massively parallel codes. Historically, theory on asynchronous iterative methods has focused on asymptotic behavior, while the transient behavior remains poorly understood. In this paper, we study a model of the asynchronous Jacobi method without communication delays, which we call simplified asynchronous Jacobi. Simplified asynchronous Jacobi can be used to model asynchronous Jacobi implemented in shared memory or distributed memory with fast communication networks. Our analysis uses the idea of a propagation matrix, which is similar in concept to an iteration matrix. We show that simplified asynchronous Jacobi can continue to reduce the residual when some processes are slower than other processes. We also show that simplified asynchronous Jacobi can converge when synchronous Jacobi does not. We verify our analysis of simplified asynchronous Jacobi using results from asynchronous Jacobi implemented in shared and distributed memory.

97 MATHEMATICS AND COMPUTING↗

Inducing polarity in [VO{sub 3}]{sub n}{sup n-} chain compounds using asymmetric hydrogen-bonding networks

1,4-Bis(3-aminopropyl)piperazine, (R)-3-aminopiperidine and (S)-3-aminopiperidine were used in the syntheses of [C{sub 10}H{sub 26}N{sub 4}][VO{sub 3}]{sub 2}{center_dot}2H{sub 2}O, [(R)-C{sub 5}H{sub 14}N{sub 2}][VO{sub 3}]{sub 2} and [(S)-C{sub 5}H{sub 14}N{sub 2}][VO{sub 3}]{sub 2}, which all contain similar [VO{sub 3}]{sub n}{sup n-} chains. Inversion symmetry within the 1,4-bis(3-aminopropyl)piperazine allows for crystallization of [C{sub 10}H{sub 26}N{sub 4}][VO{sub 3}]{sub 2}{center_dot}2H{sub 2}O in a centrosymmetric space group, while the use of enantiomerically pure sources of either (R)-3-aminopiperidine or (S)-3-aminopiperidine forces crystallographic noncentrosymmetry. Moreover, asymmetry in the hydrogen-bonding networks between the metavanadate chains and either [(R)-3-aminopiperidineH{sub 2}]{sup 2+} or [(S)-3-aminopiperidineH{sub 2}]{sup 2+} cations directs alignment of the chains and crystallization in a polar space group (C2, no. 5). Component and net dipole moments were calculated using iterative-Hirshfeld partial atomic charges. [(R)-C{sub 5}H{sub 14}N{sub 2}][VO{sub 3}]{sub 2} and [(S)-C{sub 5}H{sub 14}N{sub 2}][VO{sub 3}]{sub 2} both display type 1 phase-matching capabilities and exhibit second harmonic generation activities of {approx}140 Multiplication-Sign {alpha}-SiO{sub 2}. - Graphical abstract: One centrosymmetric and a pair of polar noncentrosymmetric templated metavanadates were synthesized under mild hydrothermal conditions. Asymmetry in the hydrogen-bonding between either [(R)-C{sub 5}H{sub 14}N{sub 2}]{sup 2+} or [(S)-C{sub 5}H{sub 14}N{sub 2}]{sup 2+} and [VO{sub 3}]{sub n}{sup n-} chains results in polar structures that exhibit type 1 phase-matching capabilities. Hirshfeld surfaces were used to probe the hydrogen-bonding networks and component and net dipole moments were calculated from atomic positions and iterative-Hirshfeld partial charges. Highlights: Black-Right-Pointing-Pointer One centrosymmetric and a pair of polar templated metavanadate chain compounds are reported. Black-Right-Pointing-Pointer Asymmetry in the hydrogen-bonding networks drives the compound polarities. Black-Right-Pointing-Pointer Iterative-Hirshfeld partitioning was used to calculate partial atomic charges. Black-Right-Pointing-Pointer Net and component dipole moments are calculated for each compound. Black-Right-Pointing-Pointer Type 1 phase-matching behavior and SHG activities of {approx}140 Multiplication-Sign {alpha}-SiO{sub 2} are found.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-Rank Incremental Methods for Computing Dominant Singular Subspaces

Computing the singular values and vectors of a matrix is a crucial kernel in numerous scientific and industrial applications. As such, numerous methods have been proposed to handle this problem in a computationally efficient way. This paper considers a family of methods for incrementally computing the dominant SVD of a large matrix A. Specifically, we describe a unification of a number of previously disparate methods for approximating the dominant SVD via a single pass through A. We tie the behavior of these methods to that of a class of optimization-based iterative eigensolvers on A'*A. An iterative procedure is proposed which allows the computation of an accurate dominant SVD via multiple passes through A. We present an analysis of the convergence of this iteration, and provide empirical demonstration of the proposed method on both synthetic and benchmark data.

99 GENERAL AND MISCELLANEOUS↗

Effect of pedestal height and internal transport barriers on International Thermonuclear Experimental Reactor target steady state simulations

The Tokamak simulation code (TSC) is used to provide initial conditions for predictive TRANSPort and integrated modeling code (PTRANSP) simulations of ITER target steady state scenarios. The PTRANSP simulations are carried out using the new multi-mode (MMM7.1) and the gyro-Landau-fluid (GLF23) transport models. It is found that there are circumstances under which the total fusion power decreases with increasing pedestal temperature height. When the total current (from magnetic axis to plasma edge) is fixed, an increased fraction of the current is concentrated in the pedestal region as the pedestal height is increased. As a consequence of the fixed total current, this results a smaller fraction of the current in the core plasma and, consequently, lower energy confinement. In previous simulations of ITER, in which the fusion power increased with increasing pedestal temperature height, the plasma current from the top of the pedestal to the magnetic axis was held fixed independent of the pedestal temperature. Simulations presented in this paper also indicate that improvement in fusion power production occurs when the lower hybrid current drive is replaced with electron cyclotron current drive. Again, the improvement results from the redistribution of plasma current since the lower hybrid power generally drives current closer to the plasma edge than does the electron cyclotron power. ITER simulation results obtained using the MMM7.1 transport model are compared with those using the GLF23 model. It is found that, in simulations of target steady state scenarios, momentum transport and flow-shear suppression features of the new MMM7.1 model can lead to predictions of internal transport barriers in temperature and rotation frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lower hybrid current drive at plasma densities required for thermonuclear reactors

Driving current in high-density plasmas is essential for the progress of thermonuclear fusion energy research based on the tokamak concept. The lower hybrid current drive (LHCD) effect, is potentially the most suitable tool for driving current at large plasma radii, consistent with the needs of ITER steady state scenario. Unfortunately, experiments at reactor grade high plasma densities with kinetic profiles approaching those required for ITER, have shown problems in penetration of the LH power into the core plasma. These plasmas represent a basic reference for designing possible methods useful for assessing the LHCD concept in ITER. On the basis of the phenomenology observed during LHCD experiments carried out in different machines, and model of the spectral broadening effect due to parametric instability, an interpretation and possible solution of the related important problem is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Progress in the MITICA beam source design

In the framework of the development of the ITER neutral beam (NB) system, a test facility is planned to be built in Padova. A full size prototype of the ITER heating NB injector (MITICA) shall be built and tested at full beam power (17 MW) as per ITER requirements. The design of the MITICA beam source has further progressed following updated optimization and overall integration criteria. In the paper, the major design choices and revisions are presented, together with some results of numerical analyses carried out in order to assess the electrostatic and thermo-mechanical behaviour of the source.

43 PARTICLE ACCELERATORS↗

Formation and sustainment of internal transport barriers in the International Thermonuclear Experimental Reactor with the baseline heating mix

Plasmas with internal transport barriers (ITBs) are a potential and attractive route to steady-state operation in ITER. These plasmas exhibit radially localized regions of improved confinement with steep pressure gradients in the plasma core, which drive large bootstrap current and generate hollow current profiles and negative magnetic shear. This work examines the formation and sustainment of ITBs in ITER with electron cyclotron heating and current drive. The time-dependent transport simulations indicate that, with a trade-off of the power delivered to the equatorial and to the upper launcher, the sustainment of steady-state ITBs can be demonstrated in ITER with the baseline heating configuration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

First operation with the JET International Thermonuclear Experimental Reactor-like wall

To consolidate International Thermonuclear Experimental Reactor (ITER) design choices and prepare for its operation, Joint European Torus (JET) has implemented ITER's plasma facing materials, namely, Be for the main wall and W in the divertor. In addition, protection systems, diagnostics, and the vertical stability control were upgraded and the heating capability of the neutral beams was increased to over 30 MW. First results confirm the expected benefits and the limitations of all metal plasma facing components (PFCs) but also yield understanding of operational issues directly relating to ITER. H-retention is lower by at least a factor of 10 in all operational scenarios compared to that with C PFCs. The lower C content (≈ factor 10) has led to much lower radiation during the plasma burn-through phase eliminating breakdown failures. Similarly, the intrinsic radiation observed during disruptions is very low, leading to high power loads and to a slow current quench. Massive gas injection using a D{sub 2}/Ar mixture restores levels of radiation and vessel forces similar to those of mitigated disruptions with the C wall. Dedicated L-H transition experiments indicate a 30% power threshold reduction, a distinct minimum density, and a pronounced shape dependence. The L-mode density limit was found to be up to 30% higher than for C allowing stable detached divertor operation over a larger density range. Stable H-modes as well as the hybrid scenario could be re-established only when using gas puff levels of a few 10{sup 21} es{sup −1}. On average, the confinement is lower with the new PFCs, but nevertheless, H factors up to 1 (H-Mode) and 1.3 (at β{sub N}≈3, hybrids) have been achieved with W concentrations well below the maximum acceptable level.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterization of onset of parametric decay instability of lower hybrid waves

The goal of the lower hybrid current drive (LHCD) program on Alcator C-Mod is to develop and optimize ITER-relevant steady-state plasmas by controlling the current density profile. Using a 4×16 waveguide array, over 1 MW of LH power at 4.6 GHz has been successfully coupled to the plasmas. However, current drive efficiency precipitously drops as the line averaged density (nМ„{sub e}) increases above 10{sup 20}m{sup −3}. Previous numerical work shows that the observed loss of current drive efficiency in high density plasmas stems from the interactions of LH waves with edge/scrape-off layer (SOL) plasmas [Wallace et al., Physics of Plasmas 19, 062505 (2012)]. Recent observations of parametric decay instability (PDI) suggest that non-linear effects should be also taken into account to fully characterize the parasitic loss mechanisms [Baek et al., Plasma Phys. Control Fusion 55, 052001 (2013)]. In particular, magnetic configuration dependent ion cyclotron PDIs are observed using the probes near nМ„{sub e}≈1.2×10{sup 20}m{sup −3}. In upper single null plasmas, ion cyclotron PDI is excited near the low field side separatrix with no apparent indications of pump depletion. The observed ion cyclotron PDI becomes weaker in inner wall limited plasmas, which exhibit enhanced current drive effects. In lower single null plasmas, the dominant ion cyclotron PDI is excited near the high field side (HFS) separatrix. In this case, the onset of PDI is correlated with the decrease in pump power, indicating that pump wave power propagates to the HFS and is absorbed locally near the HFS separatrix. Comparing the observed spectra with the homogeneous growth rate calculation indicates that the observed ion cyclotron instability is excited near the plasma periphery. The incident pump power density is high enough to overcome the collisional homogeneous threshold. For C-Mod plasma parameters, the growth rate of ion sound quasi-modes is found to be typically smaller by an order of magnitude than that of ion cyclotron quasi-modes. When considering the convective threshold near the plasma edge, convective growth due to parallel coupling rather than perpendicular coupling is likely to be responsible for the observed strength of the sidebands. To demonstrate the improved LHCD efficiency in high density plasmas, an additional launcher has been designed. In conjunction with the existing launcher, this new launcher will allow access to an ITER-like high single pass absorption regime, replicating the J{sub LH}(r) expected in ITER. The predictions from the time domain discharge scenarios, in which the two launchers are used, will be also presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Influence of impurities on the transition from minority to mode conversion heating in ({sup 3}He)-H)- plasmas

Ion cyclotron resonance heating (ICRH) is one of the main auxiliary heating systems used in present-day tokamaks and is planned to be installed in ITER. In the initial full-field phase of ITER operating with hydrogen majority plasmas, fundamental resonance heating of helium-3 ions is one of a few ICRH schemes available. Past JET experiments with the carbon wall revealed a significant impact of impurities on the ICRH performance in ({sup 3}He)-H plasmas. A significant reduction of the helium-3 concentration, at which the transition from minority ion to mode conversion heating occurs, was found to be due to a high plasma contamination with carbon ions. In this paper we discuss the effect of Be and another impurity species present at JET after the installation of a new ITER-like wall on the transition helium-3 concentration in ({sup 3}He)-H plasmas. We suggest a potential method for controlling helium-3 level needed for a specific ICRH regime by puffing an extra helium-4 gas to the plasma.

36 MATERIALS SCIENCE↗

Electronic excitation spectra of molecules in solution calculated using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model with perturbative approach

A perturbative approximation of the state specific polarizable continuum model (PCM) symmetry-adapted cluster-configuration interaction (SAC-CI) method is proposed for efficient calculations of the electronic excitations and absorption spectra of molecules in solutions. This first-order PCM SAC-CI method considers the solvent effects on the energies of excited states up to the first-order with using the zeroth-order wavefunctions. This method can avoid the costly iterative procedure of the self-consistent reaction field calculations. The first-order PCM SAC-CI calculations well reproduce the results obtained by the iterative method for various types of excitations of molecules in polar and nonpolar solvents. The first-order contribution is significant for the excitation energies. The results obtained by the zeroth-order PCM SAC-CI, which considers the fixed ground-state reaction field for the excited-state calculations, are deviated from the results by the iterative method about 0.1 eV, and the zeroth-order PCM SAC-CI cannot predict even the direction of solvent shifts in n-hexane for many cases. The first-order PCM SAC-CI is applied to studying the solvatochromisms of (2,2{sup ′}-bipyridine)tetracarbonyltungsten [W(CO){sub 4}(bpy), bpy = 2,2{sup ′}-bipyridine] and bis(pentacarbonyltungsten)pyrazine [(OC){sub 5}W(pyz)W(CO){sub 5}, pyz = pyrazine]. The SAC-CI calculations reveal the detailed character of the excited states and the mechanisms of solvent shifts. The energies of metal to ligand charge transfer states are significantly sensitive to solvents. The first-order PCM SAC-CI well reproduces the observed absorption spectra of the tungsten carbonyl complexes in several solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Design, performance, and grounding aspects of the International Thermonuclear Experimental Reactor ion cyclotron range of frequencies antenna

ITER's Ion Cyclotron Range of Frequencies (ICRF) system [Lamalle et al., Fusion Eng. Des. 88, 517–520 (2013)] comprises two antenna launchers designed by CYCLE (a consortium of European associations listed in the author affiliations above) on behalf of ITER Organisation (IO), each inserted as a Port Plug (PP) into one of ITER's Vacuum Vessel (VV) ports. Each launcher is an array of 4 toroidal by 6 poloidal RF current straps specified to couple up to 20 MW in total to the plasma in the frequency range of 40 to 55 MHz but limited to a maximum system voltage of 45 kV and limits on RF electric fields depending on their location and direction with respect to, respectively, the torus vacuum and the toroidal magnetic field. A crucial aspect of coupling ICRF power to plasmas is the knowledge of the plasma density profiles in the Scrape-Off Layer (SOL) and the location of the RF current straps with respect to the SOL. The launcher layout and details were optimized and its performance estimated for a worst case SOL provided by the IO. The paper summarizes the estimated performance obtained within the operational parameter space specified by IO. Aspects of the RF grounding of the whole antenna PP to the VV port and the effect of the voids between the PP and the Blanket Shielding Modules (BSM) surrounding the antenna front are discussed. These blanket modules, whose dimensions are of the order of the ICRF wavelengths, together with the clearance gaps between them will constitute a corrugated structure which will interact with the electromagnetic waves launched by ICRF antennas. The conditions in which the grooves constituted by the clearance gaps between the blanket modules can become resonant are studied. Simple analytical models and numerical simulations show that mushroom type structures (with larger gaps at the back than at the front) can bring down the resonance frequencies, which could lead to large voltages in the gaps between the blanket modules and perturb the RF properties of the antenna if they are in the ICRF operating range. The effect on the wave propagation along the wall structure, which is acting as a spatially periodic (toroidally and poloidally) corrugated structure, and hence constitutes a slow wave structure modifying the wall boundary condition, is examined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗