Edge Rotation Research Articles

Non-linear dependence of ion heat flux on plasma density at the L-H transition of JET NBI-heated Deuterium-Tritium plasmas

Abstract Recent JET D-T campaigns opened the possibility of unique isotope studies to investigate the L-H transition physics in view of reactor plasmas and to study the origin of the observed power threshold minimum. In the present paper, we characterise L-H transitions in the low and high-density branches of JET NBI-heated D-T plasmas. As discussed in the paper, L-H transition has been hypothesised to be determined by the transport power losses of plasma ions, i.e. the so-called ion heat flux (Qi). We present the first power balance analysis of JET NBI-heated D-T plasmas to evaluate the ion heat flux at the transition. Due to the experimental setting being similar to previous JET D experiments, we also directly compare the results, discussing the isotope effect and similarities between datasets. First, we find an isotope effect between D and D-T Qi, with a lower Qi in D-T plasmas. We confirm that the ion heat flux deviates from density linearity compared to the linear trend observed in wave-heated D plasmas of other tokamaks. The deviation we observe in NBI-heated L-H transitions happens at an isotope-dependent density. Plasma edge rotation correlates with Qi deviation from density linearity in the low-density branch. However, further investigations would be required to assess the role of rotation on Qi and the power threshold minimum at JET. At low plasma density, NBI power dominates Qi, while increasing the density makes the equipartition power dominant. We finally compare our results with hypotheses proposed from evidence in other tokamaks to present a complete overview of ion heat flux analyses in D and D-T NBI-heated plasmas at JET.

Simultaneous reduction of tungsten and rotation in the core region induced by RMP

Abstract Tungsten (W) impurity control is critical for plasma performance and a priority for ITER. The simultaneous reduction of W and rotation in the core region induced by resonant magnetic perturbations (RMPs) has been found and understood in EAST. A positive feedback loop between the W and rotation is first proposed, resulting in core W accumulation and high rotation even in low-torque plasma before the RMP application. This cycle can be reversed by the edge rotation braking induced by RMP, causing a significant simultaneous reduction of W concentration and rotation. These new mechanisms are based on several repeatable experiments and confirmed by the modeling results from TGYRO and NTVTOK. It provides a new understanding of the RMP effects on W and rotation and can be used for W and rotation control in future reactors.

Effects on the algebraic connectivity of weighted graphs under edge rotations

For a weighted graph G, the rotation of an edge uv1 from v1 to a vertex v2 is defined as follows: delete the edge uv1, set w(uv2) as w(uv1)+w(uv2) if uv2 is an edge of G; otherwise, add a new edge uv2 and set w(uv2)=w(uv1), where w(uv1) and w(uv2) are the weights of the edges uv1 and uv2, respectively. In this paper, effects on the algebraic connectivity of weighted graphs under edge rotations are studied. For a weighted graph, a sufficient condition for an edge rotation to reduce its algebraic connectivity and a necessary condition for an edge rotation to improve its algebraic connectivity are proposed based on Fiedler vectors of the graph. As applications, we show that, by using a series of edge rotations, a pair of pendent paths (a pendent tree) of a weighted graph can be transformed into one pendent path (pendent edges attached at a common vertex) of the graph with the algebraic connectivity decreasing (increasing) monotonically. These results extend previous findings of reducing the algebraic connectivity of unweighted graphs by using edge rotations.

Effect of rotation on negative triangularity plasmas in DIII-D

Abstract At the DIII-D tokamak, plasmas with negative triangularity (NT) have been found to have similar energy confinement times as H-mode plasmas with positive triangularity. These NT plasmas also have a stable edge that inhibits H-mode, lacks dangerous edge transients, and has naturally low impurity confinement. For these reasons, NT plasmas have the potential to be a transformative reactor scenario. To determine the importance of strong co-current neutral beam torque for NT performance at DIII-D, scans of neutral beam torque at constant neutral beam power have been performed. These scans have shown that the energy confinement time for a basic, inductive NT scenario ( q 95 ≈ 2.8 ) decreases by 16% when torque is reduced to reactor levels. This reduction in confinement can be replicated with gyrofluid modeling that isolates the role of E × B shear in the change in transport. In a separate set of discharges with lower plasma current ( q 95 ≈ 4.2 ), no significant correlation between confinement time and rotation was found. Throughout this investigation, excellent MHD stability was observed, even with very low toroidal rotation. Further, low impurity confinement was found at multiple rotation levels. Throughout the campaign, rotation near the edge was counter-current, consistent with the measurement of counter-current intrinsic edge rotation, and these observations agree with NT results from the TCV tokamak.

Destabilizing effects of edge infernal components on resistive wall modes in advanced tokamak scenarios

The stability of the n = 1 resistive wall modes (RWMs) dominated by the pressure-driven infernal components is investigated using the ideal magnetohydrodynamics (MHD) code AEGIS for the advanced tokamak scenarios. Here, n is the toroidal mode number. In the advanced tokamak scenarios, due to the large fraction of bootstrap current contribution, the profile of safety factor q is deeply reversed in magnetic shear in the central core region and locally flattened within the edge pedestal. Consequently, the pressure-driven infernal components develop in the corresponding flat-q regions of both core and edge. However, the edge infernal components dominate the n = 1 RWM structure and lead to lower βN limits for the advanced tokamak scenarios. In the framework of ideal MHD, the edge rotation is found the most critical to the stabilization due to the dominant influence of the edge infernal components, which should be maintained sufficiently large in magnitude and range in order for the rotation alone to fully suppress the n = 1 RWM in typical advanced tokamak scenarios.

Relationship between Edge Magnetic Field and Rotation of the Spatial Structure of Visible Light Emitted from Low Aspect RFP Plasmas on RELAX

Relationship between Edge Magnetic Field and Rotation of the Spatial Structure of Visible Light Emitted from Low Aspect RFP Plasmas on RELAX

Experimental study of the edge radial electric field in different drift configurations and its role in the access to H-mode at ASDEX Upgrade

The formation of the equilibrium radial electric field (Er) has been studied experimentally at ASDEX Upgrade (AUG) in L-modes of “favorable” (ion ∇ B-drift toward primary X-point) and “unfavorable” (ion ∇ B-drift away from primary X-point) drift configurations, in view of its impact on H-mode access, which changes with drift configurations. Edge electron and ion kinetic profiles and impurity velocity and mean-field Er profiles across the separatrix are investigated, employing new and improved measurement techniques. The experimental results are compared to local neoclassical theory as well as to a simple 1D scrape-off layer (SOL) model. It is found that in L-modes of matched heating power and plasma density, the upstream SOL Er and the main ion pressure gradient in the plasma edge are the same for either drift configurations, whereas the Er well in the confined plasma is shallower in unfavorable compared to the favorable drift configuration. The contributions of toroidal and poloidal main ion flows to Er, which are inferred from local neoclassical theory and the experiment, cannot account for these observed differences. Furthermore, it is found that in the L-mode, the intrinsic toroidal edge rotation decreases with increasing collisionality and it is co-current in the banana-plateau regime for all different drift configurations at AUG. This gives rise to a possible interaction of parallel Pfirsch–Schlüter flows in the SOL with the confined plasma. Thus, the different H-mode power threshold for the two drift configurations cannot be explained in the same way at AUG as suggested by LaBombard et al. [Phys. Plasmas 12, 056111 (2005)] for Alcator C-Mod. Finally, comparisons of Er profiles in favorable and unfavorable drift configurations at the respective confinement transitions show that also the Er gradients are all different, which indirectly indicates a different type or strength of the characteristic edge turbulence in the two drift configurations.

Stability analysis of fractured rock masses based on an extended key block theory considering the forces between blocks and block rotation

Key block theory is a widely used method in rock engineering for analyzing the stability of fractured rock masses. However, the traditional theory does not consider the forces between blocks and block rotation very well, its results may differ from real conditions. Therefore, we proposed an extended key block theory by considering the forces between blocks and block rotation. The forces between blocks were calculated by a displacement constraint method of the rigid body based on 3DEC platform. In the analysis of block rotation, block rotatability was analyzed by a geometric condition and mechanical condition. Net moments and rotational safety factors of movable blocks were calculated to judge whether the block rotates. Considering block rotation along an edge and block translation, block failure modes can be divided into free falling, single-plane sliding, double-plane sliding, edge rotation, and sliding rotation. We created a 3DEC-KBM program that incorporates the extended method into the 3DEC platform. This method not only obtains more accurate forces between blocks but also has more efficiency compared with the direct application of 3DEC. The correctness of this method was verified by the 3DEC results of a single-block slope model, and it was adopted to analyze the stability of a fractured rock slope and fractured rock masses surrounding an underground cavern. The research results showed the following: (1) The forces between blocks often decrease block stability, but also improve the stability of some blocks; (2) The forces between blocks is easier to make the blocks rotation comparing with the case only considering the gravity effect, because of the changing position and direction of the resultant force acting on a block; (3) Compared with the traditional key block theory, the extended method has higher accuracy and it is necessary to consider the blocks’ rotation when taking the forces between blocks into account.

Torsional behavior of GFRP-reinforced concrete pontoon decks with and without an edge cutout

Using glass fiber-reinforced polymer (GFRP) bars in precast concrete pontoon decks in aggressive marine environments would eliminate corrosion problems encountered with steel reinforcement. Although wave action usually subjects pontoon decks to torsion, but little is known about the behavior of such structures. Moreover, nothing is known about the effects of cutouts on the torsional behavior of pontoon decks. This study experimentally investigated the torsional behavior of GFRP-reinforced concrete (RC) pontoon decks in terms of the effect of edge cutouts, reinforcement-bar distribution, and rotation direction. The results show that the bar configuration affected the failure behavior and torsional capacity of the GFRP-reinforced concrete decks under torsion. The decks with double-layer reinforcement exhibited slower and narrower cracking growth in the post-cracking stage than the decks with single-layer reinforcement. In addition, the edge cutouts reduced the cracking torque of the solid rectangular decks by an average 17%. The torsional behavior of the GFRP-reinforced planks can be accurately described by the ACI318-14 equation in the cracking stage, while the decks’ post-cracking torsional rigidity can be predicted accurately from the contribution of the GFRP bars.

Self‐Assembly of Macrocyclic Triangles into Helicity‐Opposite Nanotwists by Competitive Planar over Point Chirality

AbstractWhile helix has elegant biomimetic structures and functionalities, it still remains a big question how the nanoscale helicity evolved from the molecular chiral building blocks across length scales. Herein, macrocyclic triangles composed of achiral edges and chiral vertices were rationally designed, in which the planar chirality emerged due to the restriction of edge rotation by intermolecular stackings and led to a unique chiral self‐assembly. In contrast to the solution systems where the chiroptical property is exclusively dominated by the point chiral vertices, the emerged planar chirality was found to control the chiral self‐assembly, resulting the nanotwist with the handedness determined by the planar chirality. Our work unveiled the self‐assembly behaviors of macrocyclic conformers for the first time and provided a deep understanding on the macrocyclic chirality evolution including the excited‐state chirality.

Self-Assembly of Macrocyclic Triangles into Helicity-Opposite Nanotwists by Competitive Planar over Point Chirality.

While helix has elegant biomimetic structures and functionalities, it still remains a big question how the nanoscale helicity evolved from the molecular chiral building blocks across length scales. Herein, macrocyclic triangles composed of achiral edges and chiral vertices were rationally designed, in which the planar chirality emerged due to the restriction of edge rotation by intermolecular stackings and led to a unique chiral self-assembly. In contrast to the solution systems where the chiroptical property is exclusively dominated by the point chiral vertices, the emerged planar chirality was found to control the chiral self-assembly, resulting the nanotwist with the handedness determined by the planar chirality. Our work unveiled the self-assembly behaviors of macrocyclic conformers for the first time and provided a deep understanding on the macrocyclic chirality evolution including the excited-state chirality.

On the interplay between interchange turbulence and sheared flows

The presence and the position of an X-point, namely, if the ion diamagnetic drift points toward it or not, strongly impact the edge plasma rotation in tokamaks. In the absence of kinetic effects such as magnetic ripple or ion orbit loss, the shape of the velocity profile results from the balance between neoclassical predictions and turbulent flow generation. In this contribution, we derive a reduced model of turbulence plunged in a shear flow. This model is based on (1) a description of the impact of a sheared flow on the interchange turbulence and (2) a prediction of the poloidal momentum generated by the turbulence. It includes the effects of both the magnetic topology and the finite shear layer width. The model is verified against 2D non-linear flux-driven simulations. Finally, the model predictions of the edge rotation resulting from the equilibrium between the neoclassical prediction and the poloidal momentum generation by the turbulence are invoked to describe the observations from experiment managed in the WEST tokamak. It points out the important role of the magnetic shear in the turbulence tilting and in the flow generation.

Physics studies of ADITYA & ADITYA-U tokamak plasmas using spectroscopic diagnostics

Several spectroscopic diagnostics encompassing the spectral emission range from the x-ray to near infrared (NIR) have been developed, installed and operated for diagnosing and physics studies in the ADITYA and ADITYA-U tokamaks. The recycling and impurity influxes and plasma Z eff after lithium (Li) coating have been studied using a PMT (photomultiplier tube)-filter based system by capturing H α , O1+, C2+, and visible continuum emissions. Significant reduction in the Z eff values has been observed in the discharge with the Li coated walls. The measured radial profile of H α emission using a filter-PMT array, has been modelled using a neutral transport code. The results show substantial contributions from the molecular hydrogen and molecular hydrogen ion dissociation (∼56%) and charge-exchange (∼30%) processes in the measured H α emission. Furthermore, a high-resolution, 1 m spectrometer with charge coupled device detector capable of multi-track measurements, has been used to study impurity transport, neutral and ion temperature and intrinsic plasma rotation. By modelling the measured radial profile of O4+ spectral line emission using an impurity transport code, substantial contribution of edge fluctuations on the oxygen transport has been observed. The toroidal ( ∼ 20 km s−1 in core) and poloidal ( ∼ 4.5 km s−1 at edge) rotation velocities are measured using C5+ (529 nm) and C2+ (464.7 nm) passive line emissions respectively. The measurement of radial profile of toroidal plasma rotation revealed a reversal of rotation direction depending on the electron density content of the ADITYA-U plasmas. The neutral temperature measurements showed a poloidal asymmetry indicating a presence of asymmetrical source of neutral heating. Moreover, the modelling of measured Fe14+ and Fe15+ vacuum ultraviolet spectral lines has revealed the neo-classical nature of iron transport in ADITYA core. Fast visible camera images captured the formation of filament structures triggered by interchange instabilities during plasma disruptions.

Modelling and analysis of electrical impedance myography of the lateral tongue

Objective: Electrical impedance myography (EIM) performed on the centre of the tongue shows promise in detecting amyotrophic lateral sclerosis (ALS). Lateral recordings may improve diagnostic performance and provide pathophysiological insights through the assessment of asymmetry. However, it is not known if electrode proximity to the muscle edge, or electrode rotation, distort spectra. We evaluated this using finite element-based modelling. Approach: Nine thousand EIM from patients and healthy volunteers were used to develop a finite element model for phase and magnitude. Simulations varied electrode proximity to the muscle edge and electrode rotation. LT-Spice simulations assessed disease effects. Patient data were assessed for reliability, agreement and classification performance. Main results: No effect on phase spectra was seen if all electrodes remained in contact with the tissue. Small effects on magnitude were observed. Cole-Cole circuit simulations indicated capacitance reduced with disease severity. Lateral tongue muscle recordings in both patients and healthy volunteers were reproducible and symmetrical. Combined lateral/central tongue EIM improved disease classification compared to either placement alone. Significance: Lateral EIM tongue measurements using phase angle are feasible. Such measurements are reliable, find no evidence of tongue muscle asymmetry in ALS and improve disease classification. Lateral measurements enhance tongue EIM in ALS.

Failure Behavior Analysis of Single-leaf Blast-resistant Door by Explosion Loads

For a blast-resistant structural system with concrete slab as the primary structural member, edge rotation based on flexural failure is generally used as an index to evaluate its structural performance. However, it has been predicted that short-span single-leaf blast doors are vulnerable to shear failure. In this study, limitations on the general application of the edge rotation as a performance evaluation index were reviewed using a finite element (FE) method. The results demonstrated that shear failure was dominant in the impulsive and dynamic response regions, while shear failure or flexural-shear combined failure was dominant in the quasi-static region. In the case of short-span single-leaf blast door, the concrete slab is vulnerable to shear failure, and therefore, the door should be designed considering pressure-impulse curves based on shear failure. For further study, several explosion tests and FE analyses will be required to verify the structural responses and failure level changes according to various specifications of the blast door, and to obtain a general evaluation index for its structural performance.

Real-time pedestal optimization and ELM control with 3D fields and gas flows on DIII-D

The capabilities of the DIII-D tokamak’s plasma control system (PCS) were expanded to allow for pedestal optimization and edge localized mode (ELM) control. Three proof of principle control schemes are presented that were successfully implemented and tested. These use multiple inputs from real-time (RT) diagnostics like a based ELM monitor and edge profile measurements from Thomson scattering (TS) as well as 3D, i.e. non-axisymmetric, magnetic fields and gas puffs as actuators to regulate the density pedestal.The first scheme targets to optimize the access of ELM suppression induced by non-axisymmetric magnetic perturbations (MPs). The conducted set of experiments identifies a path dependence of plasma confinement on the applied MP amplitude. The controller aims to transition into ELM suppression at the minimum 3D field amplitude and reduces it further afterwards, allowing for partial confinement recovery. Another pedestal control scheme is deployed to compensate the density ‘pump-out’ in MP ELM suppression by regulating the gas puff. This uses RT TS diagnostic data, extracting the pedestal height from the electron density () profiles and enables studies of the transition into and out of MP ELM suppression at constant density. A limit cycle behavior of edge rotation and MP amplitude persists under these conditions. The third control scheme combines MPs and gas puffs as actuators to perform pedestal density trajectory control to access Super high confinement mode (H-mode) and furthermore, allowing the integration of a radiative divertor in this regime. While MPs mainly impact the pedestal top density, the control scheme allows to loosen the tight coupling of pedestal top and separatrix density evolution.With respect to ITER, the achieved results emphasize the need for an advanced control system to keep MP amplitude close to but above the ELM suppression threshold at all times, enabling high confinement and, respectively, at high fusion energy gain factor (Q). Furthermore, pedestal control enables detailed physics studies in present-day tokamaks and allows the exploration of core-edge integrated plasma scenarios.

Growth of microorganisms in an interfacially driven space bioreactor analog

Fluid bioreactors in microgravity environments may utilize alternative methods of containment and mixing. The ring-sheared drop (RSD) is a containerless mixing device which functions in microgravity using surface tension for containment and mixes through interfacially-driven flow. To assess the feasibility of using interfacially driven flow devices, such as the RSD, as bioreactors, Escherichia coli growth and recombinant protein expression were analyzed in a ground-based analog of the RSD called the knife edge surface viscometer (KEV). Results demonstrated that the KEV can facilitate the growth of E. coli and that growth rate increases logarithmically with increasing knife edge rotation rate, similar to the standard growth method on Earth (orbital shaker). Furthermore, the KEV was shown to be viable for supporting recombinant protein expression in E. coli at levels comparable to those achieved using standard growth methods.

A polynomial upper bound for the mixing time of edge rotations on planar maps

We consider a natural local dynamic on the set of all rooted planar maps with $n$ edges that is in some sense analogous to “edge flip” Markov chains, which have been considered before on a variety of combinatorial structures (triangulations of the $n$-gon and quadrangulations of the sphere, among others). We provide the first polynomial upper bound for the mixing time of this “edge rotation” chain on planar maps: we show that the spectral gap of the edge rotation chain is bounded below by an appropriate constant times $n^{-11/2}$. In doing so, we provide a partially new proof of the fact that the same bound applies to the spectral gap of edge flips on quadrangulations as defined in [8], which makes it possible to generalise the result of [8] to a variant of the edge flip chain related to edge rotations via Tutte’s bijection.

Intrinsic rotation in axisymmetric devices

Toroidal rotation is critical for fusion in tokamaks, since it stabilizes instabilities that can otherwise cause disruptions or degrade confinement. Unlike present-day devices, ITER might not have enough neutral-beam torque to easily avoid these instabilities. We must therefore understand how the plasma rotates ‘intrinsically,’ that is, without applied torque. Experimentally, torque-free plasmas indeed rotate, with profiles that are often non-flat and even non-monotonic. The rotation depends on many plasma parameters including collisionality and plasma current, and exhibits sudden bifurcations (‘rotation reversals’) at critical parameter values.Since toroidal angular momentum is conserved in axisymmetric systems, and since experimentally inferred momentum transport is much too large to be neoclassical, theoretical work has focused on rotation drive by nondiffusive turbulent momentum fluxes. In the edge, intrinsic rotation relaxes to a steady state in which the total momentum outflux from the plasma vanishes. Ion drift orbits, scrape-off-layer flows, separatrix geometry, and turbulence intensity gradient all play a role. In the core, nondiffusive and viscous momentum fluxes balance to set the rotation gradient at each flux surface. Although many mechanisms have been proposed for the nondiffusive fluxes, most are treated in one of two distinct but related gyrokinetic formulations. In a radially local fluxtube, appropriate for , the lowest-order gyrokinetic formulations exhibit a symmetry that prohibits nondiffusive momentum flux for nonrotating plasmas in an up-down symmetric magnetic geometry with no shear. Many symmetry-breaking mechanisms have been identified, but none have yet been conclusively demonstrated to drive a strong enough flux to explain commonly observed experimental rotation profiles. Radially global gyrokinetic simulations naturally include many symmetry-breaking mechanisms, and have shown cases with experimentally relevant levels of nondiffusive flux. These promising early results motivate further work to analyze, verify, and validate.This article provides a pedagogical introduction to intrinsic rotation in axisymmetric devices. Intended for both newcomers to the topic and experienced practitioners, the article reviews a broad range of topics including experimental and theoretical results for both edge and core rotation, while maintaining a focus on the underlying concepts.

Fast Array Response Adjustment With Phase-Only Constraint: A Geometric Approach

This paper presents a geometric approach to fast array response adjustment with phase-only constraint. The devised algorithm can precisely and rapidly adjust the array response of a given point by only tuning the excitation phases of a preassigned weight vector. We geometrically reformulate the phase-only array response adjustment as a polygon construction problem, which can be solved by edge rotation in the complex plane. On this basis, we carry out a detailed analysis of the solution of polygon construction and specify the range of the feasible phase. To avoid the undesirable pattern distortion and obtain less pattern variations in the uncontrolled region, an effective and analytical phase determination approach is presented. The proposed algorithm provides an analytical solution and guarantees a precise phase-only adjustment without pattern distortion. In addition, our algorithm does not impose any restriction on the given weight vector and has a low computational complexity. Representative examples are presented to demonstrate the effectiveness of the proposed algorithm under various situations.