Poloidal Plasma Research Articles

Применение метода многочастотного допплеровского обратного рассеяния для исследования альфвеновских мод в токамаке

The results of the study of toroidal Alfven modes (TAE) using the multi-frequency Doppler backscattering (DBS) in the Globus-M tokamak are presented. The article is focused on the presentation of the Alfven mode registration method for multichannel probing. The possible causes of the observed oscillations of the poloidal plasma rotation velocity at the Alfvén oscillation frequencies are discussed in detail. The data on the spatial distribution of Alfvén modes revealed by multi-frequency DBS are given. The recommendations for the further development of the DBS with the aim of a more detailed study of TAE in tokamaks were determined.

Simulation of plasma turbulence in the periphery of diverted tokamak by using the GBS code

We report on the implementation of diverted magnetic equilibria in GBS and on first simulations in this geometry. GBS is a simulation code used to evolve plasma turbulence in the tokamak periphery by solving the drift-reduced Braginskii's equations. The model equations are written in toroidal coordinates, abandoning flux coordinate systems that are not defined at the X-point. A fourth order finite difference scheme is used for the implementation of the spatial operators on poloidally and toroidally staggered grids. The GBS numerical implementation is verified through the method of manufactured solutions. The code convergence properties are tested on a relatively simple analytical X-point configuration. Finally, the diverted equilibrium from a TCV tokamak discharge is implemented in the new version of GBS. The analysis of the simulation results is focused on blob formation, radial transport, and plasma poloidal rotation mechanisms.

V-band Doppler backscattering diagnostic in the TCV tokamak.

A variable configuration V-band heterodyne Doppler back-scattering diagnostic has been recently made operational in the tokamak configuration variable. This article describes the hardware setup options, flexible quasi-optical launcher antenna, data-analysis techniques, and first data. The diagnostic uses a fast arbitrary waveform generator as the main oscillator and commercial vector network analyzer extension modules as the main mm-wave hardware. It allows sweepable single or multi-frequency operation. A flexible quasi-optical launcher antenna allows 3D poloidal (10°-58°) and toroidal (-180° to 180°) steering of the beam with 0.2° accuracy. A pair of fast HE11 miter-bend polarizers allow flexible coupling to either O or X mode and programmable polarization changes during the shot. These have been used to measure the magnetic-field pitch angle in the edge of the plasma by monitoring the backscattered signal power. Ray-tracing simulations reveal an available k⊥ range between 3 and 16 cm-1 with a resolution of 2-4 cm-1. Perpendicular rotation velocity estimates compare well against ExB plasma poloidal rotation estimates from charge exchange recombination spectroscopy.

Grassy-ELM regime with edge resonant magnetic perturbations in fully noninductive plasmas in the DIII-D tokamakaaEdge-localized-mode.

Resonant magnetic perturbations (n = 3 RMPs) are used to suppress large amplitude ELMs and mitigate naturally occurring ‘grassy’-ELMs in DIII-D plasmas relevant to the ITER steady-state mission. Fully non-inductive discharges in the ITER shape and pedestal collisionality ( ≈ 0.05–0.15) are routinely achieved in DIII-D with RMP suppression of the Type-I ELMs. The residual grassy-ELMs deliver a low peak heat flux to the divertor as low as 1.2× the inter-ELM heat flux in plasmas with sustained high H-factor (H98y2 ≈ 1.2). The operating window for the RMP grassy-ELM regime is q95 = 5.3–7.1 and external torque in the range 9–0.7 Nm in the co-Ip direction, which is in the range required for a steady-state tokamak reactor. The RMP grassy-ELM regime is associated with a two-step pedestal, with strong flattening of the density around the zero crossing in the E × B shear. The edge magnetic response of the plasma to the n = 3 RMP is found to be ≈2–3× larger than for comparable ITER baseline plasmas (βN ≈ 1.8, q95 ≈ 3.1). The amplification of the RMP is consistent with the weak magnetic perturbation level (δB/B ≈ 1 × 10−4) required for effective Type-I ELM suppression. Cyclic variations in the pedestal pressure, width, and toroidal rotation are observed in these plasmas, correlated with cyclic variations in the strength and frequency of the grassy-ELMs. Extended MHD analysis and magnetic measurements indicate that these pedestal pulsations are driven by cyclic variations in the resonant field strength at the top of the pedestal. These pedestal pulsations reveal that the grassy-ELMs is correlated with the proximity of the pedestal to the low-n peeling-ballooning mode stability boundary. The use of low amplitude magnetic fields to access grassy-ELM conditions free of Type-I ELMs in high beta poloidal plasmas (βP ≈ 1.5–2.0) opens the possibility for the further optimization of the steady-state tokamak by use of edge resonant magnetic perturbations.

Dispersion analysis and calculation on Cherenkov radiation of an accelerated electron beam in poloidal magnetized plasma

In order to further study on radiation of a moving electron in poloidal magnetized plasma (PMP), theoretical analysis and simulation calculation of Cherenkov radiation (CR) under the condition of an accelerated electron beam in PMP are respectively presented in this paper. Through analysis of dielectric tensor in poloidal magnetized plasma with uniformly accelerated electron and description of beam-wave interaction in PMP by Maxwell’s equations, radiation mechanism of uniformly accelerated electron CR in PMP is described. Then eigenvalue and radiation condition are respectively obtained. Moreover, dispersion relation of radiation wave is also deduced through analysis of eigenvalues. At the same time, through analysis of effect that cyclotron frequency and plasma frequency have on eigenvalue, it is discovered that plasma frequency has great effect on not only p1 mode but also p2 mode, but cyclotron frequency only affects p2 mode. Finally, through simulation calculation, dispersion curves of both p1 mode and p2 mode are presented. Through comparing to the case of uniform moving electrons, the radiation conditions of the accelerated electrons are more relaxed, more prone to generate radiation. The theoretical analysis and simulation calculation can provide for further research of the radiation microwave in PMP.

The Role of Viscosity in Causing the Plasma Poloidal Motion in Magnetic Clouds

Abstract An interesting phenomenon, plasma poloidal motion, has been found in many magnetic clouds (MCs), and viscosity has been proposed as a possible mechanism. However, it is not clear how significant the role of viscosity is in generating such motion. In this paper, we conduct a statistical study of the MCs detected by the Wind spacecraft during 1995–2012. It is found that, for 19% of all the studied MCs (186), the poloidal velocities of the MC plasma near the MC boundaries are well correlated with those of the corresponding ambient solar wind plasma. A non-monotonic increase from inner to outer MCs suggests that the viscosity does play a role, albeit weak, on the poloidal motion in the MC statistically. The possible dependence on the solar wind parameters is then studied in detail for the nine selected crossings, which represent the viscosity characteristic. There is an evident negative correlation between the viscosity and the density, a weak negative correlation between the viscosity and the turbulence strength, and no clear correlation between the viscosity and the temperature.

EU-DEMO TF and CS Magnet Systems Design and Analyses Performed at CEA

While the ITER Tokamak is proceeding with major construction and assembly phases, design and R&D activities regarding the next step experimental reactor, the so-called DEMO machine, are underway in Europe. In particular, the magnet systems enter a refined design phase, under the general guidelines of Eurofusion, where winding packs (WP) are defined, conductor designs are proposed, and subscale analyses are performed in order to crosscheck the systems code (PROCESS) predimensioning. This paper summarizes the design iterations led at CEA on the toroidal field (TF) and central solenoid (CS) magnet systems. It presents, in particular, the optimization of the WP architecture with regard to the filling of the available space (TF) and flux maximization (CS). The paper gives the relevant electrical, thermal, and mechanical parameters for each system design, and tries to give insight on the tradeoffs and possible changes that could be implemented, given some margin on fixed systems code inputs. Finally, it also includes the refined magnetic field maps calculations performed to confirm the design operating field and explore other scenario time points that include poloidal field and plasma contributions.

Main Cause of the Poloidal Plasma Motion Inside a Magnetic Cloud Inferred from Multiple-Spacecraft Observations

Although the dynamical evolution of magnetic clouds (MCs) has been one of the foci of interplanetary physics for decades, only few studies focus on the internal properties of large-scale MCs. Recent work by Wang et al. (J. Geophys. Res.120, 1543, 2015) suggested the existence of the poloidal plasma motion in MCs. However, the main cause of this motion is not clear. In order to find it, we identify and reconstruct the MC observed by the Solar Terrestrial Relations Observatory (STEREO)-A, Wind, and STEREO-B spacecraft during 19 – 20 November 2007 with the aid of the velocity-modified cylindrical force-free flux-rope model. We analyze the plasma velocity in the plane perpendicular to the MC axis. It is found that there was evident poloidal motion at Wind and STEREO-B, but this was not clear at STEREO-A, which suggests a local cause rather than a global cause for the poloidal plasma motion inside the MC. The rotational directions of the solar wind and MC plasma at the two sides of the MC boundary are found to be consistent, and the values of the rotational speeds of the solar wind and MC plasma at the three spacecraft show a rough correlation. All of these results illustrate that the interaction with ambient solar wind through viscosity might be one of the local causes of the poloidal motion. Additionally, we propose another possible local cause: the existence of a pressure gradient in the MC. The significant difference in the total pressure at the three spacecraft suggests that this speculation is perhaps correct.

Drift-based scrape-off particle width in X-point geometry

The Goldston heuristic estimate of the scrape-off layer width (Goldston 2012 Nucl. Fusion 52 013009) is reconsidered using a fluid description for the plasma dynamics. The basic ingredient is the inclusion of a compressible diamagnetic drift for the particle cross field transport. Instead of testing the heuristic model in a sophisticated numerical simulation including several physical mechanisms working together, the purpose of this work is to point out basic consequences for a drift-dominated cross field transport using a reduced fluid model. To evaluate the model equations and prepare them for subsequent numerical solution a specific analytical model for 2D magnetic field configurations with X-points is employed. In a first step parameter scans in high-resolution grids for isothermal plasmas are done to assess the basic formulas of the heuristic model with respect to the functional dependence of the scrape-off width on the poloidal magnetic field and plasma temperature. Particular features in the 2D-fluid calculations—especially the appearance of supersonic parallel flows and shock wave like bifurcational jumps—are discussed and can be understood partly in the framework of a reduced 1D model. The resulting semi-analytical findings might give hints for experimental proof and implementation in more elaborated fluid simulations.

Calculation of edge ion temperature and poloidal rotation velocity from carbon III triplet measurements on the COMPASS tokamak

Abstract A high-resolution spectroscopic system for the measurements of the CIII triplet at 465 nm was installed at the COMPASS tokamak. The Doppler broadening and shift of the measured spectral lines are used to calculate the edge ion temperature and poloidal plasma rotation. At first, the spectroscopic system based on two-grating spectrometer and the calibration procedure is described. The signal processing including detection and removal of spiky features in the signal caused by hard X-rays based on the difference in the behaviour of Savitzky-Golay and median filters is explained. The detection and position estimation of individual spectral lines based on the continuous wavelet transform is shown. The method of fitting of Gaussians using the orthogonal distance regression and estimation of the error of estimation of the rotation velocity and ion temperature is described. At the end, conclusions about the performance of the spectroscopic system and its shortcomings based on summary of results calculated from 2033 processed spectral lines measured in 61 shots are drawn and the possible enhancements are suggested.

Application of poloidal beta and plasma internal inductance in determination of input power time of Damavand tokamak

In this study, magnetic measurement of poloidal fields were used to determine poloidal beta and plasma internal inductance of Damavand tokamak combination of poloidal beta and plasma internal inductance ( $$\beta _p+\dfrac{l_i}{2}$$ ), known as Shafranov parameter, was obtained experimentally in terms of normal and tangential components of the magnetic field. Plasma internal inductance and poloidal beta were obtained using parametrization method based on analytical solution of Grad-Shafranov equation (GSE) and compared with parabolic-like profile of toroidal current density approach for determination of the plasma internal inductance. Finding evolution of $$\beta _p+\dfrac{l_i}{2}$$ and plasma internal inductance. Finding poloidal beta (Shafranov parameter and internal inductance) and using energy balance equation, thermal energy and energy confinement were determined qualitatively in terms of poloidal beta during a regular discharge of Damavand tokamak.

Impact of ion diamagnetic drift on MHD stability at edge pedestal in JT-60U rotating plasmas

The effect of ion diamagnetic drift on the stability of peeling–ballooning modes in rotating tokamak plasmas has been analyzed numerically. The results show that plasma toroidal rotation can not only destabilize the peeling–ballooning mode but also can reduce the ion diamagnetic drift effect on the mode stability, even though the ion diamagnetic drift effect stabilizes the mode in a static plasma. Plasma poloidal rotation can also destabilize the mode and cancel the ion diamagnetic drift effect, even when the rotation frequency is much smaller than the toroidal one. These impacts of the rotation on the stability can resolve the discrepancy between the result of the numerical stability analysis and the experimental result in type-I ELMy H-mode plasmas in JT-60U. The reduction of the ion diamagnetic drift effect on ELM stability due to plasma rotation is shown to depend on the direction of the rotation, so that the ion diamagnetic drift effect becomes negligible only when the JT-60U plasma rotates in the direction counter to the plasma current.

RETRACTED: Feedback controller input design for ignition of deuterium–tritium in NSTX tokamak

Nuclear fusion is a nuclear reaction in which two or more atomic nuclei (such as a deuterium–tritium) come very close and then collide at a very high speed and join to form a new high energy nucleus (Helium). Determination of accurate plasma horizontal position during plasma discharge is essential to transport it to a control system based on feedback. The solutions of Grad-Shafranov equation (GSE) analytically can be used for theoretical studies of plasma equilibrium, transport and magneto hydrodynamic stability. Here we have presented specific choices for source functions, kinetic pressure and poloidal plasma current, to be quadratic in poloidal magnetic flux and derive an analytical solution for Grad-Shafranov equation. With applying this solution to NSTX tokamak, we calculated poloidal magnetic flux, toroidal current density and normalized pressure profiles for this tokamak. Toroidal and poloidal flows can considerably change the equilibrium parameters of tokamak. These effects on the equilibrium of tokamak plasmas are numerically investigated using the code FLOW. As a comparative approach to equilibrium problem, the code is used to model equilibrium of NSTX tokamak for case pure toroidal flow. Comparison of the results of these two methods for NSTX tokamak shows good agreement between two and that our analytical solution can be served as good benchmark against the equilibrium code FLOW.

FPGA Based ASFSRBN Controller for Low Offset Integrator for Long Pulse Operation in Aditya Tokamak

Tokamaks are the most proficient devices for acquiring nuclear fusion energy from high-temperature, ionized gas termed as Plasma. Mostly, tokamaks are utilized the toroidal magnetic plasma component and poloidal magnetic plasma component to retain and automatic control. Similar characteristics of two operational amplifiers should be needed in the integration system to calculate the drift value. Inductive magnetic sensors are routinely utilized on existing Tokamaks, are well comprehended and they oblige signal integration to focus the strength of the magnetic field. However, the signal integration failed to solve the problem of deciding the stability of the controlled systems. The Sample and Hold Amplifier (SHA) is an essential part of the sampling (Analog Devices, 2009) to digital convert (ADC). The proposed method is used for eliminating the offset drift of the Integrator for long pulse operations. Adaptive Self Organizing Fuzzy Radial Basis-Function Neural Network Controller (ASFRBNC) and DAC amplifiers are able to adjust the signal for utilization of the PCS and DAS dynamic ranges. The loop processing has done with MATLAB Simulink process. This tokamak has 100s pulse lengths, oblige integrators with better attributes in drift and noise with the long pulse lengths. The proposed system was implemented in Field Programmable Gate Array (FPGA) chip with the use of Verilog Hardware Description-Language (Verilog HDL). The experimental results shown that the proposed method obtained 745 Slices, 61 Flip-Flops (FF), 46 I/O buffers (IOBs), 1221 4bit Look up Tables (LUT) and synchronized with the maximum 50.36MHz clock frequency. The obtained hardware results have been matched with the MATLAB simulation results.

2-D soft x-ray arrays in the EAST.

A high spatial and temporal resolution soft x-ray (SXR) imaging diagnostic has been installed in EAST for the study of magnetohydrodynamics activities and core high-Z impurity transport. Up to 122 lines of sight view the poloidal plasma from three directions (two up-down symmetrical horizontal arrays and one vertical array), which renders the diagnostic able to provide detailed tomographic reconstructions under various conditions. Fourier-Bessel method based on flux coordinates was employed for 2-D SXR tomographic reconstruction. Examples of several events measured by SXR diagnostic in EAST are shown, namely the crash patterns of sawtooth, periodical burst of edge localized modes, and the transport of high-Z intrinsic impurities.

RETRACTED ARTICLE: Low Dissipation with Normalized Flux Surfaces in 2-Dimensional Coordinate for IR-T1 Tokamak Using Grad–Shafranov Equation Solution

Together with the problem of confinement, plasma–wall interactions present the major constraints toward a magnetic fusion reactor. The solutions of Grad–Shafranov equation (GSE) analytically can be used for theoretical studies of plasma equilibrium, transport and magneto-hydrodynamic stability. Here we introduce specific choices for source functions, kinetic pressure and poloidal plasma current, to be quadratic in poloidal magnetic flux and derive an analytical solution for GS equation. With applying this solution to IR-T1 tokamak, we have calculated the poloidal magnetic flux, toroidal current density and normalized pressure profiles for this tokamak. Toroidal and poloidal flows can considerably change the equilibrium parameters of tokamak. These effects on the equilibrium of tokamak plasmas are numerically investigated using a code FLOW. As a comparative approach to equilibrium problem, the code is used to model equilibrium of IR-T1 tokamak for case pure toroidal flow.

Shock formation induced by poloidal flow and its effects on the edge stability in tokamaks

In the high confinement mode of tokamaks, magnitude of the radial electric field increases at the edge. Thus, the poloidal flow inside the transport barrier can be sonic when the edge pressure gradient is not steep enough to make the poloidal flow subsonic. When the poloidal Mach number is close to unity, a shock appears in the low field side and causes a large density perturbation. In this study, we describe a shock induced by the sonic poloidal plasma flow. Then, an entropy production across the shock is calculated. Finally, we introduce a simple model for Type III edge localized modes using the poloidal density variation driven by the sonic poloidal flow.

Capability Assessment of the Equilibrium Field System in KTX**supported by the Ministry of Science and Technology of China (No. 2011GB106000)

Radial equilibrium of the KTX plasma column is maintained by the vertical field which is produced by the equilibrium field coils. The equilibrium is also affected by the eddy current, which is generated by the coupling of copper shell, plasma and poloidal field coils. An equivalent circuit model is developed to analyze the dynamic performance of equilibrium field coils, without auxiliary power input to equilibrium field coils and passive conductors. Considering the coupling of poloidal field coils, copper shell and plasma, the evolution of spatial distribution of the eddy current density on the copper shell is estimated by finite element to analyze the effect of shell to balance. The simulation results show that the copper shell and equilibrium field coils can provide enough vertical field to balance 1 MA plasma current in phase 1 of a KTX discharge. Auxiliary power supply on the EQ coils is necessary to control the horizontal displacement of KTX due to the finite resistance effect of the shell.

The tri-band high-resolution spectrometer for the ITER CXRS diagnostic system

A tri-band high-resolution spectrometer, which was designed for performing diagnostics on the ITER facility using the charge-exchange recombination spectroscopy (CXRS), is described. The CXRS allows measurements of such plasma parameters as the ion temperature, the speed of the toroidal and poloidal plasma rotation, and the concentration of light impurities. The spectrometer is based on three transparent holographic diffraction gratings and is designed to operate simultaneously in three spectral bands: 468 ± 6 nm, 529 ± 6 nm, and 656 ± 8 nm. The results of measuring the main performance parameters of the transparent diffraction gratings and the spectrometer as a whole are presented. It was established that the characteristics of the developed spectrometer satisfy the requirements for the spectroscopic equipment for the ITER CXRS diagnostic system.

Experimental determination of some equilibrium parameter of Damavand tokamak by magnetic probe measurements for representing a physical model for plasma vertical movement.

This investigation is about plasma modeling for the control of vertical instabilities in Damavand tokamak. This model is based on online magnetic measurement. The algebraic equation defining the vertical position in this model is based on instantaneous force-balance. Two parameters in this equation, including decay index, n, and lambda, Λ, have been considered as functions of time-varying poloidal field coil currents and plasma current. Then these functions have been used in a code generated for modeling the open loop response of plasma. The main restriction of the suitability analysis of the model is that the experiments always have to be performed in the presence of a control loop for stabilizing vertical position. As a result, open loop response of the system has been identified from closed loop experimental data by nonlinear neural network identification method. The results of comparison of physical model with identified open loop response from closed loop experiments show root mean square error percentage less than 10%. The results are satisfying that the physical model is useful as a Damavand tokamak vertical movement simulator.