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At least 73 records · Page 4

Modelling the limiter ramp-up of WEST for addressing the future challenges of ITER

This paper presents a joint experimental and numerical investigation into the physics of long limited plasma ramp-up in tokamaks with tungsten (W) first walls, a critical phase for ITER operation. The comparison between the average plasma quantities simulated using the SolEdge-HDG code and the measurements taken during three successive WEST discharges after boronisation shows how challenging it is to predict this phase. While simulations reproduce the general trends at the midplane, with reasonable match in density profiles, they consistently underestimate core temperatures possibly due to too large perpendicular heat conductivity. On the contrary, at the high field side (HFS) limiter, simulations overestimate the measured quantities, and highlights the limitation of using Bohm boundary conditions at grazing magnetic angles. Experimental measurements reveal that the boron layer is rapidly eroded, on a timescale comparable to a single ITER discharge. The subsequent transition from a boron-coated to a tungsten wall increases recycling and significantly degrades the core plasma, reducing the electron temperature by nearly half due to W contamination, despite wall parameters remaining stable. Furthermore, comparisons with Langmuir probes, bolometry, reflectometry, and spectroscopy indicate that the experimental far scrape-Off layer (SOL) is significantly wider than simulated. This wide SOL implies that boron erosion extends along the entire HFS limiter rather than being confined to the contact point. This work highlights some characteristics of the plasma during this phase of the discharge and emphasizes the current modelling issues that need to be resolved in order to obtain reliable predictions concerning the ITER ramp-up.

ITER

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING

In-Field Testing of Components for Feedback and Control of the ITER Disruption Mitigation System

Here, the shattered pellet injection (SPI) method has been chosen as the disruption mitigation system (DMS) for ITER. To protect the device from plasma disruptions that cause damaging heat and electromagnetic loads, SPI is used to inject high-Z material into the plasma. The process of SPI utilizes cryogenic cooling to form solid pellets. Pellets are accelerated down a barrel and into an angled surface, causing the pellet to shatter prior to entering the tokamak chamber. For the DMS to function reliably, the 27 separate shattered pellet injectors planned for ITER must rely on many components to provide accurate feedback data and for control functions. Each component in the DMS is exposed to an elevated background magnetic field depending on its placement and proximity to the plasma chamber. A Helmholtz coil test stand that is operated at Oak Ridge National Laboratory was utilized to test the components in relevant background field levels to assess component performance. This paper details the test design and results for in-field component operation for a variety of components. This list includes the following components: two different network switches for camera connectivity, a VAT fast shutter valve intended to reduce the flow of SPI propellant gas into the torus, a solenoid control valve intended for use in the pellet formation process, pressure/vacuum switches to be used for feedback and control, a printed circuit board piezo pressure sensor to be used to measure breech pressure, and various relays for the high-voltage pulsed power supply used to drive the SPI propellant valve.

Disruption mitigation

Multi-device analysis of energy loss duration and pellet penetration with implications for shattered pellet injection in ITER

A robust disruption mitigation system (DMS) requires accurate characterization of key disruption timescales, one of the most notable being the thermal quench (TQ). Recent modeling of shattered pellet injection (SPI) into ITER plasmas, using JOREK and INDEX, suggests long TQ durations (6–10 ms) and slow cold front propagation due to the large plasma size. If validated, these predictions would have an impact on the desired pellet parameters and mitigation strategies for the ITER DMS. To resolve these questions, a database of SPI experiments from several small-to-large sized devices (J-TEXT, KSTAR, AUG, DIII-D, and JET) has been compiled under the auspices of the International Tokamak Physics Activity MHD, disruptions, and control topical group. Analysis of the energy loss duration (proxy for the TQ duration) with machine size is presented for both mixed neon/deuterium (Ne/D) SPI and pure deuterium (D) SPI. Several metrics for the energy loss onset (e.g. soft x-ray signal drop, I p dip, and radiation flash) were considered as the conventional metric, electron cyclotron emission, is often cut-off during SPI. Several scalings with different onset metrics showed an increase in energy loss duration with machine size. The energy loss duration was additionally shown to be a function of the ratio between the number of SPI neon atoms injected and the stored energy. Analysis of the pellet shard position relative to the cold front found that in larger devices, pellets are typically found inboard of the q = 2 surface at the energy loss onset. Lastly, the delay between the pellet shards hitting the q = 2 surface and the energy loss onset was additionally found to increase with machine size. This suggests that the pellet shards in large devices will penetrate faster and further than the cooling front.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Impact of window temperature variations on ITER toroidal interferometer and polarimeter (TIP) measurements

Abstract The toroidal interferometer and polarimeter (TIP) is one of the primary electron density diagnostics on ITER. To meet measurement requirements over several thousand seconds, environmental factors such as changes in the window temperature, air temperature, and humidity, which can cause uncompensated phase drifts, must be minimized. This paper reports measurements of the phase shift induced by ZnSe and BaF₂ windows as their temperature is varied utilizing the TIP prototype. To accomplish these measurements, test pieces of BaF₂ and ZnSe are placed in a small oven that is located in one leg of the 10.59/5.22 micron two-color interferometer TIP prototype. The oven temperature was varied from room temperature to ∼90 °C, which is slightly higher than the expected window temperatures on ITER. The vibration compensated phase shifts measured for these two materials are dϕᵥ꜀ /dT/L = 0.0121 and −0.275 deg. /°C/cm −1 for BaF₂ and ZnSe, respectively. From these measurements, it was concluded that temperature variations of the environmental/secondary confinement barrier window and primary vacuum window have to be suppressed within approximately 1°C and 2°C, respectively, in order to passively meet the electron density measurement requirements in ITER.

Akiyama, T (ORCID:0000000198469795)

Overview of T and D–T results in JET with ITER-like wall

In 2021 JET exploited its unique capabilities to operate with T and D–T fuel with an ITER-like Be/W wall (JET-ILW). This second major JET D–T campaign (DTE2), after DTE1 in 1997, represented the culmination of a series of JET enhancements—new fusion diagnostics, new T injection capabilities, refurbishment of the T plant, increased auxiliary heating, in-vessel calibration of 14 MeV neutron yield monitors—as well as significant advances in plasma theory and modelling in the fusion community. DTE2 was complemented by a sequence of isotope physics campaigns encompassing operation in pure tritium at high T-NBI power. Carefully conducted for safe operation with tritium, the new T and D–T experiments used 1 kg of T (vs 100 g in DTE1), yielding the most fusion reactor relevant D–T plasmas to date and expanding our understanding of isotopes and D–T mixture physics. Furthermore, since the JET T and DTE2 campaigns occurred almost 25 years after the last major D–T tokamak experiment, it was also a strategic goal of the European fusion programme to refresh operational experience of a nuclear tokamak to prepare staff for ITER operation. The key physics results of the JET T and DTE2 experiments, carried out within the EUROfusion JET1 work package, are reported in this paper. Progress in the technological exploitation of JET D–T operations, development and validation of nuclear codes, neutronic tools and techniques for ITER operations carried out by EUROfusion (started within the Horizon 2020 Framework Programme and continuing under the Horizon Europe FP) are reported in (Litaudon et al Nucl. Fusion accepted), while JET experience on T and D–T operations is presented in (King et al Nucl. Fusion submitted).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Eliminating Signal Bias Caused by Vacuum System Backstreaming in the Diagnostic Residual Gas Analyzer of ITER

In fusion neutral gas analysis, such as with the Diagnostic Residual Gas Analyzer (DRGA) for ITER, the primary measurement range of interest comprises the low-amu species (1 to 6), especially deuterium and helium. The challenge in successfully obtaining accurate measurements is two-fold. First, the sensitivity of the method must be sufficient to resolve trace amounts accurately; typically, one percent or less. Second, the gas signal from the fusion processes must be free of bias caused by the latent presence (from system outgassing and/or vacuum backstreaming) of these gases to enable accurate interpretation of the measured signal. This latter criterion can be problematic for the lightest gases since there is a propensity for some fraction of the pumped gas load to undergo a phenomenon known as backstreaming. This behavior is manifested in pumping systems for gas properties related to relative atomic weight (lightest) and size (smallest). Backstreaming results in a significant amount of the pumped gas undertaking a reverse flow and re-entering the measurement region; thus, contaminating the forward, real-time measurement. To fully eliminate this adverse effect, a conductance-limiting device – or orifice – has been installed in the high-vacuum pumping system of the present ITER DRGA prototype. The system was already equipped with a secondary turbomolecular pump (TMP), but with limited effectiveness against backstreaming in the inter-pump volume (IPV). This orifice is placed within the suction inlet coupling of the secondary TMP, which is downstream of the IPV. Its objective is to eliminate the backstreaming phenomenon by increasing the back pressure in the IPV. However, the orifice sizing must take into consideration other factors, such as the diagnostic measurement objectives. For example, in the ITER DRGA, one of the measurement requirements is a dynamic response time of ~1s. Fortunately, an added benefit of the pumping restriction created by the orifice is that the upstream pressure increase is beneficial for the DRGA’s optical gas analysis (OGA) sensors. These sensors are attached to the IPV in the present design. The glow discharges, when used as an OGA light source, will typically have a brighter light emission with increasing plasma cell pressure. In addition to the fusion machine research sector, there are other potential applications of this pumping technique where the monitoring of lighter gas concentrations is essential, such as the photolithography process for the semiconductor fabrication of integrated circuits. This presentation will describe the vacuum system used to demonstrate a process to eliminate backstreaming as well as show test results to verify the accomplishment of this critical objective.

Marcus, Chris

A successive overrelaxation iterative technique for an adaptive equalizer

An adaptive strategy for the equalization of pulse-amplitude-modulated signals in the presence of intersymbol interference and additive noise is reported. The successive overrelaxation iterative technique is used as the algorithm for the iterative adjustment of the equalizer coefficents during a training period for the minimization of the mean square error. With 2-cyclic and nonnegative Jacobi matrices substantial improvement is demonstrated in the rate of convergence over the commonly used gradient techniques. The Jacobi theorems are also extended to nonpositive Jacobi matrices. Numerical examples strongly indicate that the improvements obtained for the special cases are possible for general channel characteristics. The technique is analytically demonstrated to decrease the mean square error at each iteration for a large range of parameter values for light or moderate intersymbol interference and for small intervals for general channels. Analytically, convergence of the relaxation algorithm was proven in a noisy environment and the coefficient variance was demonstrated to be bounded.

Kosovych, O. S.

Iterative methods for plasma sheath calculations: Application to spherical probe

The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.

Parker, L. W.

Convergence of an iterative procedure for large-scale static analysis of structural components

The paper proves convergence of an iterative procedure for calculating the deflections of built-up component structures which can be represented as consisting of a dominant, relatively stiff primary structure and a less stiff secondary structure, which may be composed of one or more substructures that are not connected to one another but are all connected to the primary structure. The iteration consists in estimating the deformation of the primary structure in the absence of the secondary structure on the assumption that all mechanical loads are applied directly to the primary structure. The j-th iterate primary structure deflections at the interface are imposed on the secondary structure, and the boundary loads required to produce these deflections are computed. The cycle is completed by applying the interface reaction to the primary structure and computing its updated deflections. It is shown that the mathematical condition for convergence of this procedure is that the maximum eigenvalue of the equation relating primary-structure deflection to imposed secondary-structure deflection be less than unity, which is shown to correspond with the physical requirement that the secondary structure be more flexible at the interface boundary.

Austin, F.

An iterative decoupling solution method for large scale Lyapunov equations

A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

Athay, T. M.

Comparison of results obtained by solving the radiative transfer equation with an iterative method and a spherical harmonics method

Fluxes and intensities of light scattered by a model atmosphere are computed by a spherical harmonics approximation and by an iterative method of solving the radiative transfer equation and are compared. The large differences in the net fluxes and intensities reported by Dave and Armstrong (1974) for the two methods are reduced here by making a few changes in the iterative routine. Decreasing the polar angle increment from 2 to 1 deg in the iterative method of computing the source function does not improve the results as suggested by Dave and Armstrong.

Bahethi, O. P.

A block iterative LU solver for weakly coupled linear systems

A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.

Cooke, C. H.

A multigrid algorithm for steady transonic potential flows around aerofoils using Newton iteration

The application of multigrid relaxation to transonic potential flow calculation was investigated. Conservative potential flows around aerofoils were taken as test problems. The solution algorithm was based on Newton iteration. It was found that the iteration to the circulation has to be kept outside the multigrid algorithm. To obtain meaningful norms of residuals, difference formulas with asymptotic scaling were introduced. Nonlinear instability problems were solved by upwind differencing using mass flux vector splitting instead of artificial viscosity or artificial density. It is suggested that the algorithms efficiency be increased by improving the iteration on the shock positions even though this is a highly nonlinear process.

Boestoel, J. W.

An iterative finite element-integral technique for predicting sound radiation from turbofan inlets

A new iterative solution technique for predicting the sound field radiated from a turbofan inlet is presented. The sound field is divided into two regions; the sound field within the inlet which is computed using the finite element method and the radiation field outside the inlet which is calculated using an integral solution technique. A 'unified' solution is obtained by matching the finite element and integral solutions at the interface between the interior and exterior regions. The applicability of the iterative technique is demonstrated by considering several simple cases for which exact or 'classical' solutions for the sound field are available. These examples show that the proper solution is obtained within five iterations. The overall accuracy of the method is demonstrated by comparison with experimental data.

Horowitz, S. J.

An iterative finite element-integral technique for predicting sound radiation from turbofan inlets in steady flight

A new iterative solution technique for predicting the sound field radiated from a turbofan inlet in steady flight is presented. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. The applicability of the iterative technique is demonstrated by comparison of experimental results with the theoretical results for several different inlet configurations with and without flow. These examples show that good agreement between experiment and theory is obtained within five iterations.

Horowitz, S. J.

Accelerating an iterative process by explicit annihilation

A slowly convergent stationary iterative process can be accelerated by explicitly annihilating (i.e., eliminating) the dominant eigenvector component of the error. The dominant eigenvalue or complex pair of eigenvalues can be estimated from the solution during the iteration. The corresponding eigenvector or complex pair of eigenvectors can then be annihilated by applying an explicit Richardson process over the basic iterative method. This can be done entirely in real arithmetic by analytically combining the complex conjugate annihilation steps. The technique is applied to an implicit algorithm for the calculation of two dimensional steady transonic flow over a circular cylinder using the equations of compressible inviscid gas dynamics. This demonstrates the use of explicit annihilation on a nonlinear problem.

Jespersen, D. C.

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.