scholarly journals Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

2019 ◽  
Vol 85 (2) ◽  
Author(s):  
Thomas Antonsen ◽  
Elizabeth J. Paul ◽  
Matt Landreman
Keyword(s):  
Figure Of Merit ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Flux Surface ◽  
Shape Gradient ◽  
Onsager Symmetry ◽  
Mhd Equilibria ◽  
Gradient Based ◽  
Adjoint Approach

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.

scholarly journals Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Part 2. Applications

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Elizabeth J. Paul ◽  
Thomas Antonsen ◽  
Matt Landreman ◽  
W. Anthony Cooper
Keyword(s):  
Figure Of Merit ◽  
Three Dimensional ◽  
Plasma Boundary ◽  
Plasma Phys ◽  
Numerical Verification ◽  
Shape Gradient ◽  
Characteristic Quantity ◽  
Mhd Equilibria ◽  
Adjoint Approach ◽  
Magnetic Well

The shape gradient is a local sensitivity function defined on the surface of an object which provides the change in a characteristic quantity, or figure of merit, associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity analysis and tolerance calculations. However, it is generally expensive to compute from finite-difference derivatives for shapes that are described by many parameters, as is the case for typical stellarator geometry. In an accompanying work (Antonsen, Paul & Landreman J. Plasma Phys., vol. 85 (2), 2019), generalized self-adjointness relations are obtained for magnetohydrodynamic (MHD) equilibria. These describe the relation between perturbed equilibria due to changes in the rotational transform or toroidal current profiles, displacements of the plasma boundary, modifications of currents in the vacuum region or the addition of bulk forces. These are applied to efficiently compute the shape gradient of functions of MHD equilibria with an adjoint approach. In this way, the shape derivative with respect to any perturbation applied to the plasma boundary or coil shapes can be computed with only one additional MHD equilibrium solution. We demonstrate that this approach is applicable for several figures of merit of interest for stellarator configuration optimization: the magnetic well, the magnetic ripple on axis, the departure from quasisymmetry, the effective ripple in the low-collisionality $1/\unicode[STIX]{x1D708}$ regime $(\unicode[STIX]{x1D716}_{\text{eff}}^{3/2})$ (Nemov et al. Phys. Plasmas, vol. 6 (12), 1999, pp. 4622–4632) and several finite-collisionality neoclassical quantities. Numerical verification of this method is demonstrated for the magnetic well figure of merit with the VMEC code (Hirshman & Whitson Phys. Fluids, vol. 26 (12), 1983, p. 3553) and for the magnetic ripple with modification of the ANIMEC code (Cooper et al. Comput. Phys. Commun., vol. 72 (1), 1992, pp. 1–13). Comparisons with the direct approach demonstrate that, in order to obtain agreement within several per cent, the adjoint approach provides a factor of $O(10^{3})$ in computational savings.

scholarly journals Low-shear three-dimensional equilibria in a periodic cylinder

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
Erin Jaquiery ◽  
Wrick Sengupta
Keyword(s):  
Three Dimensional ◽  
Power Series Expansion ◽  
Flat Torus ◽  
Flux Surface ◽  
Mhd Equilibria ◽  
Convergence Proofs ◽  
Field Lines ◽  
Ideal Magnetohydrodynamic ◽  
Physical Quantities ◽  
Low Shear

We carry out expansions of non-symmetric toroidal ideal magnetohydrodynamic (MHD) equilibria with nested flux surfaces about a periodic cylinder, in which physical quantities are periodic of period$2\unicode[STIX]{x03C0}$in the cylindrical angle$\unicode[STIX]{x1D703}$and$z$. The cross-section of a flux surface at a constant toroidal angle is assumed to be approximately circular, and data are given on the cylindrical flux surface$r=1$. Furthermore, we assume that the magnetic field lines are closed on the lowest-order flux surface, and the magnetic shear is relatively small. We extend earlier work in a flat torus by Weitzner (Phys. Plasmas, vol. 23, 2016, 062512) and demonstrate that a power series expansion can be carried out to all orders using magnetic flux as an expansion parameter. The cylindrical metric introduces certain new features to the expansions compared to the flat torus. However, the basic methodology of dealing with resonance singularities remains the same. The results, even though lacking convergence proofs, once again support the possibility of smooth, low-shear non-symmetric toroidal MHD equilibria.

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

Experimental and simulation study of impurity transport response to RMPs in RF-heated H-mode plasmas at EAST

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Germán Vogel ◽  
Hongming Zhang ◽  
Yongcai Shen ◽  
Shuyu Dai ◽  
Youwen Sun ◽  
...  
Keyword(s):  
Inner Core ◽  
Extreme Ultraviolet ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Line Emission ◽  
Core Region ◽  
Emission Mitigation ◽  
One Dimensional ◽  
Impurity Transport ◽  
Transport Code

Spatial profiles of impurity emission measurements in the extreme ultraviolet (EUV) spectroscopic range in radiofrequency (RF)-heated discharges are combined with one-dimensional and three-dimensional transport simulations to study the effects of resonant magnetic perturbations (RMPs) on core impurity accumulation at EAST. The amount of impurity line emission mitigation by RMPs appears to be correlated with the ion Z for lithium, carbon, iron and tungsten monitored, i.e. stronger suppression of accumulation for heavier ions. The targeted effect on the most detrimental high-Z impurities suggests a possible advantage using RMPs for impurity control. Profiles of transport coefficients are calculated with the STRAHL one-dimensional impurity transport code, keeping $\nu /D$ fixed and using the measured spatial profiles of $\textrm{F}{\textrm{e}^{20 + }}$ , $\textrm{F}{\textrm{e}^{21 + }}$ and $\textrm{F}{\textrm{e}^{22 + }}$ to disentangle the transport coefficients. The iron diffusion coefficient ${D_{\textrm{Fe}}}$ increases from $1.0- 2.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ to $1.5- 3.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ from the core region to the edge region $(\rho \gt 0.5)$ after the onset of RMPs. Meanwhile, an inward pinch of iron convective velocity ${\nu _{\textrm{Fe}}}$ decreases in magnitude in the inner core region and increases significantly in the outer confined region, simultaneously contributing to preserving centrally peaked $\textrm{Fe}$ profiles and exhausting the impurities. The ${D_{\textrm{Fe}}}$ and ${\nu _{\textrm{Fe}}}$ variations lead to reduced impurity contents in the plasma. The three-dimensional edge impurity transport code EMC3-EIRENE was also applied for a case of RMP-mitigated high-Z accumulation at EAST and compared to that of low-Z carbon. The exhaust of ${\textrm{C}^{6 + }}$ toward the scrape-off layer accompanying an overall suppression of heavier ${\textrm{W}^{30 + }}$ is observed when using RMPs.

Instability of isolated three-dimensional magnetic null points

1998 ◽  
Vol 59 (3) ◽  
pp. 537-541 ◽  
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Null Point ◽  
Static Equilibrium ◽  
Flux Surface ◽  
Form Part ◽  
Magnetic Null ◽  
Transverse Oscillations

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

A High Fidelity Quality Assessment of High Pressure Turbine Blades Using Surface Curvature and Gradient-Based Adjoint

2018 ◽  
Author(s):  
Akhil Mulloth ◽  
Gabriel Banks ◽  
Giulio Zamboni ◽  
Simon Bather
Keyword(s):  
Quality Assessment ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Surface Curvature ◽  
Assessment Process ◽  
Screening Process ◽  
Profile Tolerance ◽  
Gradient Based ◽  
Parts Manufacturing ◽  
The Impact

Gas turbine performance is highly dependent on the quality of the manufactured parts. Manufacturing variations in the parts can significantly alter the performance, especially efficiency and thus SFC. The legacy process is to accept variations within predefined profile tolerance limits and a few other qualitative parameters, mostly at a few, key two-dimensional aerofoil sections. With the widespread use of White light scans and other similar three-dimensional scans, this has improved to include the three-dimensional profile. The future however may lie with performance based quality assessment of manufactured parts, combined with quantitative surface quality assessment to implement an intelligent screening process for the parts. The adjoint method, typically used for shape optimization is adapted to provide a prediction of the impact on performance due to manufacturing variations. The work presented outlines a three stage quality assessment process for manufactured parts, involving three-dimensional profile tolerance based screening, followed by a surface curvature based screening and finally an Adjoint based performance prediction.

Three-Dimensional CFD Model of Pressure Drop in µTAS Devices in a Microchannel

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Damena D. Agonafer ◽  
J. Yeom ◽  
M. A. Shannon
Keyword(s):  
Pressure Drop ◽  
Figure Of Merit ◽  
Flow Resistance ◽  
Three Dimensional ◽  
Design Rule ◽  
Dynamics Model ◽  
Enhance Heat Transfer ◽  
Micro Total Analysis Systems ◽  
Total Analysis ◽  
Adsorption Desorption

Microposts are utilized to enhance heat transfer, adsorption/desorption, and surface chemical reactions. In a previous study [Yeom et al., J. Micromech. Microeng., 19, p. 065025 (2009)], based in part on an experimental study, an analytical expression was developed to predict the pressure drop across a microchannel filled with arrays of posts with the goal of fabricating more efficient micro-total analysis systems (µTAS) devices for a given pumping power. In particular, a key figure of merit for the design of micropost-filled reactors, based on the flow resistance models was reported thus providing engineers with a design rule to develop efficient µTAS devices. The study did not include the effects of the walls bounding the microposts. In this paper, a three-dimensional computational fluid dynamics model is used to include the effects of three-dimensionality brought about by the walls of the µTAS devices that bound the microposted structures. In addition, posts of smaller size that could not be fabricated for the experiments were also included. It is found that the two- and three-dimensional effects depend on values of the aspect ratio and the blockage ratios. The Reynolds number considered in the experiment that ranged from 1 to 10 was extended to 300 to help determine the range of Re for which the FOM model is applicable.

scholarly journals Densely distributed and real-time scour hole monitoring using piezoelectric rod sensors

2019 ◽  
Vol 22 (16) ◽  
pp. 3395-3411
Author(s):  
Morgan L Funderburk ◽  
Shieh-Kung Huang ◽  
Chin-Hsiung Loh ◽  
Kenneth J Loh
Keyword(s):  
Monitoring System ◽  
Fundamental Frequency ◽  
Polyvinylidene Fluoride ◽  
Three Dimensional ◽  
Piezoelectric Element ◽  
Direct Calculation ◽  
Thin Strip ◽  
Scour Depth ◽  
Scour Monitoring ◽  
Dry Conditions

This study aims to validate a piezoelectric driven-rod scour monitoring system that can sense changes in scour depth along the entire rod at its instrumented location. The proposed sensor is a polymeric slender rod with a thin strip of polyvinylidene fluoride that runs through its midline. Extraction of the fundamental frequency allows the direct calculation of the exposed length (or scour depth) of the slender rod undergoing fluid flow excitation. First, laboratory validation in dry conditions is presented. Second, hydrodynamic testing of the sensor system in a soil-bed flume is discussed. Each rod was installed using a three-dimensional-printed footing designed for ease of installation and stabilization during testing. The sensors were installed in a layout designed to capture symmetric scour conditions around a scaled pier. In order to analyze the system out of steady-state conditions, water velocity was increased in stages during testing to induce different degrees of scour. As ambient water flow excited the portion of the exposed rods, the embedded piezoelectric element outputted a time-varying voltage signal. Different methods were then employed to extract the fundamental frequency of each rod, and the results were compared. Further testing was also performed to characterize the relationship between frequency outputs and flow velocity, which were previously thought to be independent. In general, the proposed driven-rod scour monitoring system successfully captured changing frequencies under varied flow conditions.

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