Poloidal Direction Research Articles

Nonlinear feedback algorithm for tearing-mode magnetic control in tokamak

Results of calculations and analysis of the tearing-mode evolution under the effect of resonant magnetic perturbation produced by a nonlinear feedback system in rotating tokamak plasma are presented. The TEAR-code used for calculations is based on the visco-resistive magnetohydrodynamic approximation that gives coupled diffusion-type equations for the magnetic flux perturbation and for the plasma rotation velocities in toroidal and poloidal directions. The code is supplemented by a computational unit simulating the nonlinear algorithm of the feedback system. The feedback gain and phase shift are automatically regulated in real time. The gain depends on the tearing-mode amplitude. At high feedback input signals, the gain does not exceed some finite value to reduce technical requirements for the feedback actuator and to mitigate the phase instability. In the process of the tearing-mode suppression, the gain gradually increases to provide the mode control under reduction of feedback input signal and rise of the intrinsic tearing-mode stability index. Besides that, the real-time control of the feedback phase shift is provided to additionally mitigate the phase instability. According to simulation, the used nonlinear characteristics of the feedback algorithm improve the efficiency of the tearing-mode suppression.

Conceptual design of heavy ion beam probes on the PLATO tokamak.

Heavy ion beam probe (HIBP) systems have been designed for the new tokamak, PLATO [A. Fujisawa, AIP Conf. Proc. 1993, 020011 (2018)]. The designs have been completed, and the installations are in progress. Two HIBPs are being installed in toroidal sections 180° apart to investigate long-range correlations in the toroidal direction. Each HIBP consists of an injection beamline and a detection beamline as usual. Yet, one of the HIBPs is equipped with an additional detection beamline; the measurement positions of its two detection beamlines can be placed on almost the same magnetic surface yet at poloidal angles that differ by ∼180°. The use of three detection beamlines allows us to investigate spatial asymmetry and long-range correlations in both the toroidal and poloidal directions, simultaneously. The detected beam intensity is expected to be enough for turbulence measurements in almost the entire plasma region when the electron density is up to 1 × 1019 m-3 by selecting appropriate ion species for the probe beam. Each detector has three channels 10mm apart, allowing measurement of local structures of micro-scale turbulence. Therefore, using the HIBPs on the PLATO tokamak will enable both local and global properties of plasma turbulence to be investigated, simultaneously.

Development of a thin high-frequency and high-precision magnetic probe array in Sino-United Spherical Tokamak

Since the major/minor radius of the Sino-United Spherical Tokamak (SUNIST) is 0.3/0.23m, respectively, the space left for magnetic diagnostics in the high field side (HFS) is quite limited. At the same time, a good signal-to-noise ratio and a high-frequency response (up to 1MHz) are required for equilibrium reconstruction (ER) and Alfven eigenmode studies. Such a magnetic probe array must be extremely thin and tightly close to the central column, not exceeding the inner limiter and leaving the aspect ratio of the spherical tokamak unchanged. Therefore, the turn number and the shape of windings should be highly optimized to enable both a high-frequency response and an enough effective area. A 32-channel magnetic probe array fulfilling these requirements on the central column is designed, calibrated, and installed in the SUNIST. The array consists of 16 probes. Each of them consists of two perpendicular windings, which can measure toroidal and poloidal magnetic fields simultaneously. The effective area and frequency response of each probe are calibrated using a Helmholtz coil and an LCR bridge based on an equivalent probe-and-cable circuit model. After that, an expression of the magnetic diagnostic response to the field coil currents is used to calibrate the installation error. With the full coverage of magnetic probes in the poloidal direction, more reliable ER can be obtained, and the features of magnetohydrodynamic activities in the HFS can be studied.

Characteristics of neutron emission profile from neutral beam heated plasmas of the Large Helical Device at various magnetic field strengths

The neutron emission profile of deuterium plasma in the Large Helical Device was measured with a multi-sightline vertical neutron camera under various magnetic field strength conditions. It was found that the line-integrated neutron emission profile shifts outward in the co-neutral beam (NB) case and inward in the counter NB case. Here, co- and counter directions correspond to enhance and reduce the poloidal magnetic field directions, respectively. The shift becomes more significant when the magnetic field decreased in strength. The experimentally obtained neutron emission profile was compared with the orbit-following models simulated through the DELTA5D code. The calculated neutron emission profiles vary according to the magnetic field strength because of the change of beam ion orbit and the slowing down due to the plasma parameter changes. Although a relatively narrow profile was obtained in the calculations at the inboard side for the co-NB case in the relatively low field condition, the profiles obtained through calculation and experiment were almost qualitatively aligned.

Finite electron temperature gradient effects on blob formation in the scrape-off layer of a tokamak plasma

Nonlinear coherent dense plasma structures—‘blobs’—that form in the turbulent edge plasma of a tokamak play an important role in the anomalous nature of the plasma transport in that region. A plasma blob is normally formed when another kind of coherent structure—a radially elongated streamer structure—breaks due to differential stretching in the radial and poloidal directions. We investigate the nature of such a blob formation in the scrape-off layer region by taking into account electron temperature effects. It is found that the shear related to the poloidal gradient of the poloidal electric field plays a major role. A blob is predicted to form when this shear exceeds the interchange mode growth rate within the radially elongated region. Our theoretical estimate of this extended criterion for blob formation is validated from three-dimensional numerical simulation results using the BOUT++ framework and could be useful in the interpretation of blob formation in the presence of finite electron temperature gradient that is applicable in the H and L mode discharges.

Determination of poloidal mode numbers of MHD modes and their radial location using a soft x-ray camera array in the Wendelstein 7-X stellarator

A forward modeling technique is developed for determining the characteristic features of observed MHD modes from the line-of-sight data of the soft x-ray (SXR) tomography diagnostics in the Wendelstein 7-X (W7-X) stellarator. In particular, forward modeling is used to evaluate the poloidal mode numbers m, radial location, poloidal rotation direction and ballooning character of the MHD modes. The poloidal mode structures have been modeled by the radially localized Gaussian-shaped emission regions rotating along the magnetic surfaces. In the present study the cases of rigid-shape emission regions and flexible emission regions are modeled. Various mode phase velocity dependences on the magnetic surface position are simulated. The modeled phase dynamics of line-integrated oscillations and the distribution of oscillation amplitudes are compared with the experimental signals of the SXR cameras which observe the plasma at various viewing angles in the poloidal cross-section. Application of this technique enables describing of the 1–50 kHz modes. In particular, in the discharge W7X-PID 20180918.045 three identified branches with the poloidal mode numbers m= 8, m= 10 and m= 11 localized at ρ ≈ 0.3 are rotating in the clockwise poloidal direction. The present paper reports the first application of the forward modeling technique to the data from the SXR diagnostics in W7-X. The high m-modes are identified by forward modeling in W7-X.

Continuum gyrokinetic simulations of edge plasmas in single-null geometries

The first continuum gyrokinetic calculations of electrostatic ion scale turbulence are presented for the case of a diverted tokamak geometry. The simulation model solves the long-wavelength limit of the full-F gyrokinetic equation for ion species coupled to the quasi-neutrality equation for electrostatic potential variations, where a fluid model is used for an electron response. In order to facilitate simulations of highly-anisotropic microturbulence in the presence of strong magnetic shear and a magnetic X-point, a numerical algorithm utilizing a locally field-aligned multiblock coordinate system has been developed and implemented in the 5D finite-volume code COGENT. In this approach, the toroidal direction is divided into blocks, such that within each block, the cells are field-aligned and a non-matching grid interface is allowed at block boundaries. The toroidal angle corresponds to the “coarse” field-aligned coordinate, whereas the poloidal cross section, comprised of the radial and poloidal directions, is finely gridded to resolve short-scale perpendicular turbulence structures and to support accurate re-mapping (interpolation) at block boundaries. The 5D simulations explore cross-separatrix ion scale turbulence in the presence of a self-consistent radial electric field and address the effects of magnetic-shear stabilization in the X-point region.

Preliminary thermal-hydraulic influence of the poloidal nonuniform neutron wall loading on the CFETR HCCB blanket

Abstract Helium Cooled Ceramic Breeder (HCCB) blanket, which has been determined as one of the blanket candidates for China Fusion Engineering Test Reactor (CFETR), is the critical component of the fusion reactor. The neutronics and thermal-hydraulic performances of the blanket are the bases of the safe operation, and they are also the initial boundary conditions for the other performance analyses. Both performances are influenced by the neutron wall loading (NWL) distribution on the blanket and the radial structural arrangement of the internal functional zones. In our previous work, the influences of the poloidal nonuniform NWL on the neutronics performances of the blanket have been investigated preliminarily. However, as the nuclear power deposition in each blanket component is the internal heat source for the thermal-hydraulic analyses, it’s essential to further investigate the influence of the poloidal nonuniform NWL on the thermal-hydraulic performances of the blanket. In this paper, taking the typical CFETR HCCB blanket module as the research object, firstly, both the neutronics and the thermal-hydraulic models are established. For investigating the influence of the poloidal nonuniform NWL on blanket performances, both models are divided into five identical parts along the poloidal direction. Afterwards, by referencing the actual poloidal NWL distribution in CFETR, we have aggregately proposed three kinds of poloidal nonuniform NWL distribution forms, including two symmetrical and one stepped NWL. On these bases, both the neutronics and the thermal-hydraulic analyses under the poloidal nonuniform NWL distributions are conducted, and the calculation results are compared with those corresponding to the uniform NWL distribution. The comparison results show that the maximum temperature of every functional zone calculated under the three nonuniform NWL distributions is generally higher than that corresponding to the uniform NWL distribution, which means that the thermal-hydraulic results calculated under the simplified uniform NWL distribution are not conservative. Under the condition of nonuniform NWL distributions, there is obvious poloidal temperature nonuniformity in every functional zone. Besides, the temperature deviations between the stepped and the uniform NWL distributions are generally larger than those between the symmetrical and the uniform ones. This paper can provide some valuable references for the detailed engineering design, analyses, and optimizations of the CFETR HCCB blanket.

Fluctuations of the Magnetic Field of Plasma Currents in Uragan-3M Stellarator

At the torsatron-type stellarator Uragan-3M, frequency spectrum and spatial structures of the fluctuations of the poloidal component of the magnetic field in frequency range 0.3–52 kHz, which are caused by the plasma current, are studied with a set of magnetic sensors. The studies were carried out in the microwave heating regime in confining magnetic fields of different strength. The magnetic field fluctuations were studied in weakly and strongly collisional plasmas. Studies showed that the spectrum of the recorded magnetic field fluctuations consists of a relatively narrowband number of frequencies. The fluctuating magnetic fields are caused by plasma currents, which can be presented as a number of poloidal structures with wave numbers m = 0, 1, 2, and 3 (and, possibly, also 4). Each spatial structure of plasma currents (expect the one with m = 0) can be represented as a sum of two oscillation types: a rotating and a standing structure. The rotating structure moves in the poloidal direction with a rotation frequency close to the frequency of the standing structure. The rotation direction is not constant and it changes during the discharge. The standing structure does not change its position (phase) and oscillates at a fixed frequency. The conducted analysis showed that the observed fluctuations of the magnetic field are a result of plasma instabilities, which cause perturbations of the plasma pressure. These oscillations have the growth rate and damping rate of the order of the carrier frequency. The perturbation of the plasma density initiates the appearance of polarization removal currents whose magnetic field is recorded in the described experiments. Estimates show that the fluctuation level reaches 4 × 10–3 relative to the average plasma pressure in the discharge. It was also shown that, in these experiments, microwave heating does no cause the observed instabilities. The time behavior of the discharge parameters and the energy of magnetic field fluctuations at the boundary of the confinement region allows us to conclude that at the quasi stationary stages of the discharge, the observed instabilities determine the main energy losses from the plasma volume.

Reactance Regulation Using Coils with Perpendicular Magnetic Field in the Tubular Core design

This article presents an efficient method for prosumer connection to the distribution line. The prosumers can be connected to the distribution line using specially designed controllable reactive impedance. The reactive impedance is controlled using specially designed coils and magnetic core. The internal coil is wound in the toroidal direction (across the z-axis) and creates a toroidal shape. A thin ferromagnetic strip is coiled on this toroidal shape in the poloidal direction to form the ferromagnetic core. Then, an external coil is wound on this ferromagnetic core in the poloidal direction. The internal coil is controlled by the inductive impedance of the external coil, which is related to the anisotropic properties of ferromagnetic strips. The internal coil is connected between the power supply line and a prosumer. This arrangement confirms the magnetic independence of coils and the symmetry of the current in the internal coil. The magnetic coupling between both coils is very low (~0.015–0.017) and appropriate for engineering applications. It is approved that the impedance of the internal coil is changed due to the anisotropic magnetic properties of the core material.

Excitation of the beta-induced Alfvén-acoustic eigenmode during sawtooth-like oscillation in EAST

The characteristics and excitation conditions of the beta-induced Alfvén-acoustic eigenmode (BAAE) have been investigated during sawtooth-like oscillation in the Experimental Advanced Superconducting Tokamak (EAST). The sawtooth-like events are triggered periodically by the double-tearing reconnection crash (DTRC), and the oscillations with period τo≥ 100 ms, where m and n are the poloidal and toroidal mode numbers respectively. The BAAE coexists with beta-induced Alfvén eigenmodes (BAEs) and reversed-shear Alfvén eigenmodes (RSAEs), and the BAAE has similar characteristics to the pairing of BAEs–RSAEs. The radial structures of the BAAE and BAEs are deformed into analogous triangle shapes along the poloidal direction, and the BAAE is located more outward with broadened radial coverage. The frequencies of the BAAE and RSAEs sweep upward synchronously with decreasing ( < 1), and the BAAE can also provide valuable constraint conditions for the q-profile measurements. Furthermore, the mode structure of the BAAE is achieved experimentally with m = 4/n ≈ 4.The period τo of DTRC is an important factor, which can be adopted for evaluating the excitation conditions of BAAE; namely, the BAAE can be excited when τo achieves the threshold condition. τo increases when the total injected power of neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH) increases, where the NBI beam direction is perpendicular to the plasma current. The gradient of electron temperature at the vicinity of increases with τo, and the portion of energetic ions in the central region increases as well. Therefore, the BAAE in EAST should be excited by the special distribution of trapped energetic ions through toroidal precessional resonances, and is also an important constraint condition for the excitation.

Axisymmetric flows on the torus geometry

Abstract

Neutronics influence of poloidal nonuniform neutron wall loading on helium-cooled ceramic breeder blanket for CFETR

Abstract After its conceptual design, the Chinese Fusion Engineering Test Reactor (CFETR) is now at the stage of detailed engineering design. During this stage, many detailed factors should be considered for the components in the CFETR. In this paper, the neutronics influence of poloidal nonuniform neutron wall loading (NWL) is studied for helium-cooled ceramic breeder (HCCB) blanket of the CFETR. The blanket is divided into five parts along the poloidal direction. Each part is composed of the armor, the first wall, tritium breeders, neutron multipliers, and the manifold in the flow distribution zone. The nuclear heat deposition and the tritium breeding performance of the CFETR HCCB blanket are studied with symmetrical and stepped NWL distributions. The results obtained from the uniform NWL distribution are also presented as the reference. For each NWL distribution, the nuclear heat deposition and the tritium breeding capability in different blanket parts are compared. The results show that the nonuniform NWL distribution has almost no influence on the total nuclear heat deposition or the total tritium production. The overall variation is less than 1 ‰ compared to the results under the uniform NWL distribution. However, the local performances of different blanket parts are affected obviously. The maximum variation is over 20 %, which should be focused on during the design for the flow distribution of helium coolant and purge gas. The present work aims to provide an important guidance for the detailed design and structural optimization of the blanket for the CFETR, especially for consideration of the high-level fusion power during phase II (over 1 GW).

Reduction of blob-filament radial propagation by parallel variation of flows: Analysis of a gyrokinetic simulation

Data from the XGC1 gyrokinetic simulation are analyzed to understand the three-dimensional spatial structure and the radial propagation of blob-filaments generated by quasi-steady turbulence in the tokamak edge pedestal and scrape-off layer plasma. Spontaneous toroidal flows vary in the poloidal direction and shear the filaments within a flux surface, resulting in a structure that varies in the parallel direction. This parallel structure allows the curvature and grad-B induced polarization charge density to be shorted out via parallel electron motion. As a result, it is found that the blob-filament radial velocity is significantly reduced from estimates that neglect parallel electron kinetics, broadly consistent with experimental observations. Conditions for when this charge shorting effect tends to dominate blob dynamics are derived and compared with the simulation.

Optimization of the first wall cooling system for the DEMO WCLL blanket

• Thermal-hydraulic analyses of WCLL FW cooling systems in different poloidal position. • FW systems optimization to reduce the number of water channels, not exceeding the temperature limit of 550 °C. • Steady-state analyses to evaluate the cooling capability of the optimized systems. • Transient analysis to demonstrate the fully withstanding of the DEMO thermal loads. • Thermal-hydraulic aspects of FW designs are discussed and CHF evaluated. The Water-Cooled Lithium-Lead (WCLL) Breeding Blanket (BB) is a key component in charge of ensuring Tritium production, shield the Vacuum Vessel and remove the heat generated by plasma thermal radiation and nuclear reactions. It relies on PbLi eutectic alloy adopted as breeder and neutron multiplier and refrigerate by subcooled pressurized water. The last function is fulfilled by two independent cooling systems: First Wall (FW) that faces the plasma heat flux and the Breeding Zone (BZ) that removes the deposited power of neutron and photon interaction. Several layouts of WCLL BB system have been investigated in the last years to identify a configuration that guarantees Eurofer temperature below the limit (550 °C) and good thermal-hydraulic performances. This research activity focuses on the FW cooling system based on the WCLL BB 2018 design of DEMO 2017 baseline, investigating the cooling performances in order to optimize the FW design, reducing the amount of water that affects the Tritium Breeding Ratio (TBR) and improves the efficiency of the Primary Heat Transfer System (PHTS), verifying the reliability to deliver coolant at adequate design temperature (328 °C) to the PHTS. Different solutions have been considered and analyzed focusing on three specific positions along the poloidal direction: the equatorial cells in the Central Outboard Segment (COB) and Inboard Segment (IB), where there is the maximum deposited power and low Heat Flux (HF), and the apical cell of the IB, impacted by the highest HF but with low deposited power. For each FW design, several thermal-hydraulic steady-state analyses have been performed, as well as sensitivity analyses to evaluate the response of the systems under different cooling configuration, changing the position and the number of channels. Furthermore, a transient analysis reproducing the Dwell-Pulse phase of the DEMO fusion reactor with the optimized configuration of the Outboard FW layout has been performed to study the behavior of the FW cooling system subjected to the pulsed operation. The research activity aims at laying the basis for the finalization of the WCLL BB design, pointing out relevant thermal-hydraulic aspects. The analyses have been carried out using a CFD approach, thus a 3D finite volume model of each configuration has been developed, adopting the commercial ANSYS CFX code. The goal of the study is to compare the different FW cooling system layouts, identifying and discussing advantages and key issues from the thermal-hydraulic point of view. The results show that the coolant system of FW can safely remove the high plasma HF and nuclear heat deposition with a reduction of water channels, delivering coolant to the FW PHTS heat exchanger at the design temperature.

Transition from non-swirling to swirling axisymmetric turbulence

Strictly axisymmetric turbulence, i.e., turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two-and three-dimensional turbulence. We investigate statistically steady states of this system by direct numerical simulation using a forcing protocol, which allows the injected energy in the toroidal and in the poloidal directions to be tuned independently. A sharp transition between a two-dimensional two-component (2D2C, non-swirling) flow and a two-dimensional three-component (2D3C, swirling) flow is observed. We derive a statistical model which reproduces this transition.

Development of a 32-channel Beam Emission Spectroscopy diagnostic based on Neutral Beam Injection on HL-2A tokamak

Abstract A 32-channel Beam Emission Spectroscopy (BES) diagnostic has been installed and operated on HL-2A tokamak. It covers a wide spatial range of 32 cm in the radial direction (from r = 12 c m / ρ = 0.27 to r = 44 c m / ρ = 0.98 ) and 27 cm in the poloidal direction (from -13.5 cm to +13.5 cm) inside the plasma, providing a capability of measuring density fluctuations in different spatial locations. It has high temporal resolution, 2 MHz, and good spatial resolution, about 1 cm in radial direction and 1.2 cm in poloidal direction. A 2D fiber mount with 135 slots is designed and installed on the curved image plane. Each slot corresponds to a different spatial location inside the plasma. BES channels can be placed in any slots as needed for desired spatial location measurement. More channels can be added up to 128 channels without re-designing collecting optical path & replacing optical components. First experimental results have demonstrated great performance of the system with high signal to noise ratio. Turbulence eddy dynamics can be measured and studied from 2D fast imaging. It will be a keen diagnostic in future plasma turbulence research on HL-2A.

Anomalous losses of energetic particles in the presence of an oscillating radial electric field in fusion plasmas

The confinement of energetic particles in nuclear fusion devices is studied in the presence of an oscillating radial electric field and an axisymmetric magnetic equilibrium. It is shown that, despite the poloidal and toroidal symmetries, initially integrable orbits turn into chaotic regions that can potentially intercept the wall of the tokamak, leading to particle losses. It is observed that the losses exhibit algebraic time decay different from the expected exponential decay characteristic of radial diffusive transport. A dynamical explanation of this behaviour is presented, within the continuous time random walk theory. The central point of the analysis is based on the fact that, contrary to the radial displacement, the poloidal angle is not bounded and a proper statistical analysis can therefore be made, showing for the first time that energetic particle transport can be super-diffusive in the poloidal direction and characterised by asymmetric poloidal displacement. The connection between poloidal and radial positions ensured by the conservation of the toroidal canonical momentum, implies that energetic particles spend statistically more time in the inner region of the tokamak than in the outer one, which explains the observed algebraic decay. This indicates that energetic particles might be efficiently slowed down by the thermal population before leaving the system. Also, the asymmetric transport reveals a new possible mechanism of self-generation of momentum.

Induced scattering of a pump wave during electron Bernstein wave heating in the high poloidal beta regime

In the present paper we investigate induced scattering of the pump microwave during electron Bernstein wave heating in the regimes with the high poloidal beta. It occurs in the upper hybrid resonance vicinity and leads to the nonlinear excitation of electron Bernstein waves confined within a finite 3D region limited in the radial direction by a potential well at the LFS and in the poloidal and toroidal directions by the dimensions of the spot on the magnetic flux surface illuminated by the pump beam.

Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST)

An axisymmetric magnetic oscillation (AMO) of 5–10 kHz in the L-mode plasma edge has been studied on an experimental advanced superconducting tokamak. The analysis shows that this oscillation only occurs at the plasma very close to the L-H transition. The structure of magnetic oscillation is axisymmetric (n = 0) toroidally and demonstrates an m = 2 standing wave in the poloidal direction. The density fluctuation of AMO measured by reflectometry at the midplane is nearly in phase, indicating that the AMO is not a radial traveling wave. The AMO shows an obvious modulation effect on the background magnetic/density fluctuation, and as a result, the edge density/density gradient and particle flux onto the divertor are also modulated by the AMO. The frequency scaling of the AMO is fm∝(∇ne/Ip2)−1. The bicoherence analyses show a strong nonlinear interaction between the AMO and the background turbulence, and other nonlinear interactions between the AMO and three other coherent fluctuations with frequencies (∼4, ∼11, and ∼15 kHz) are also found.