Diagnostics of MHD instability in the Globus-M spherical tokamak

The paper describes a diagnostic system for studying MHD plasma perturbations in the Globus-M spherical tokamak (a major radius of 0.36 m, a minor radius of 0.24 m, and an aspect ratio of 1.5). The system includes a poloidal and a toroidal array consisting of 28 and 16 Mirnov probes, respectively, as well as a 32-channel proportional soft X-ray detector. Methods are described for calculating the poloidal and toroidal numbers of the dominant helical perturbations by using data from probe measurements. Results are presented of processing the experimental data from some tokamak discharges with a plasma current of 150–250 kA, an average electron density of up to 10²⁰ m^?3, and a toroidal magnetic field of 0.4 T. Specific features of MHD perturbations and their influence on the parameters of the plasma column in different stages of a discharge are briefly discussed.     

MHD diagnostics in the T-11M tokamak

An MHD diagnostic system for investigating the dynamics of disruption and the preceding phase of the discharge in the T-11M tokamak is described. This system makes it possible to study the structure of magnetic fluctuations in the plasma column. The diagnostic system includes a set of magnetic pick-up loops (Mirnov coils) arranged in several poloidal cross sections of the tokamak, a data acquisition system that provides synchronous recording of Mirnov coil signals, a synchronization system for triggering the data acquisition system during a disruption, and a system for processing and representation of the experimental data on magnetic fluctuations in the plasma column. Examples of how the MHD diagnostic system operates in the T-11M tokamak are presented.     

Hilbert-Huang transform in MHD plasma diagnostics

A new method for processing experimental data from MHD diagnostics is discussed that provides a more detailed study of the dynamics of large-scale MHD instabilities. The method is based on the Hilbert-Huang transform method and includes an empirical mode decomposition algorithm, which is used to decompose the experimental MHD diagnostic signals into a set of frequency-and amplitude-modulated harmonics in order to construct the time evolutions of the amplitudes and frequencies of these harmonics with the help of the Hilbert transform. The method can also be applied to analyze data from other diagnostics that measure unsteady oscillating signals.     

Influence of plasma pedestal profiles on access to ELM-free regimes in ITER

The influence of current density and pressure gradient profiles in the pedestal on the access to the regimes free from edge localized modes (ELMs) like quiescent H-mode in ITER is investigated. Using the simulator of MHD modes localized near plasma boundary based on the KINX code, calculations of the ELM stability were performed for the ITER plasma in scenarios 2 and 4 under variations of density and temperature profiles with the self-consistent bootstrap current in the pedestal. Low pressure gradient values at the separatrix, the same position of the density and temperature pedestals and high poloidal beta values facilitate reaching high current density in the pedestal and a potential transition into the regime with saturated large scale kink modes. New version of the localized MHD mode simulator allows one to compute the growth rates of ideal peeling-ballooning modes with different toroidal mode numbers and to determine the stability region taking into account diamagnetic stabilization. The edge stability diagrams computations and sensitivity studies of the stability limits to the value of diamagnetic frequency show that diamagnetic stabilization of the modes with high toroidal mode numbers can help to access the quiescent H-mode even with high plasma density but only with low pressure gradient values at the separatrix. The limiting pressure at the top of the pedestal increases for higher plasma density. With flat density profile the access to the quiescent H-mode is closed even with diamagnetic stabilization taken into account, while toroidal mode numbers of the most unstable peeling-ballooning mode decrease from n = 10?40 to n = 3?20.     

Reduced MHD equations with allowance for slow magnetosonic waves

The so-called reduced magnetohydrodynamics, which deals with the motion of incompressible fluids and is usually applied to describe plasma flows in a strong toroidal magnetic field, has a number of drawbacks and, in some cases, fails to produce correct results. The equations proposed here are simpler than the original MHD equations and are free of these drawbacks. These equations, like reduced MHD equations, make it possible to remove from consideration fast magnetosonic waves and to introduce the vector potential for the poloidal magnetic field. However, our equations differ from the reduced MHD equations in that they completely incorporate slow magnetosonic waves, the specific features of the toroidal geometry, and the effects of the toroidal velocity.     

Stability of a quasi-flute mode under the Bernstein-Kadomtsev condition in a toroidal confinement system

It is shown that the growth rate of the MHD instability in toroidal configurations is slower in a situation in which the Bernstein-Kadomtsev condition is satisfied while the Mercier stability criterion is not. Under the Bernstein-Kadomtsev condition, Alfvénic Mercier modes are not excited, but quasi-flute acoustic Mercier modes develop instead. In confinement systems with closed magnetic field lines, the Bernstein-Kadomtsev condition ensures MHD stability; however, a small rotational transform produced by magnetic perturbations can give rise to a quasi-flute acoustic instability whose growth rate is proportional to the perturbation amplitude, in which case the fastest growing oscillations are those with the shortest wavelengths.     

Role of the plasma interaction with magnetic field in the “missing power” problem

It is shown that, at rapid changes of the heating power, the magnetically confined equilibrium plasma almost completely absorbs the injected energy, so that its only small part goes to the magnetic field. The result is obtained within the standard MHD theory with use of exact consequences of the force-balance equations in toroidal geometry. It is assumed that, when heated, the plasma evolves from one equilibrium state to another with the magnetic field frozen-in. Another constraint is the conservation of the toroidal magnetic flux in the plasma-wall vacuum gap. It is shown that the plasma interaction with magnetic field (which is traditionally neglected in the analysis of heat transport in tokamaks and stellarators) is the natural mechanism of fast redistribution of energy in the plasma, observed in some experiments in these devices at switchon of powerful heat sources.     

Three-dimensional rotational plasma flows near solid surfaces in an axial magnetic field

A rotational flow of a conducting viscous medium near an extended dielectric disk in a uniform axial magnetic field is analyzed in the magnetohydrodynamic (MHD) approach. An analytical solution to the system of nonlinear differential MHD equations of motion in the boundary layer for the general case of different rotation velocities of the disk and medium is obtained using a modified Slezkin–Targ method. A particular case of a medium rotating near a stationary disk imitating the end surface of a laboratory device is considered. The characteristics of a hydrodynamic flow near the disk surface are calculated within the model of a finite-thickness boundary layer. The influence of the magnetic field on the intensity of the secondary flow is studied. Calculations are performed for a weakly ionized dense plasma flow without allowance for the Hall effect and plasma compressibility. An MHD flow in a rotating cylinder bounded from above by a retarding cap is considered. The results obtained can be used to estimate the influence of the end surfaces on the main azimuthal flow, as well as the intensities of circulating flows in various devices with rotating plasmas, in particular, in plasma centrifuges and laboratory devices designed to study instabilities of rotating plasmas.     

Characteristics of major plasma discharge disruption in the Globus-M spherical tokamak

The characteristics of the major disruption of plasma discharges in the Globus-M spherical tokamak are analyzed. The process of current quench is accompanied by the loss of the vertical stability of the plasma column. The plasma boundary during the disruption is reconstructed using the algorithm of movable filaments. The plasma current decay is preceded by thermal quench, during which the profiles of the temperature and electron density were measured. The data on the time of disruption, the plasma current quench rate, and the toroidal current induced in the tokamak vessel are compared for hydrogen and deuterium plasmas. It is shown that the disruption characteristics depend weakly on the ion mass and the current induced in the vessel increases with the disruption time. The decay rate of the plasma toroidal magnetic flux during the disruption is determined using diamagnetic measurements. Such a decay is a source of the poloidal current induced in the vessel; it may also cause poloidal halo currents.     

Alfvén eigenmode evolution computed with the VENUS and KINX codes for the ITER baseline scenario

A new application of the VENUS code is described, which computes alpha particle orbits in the perturbed electromagnetic fields and its resonant interaction with the toroidal Alfvén eigenmodes (TAEs) for the ITER device. The ITER baseline scenario with Q = 10 and the plasma toroidal current of 15 МА is considered as the most important and relevant for the International Tokamak Physics Activity group on energetic particles (ITPA-EP). For this scenario, typical unstable ТАЕ-modes with the toroidal index n = 20 have been predicted that are localized in the plasma core near the surface with safety factor q = 1. The spatial structure of ballooning and antiballooning modes has been computed with the ideal MHD code KINX. The linear growth rates and the saturation levels taking into account the damping effects and the different mode frequencies have been calculated with the VENUS code for both ballooning and antiballooning TAE-modes.     

Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.     

Review of mixing length estimates and effects of toroidicity in a fluid model for turbulent transport in tokamaks

Basic aspects of turbulent transport in toroidal magnetized plasmas are discussed. In particular the fluid closure has strong effects on zonal flows which are needed to create an absorbing boundary for long wave lengths and also to obtain the Dimits nonlinear upshift. The fluid resonance in the energy equation is found to be instrumental for generating the L–H transition, the spin-up of poloidal rotation in internal transport barriers, as well as the nonlinear Dimits upshift. The difference between the linearly fastest growing mode number and the corresponding longer nonlinear correlation length is also addressed. It is found that the Kadomtsev mixing length result is consistent with the non-Markovian diagonal limit of the transport at the nonlinearly obtained correlation length.     

Empirical mode decomposition method for investigating the structure of large-scale MHD instabilities in a tokamak

A new approach to the processing of experimental data from MHD diagnostics is developed for the purpose of investigating the spatial structure of large-scale MHD instabilities in a tokamak. The empirical mode decomposition method is applied to expand a multimode MHD perturbation in individual modes, which are then identified by constructing a spatial analytic signal with the help of the Hilbert transform. The method can be used to analyze the structure of the tearing instability and of the resistive wall modes.     

Integrated predictive modeling of JET H-mode plasma with type-I and type-III ELMs

Edge plasma parameters influence plasma performance in many different ways (profile stiffness is probably one of the best known examples). In the ELMy H-mode plasma, a thin region with improved transport characteristics (the edge transport barrier) links the core and the scrape-off layer. There is a strong coupling between these three areas, so that even a modest variation of plasma parameters in one region can lead to a dramatic change in the overall plasma performance. A systematic MHD stability analysis and self-consistent integrated predictive modeling of a series of JET ELMy H-mode plasmas, including scans in gas fueling and triangularity, are presented. The main conclusion is that plasma performance indeed sensitively depends on the edge plasma parameters, which should be modeled in a self-consistent way.     

A fast and reliable method for simultaneous waveform, amplitude and latency estimation of single-trial EEG/MEG data

The amplitude and latency of single-trial EEG/MEG signals may provide valuable information concerning human brain functioning. In this article we propose a new method to reliably estimate single-trial amplitude and latency of EEG/MEG signals. The advantages of the method are fourfold. First, no a-priori specified template function is required. Second, the method allows for multiple signals that may vary independently in amplitude and/or latency. Third, the method is less sensitive to noise as it models data with a parsimonious set of basis functions. Finally, the method is very fast since it is based on an iterative linear least squares algorithm. A simulation study shows that the method yields reliable estimates under different levels of latency variation and signal-to-noise ratio?s. Furthermore, it shows that the existence of multiple signals can be correctly determined. An application to empirical data from a choice reaction time study indicates that the method describes these data accurately.     

Effect of elution modes on protein separation by cross-axis coil planet centrifuge with two different types of coiled columns

Effect of elution modes on protein separation was investigated using cross-axis coil planet centrifuge (cross-axis CPC) with two different types of coiled columns, i.e., eccentric coil and toroidal coil assemblies. Myoglobin and lysozyme were separated with an aqueous two-phase solvent system composed of 12.5% (w/w) polyethylene glycol 1000 and 12.5% (w/w) dibasic potassium phosphate. The substantial effect of elution modes was observed by the toroidal coil, while the negative result was given at the eccentric coil. Using the toroidal coil, higher peak resolution of proteins was attained at the tail to head elution mode. In the outward lower phase mobile elution mode, the satisfactory separation was obtained by both eccentric coil and toroidal coil assemblies. However, in the inward upper phase mobile elution mode, the toroidal coil produced a broad and asymmetric myoglobin peak. The analysis using polyacrylamide gel electrophoresis revealed that the toroidal coil partially separated the components originally present in the myoglobin sample. As the result, a modified equation was devised to express the peak resolution (Rs) using the lysozyme peak. The overall results indicated that the toroidal coil produced better partition efficiency than the eccentric coil under the optimized experimental condition including the direction of the Coriolis force acting on the mobile phase in the toroidal coil.     

Analysis of phasic and tonic electromyographic signal characteristics: Electromyographic synthesis and comparison of novel morphological and linear-envelope approaches

The pattern of tonic and phasic components in an EMG signal reflects the underlying behaviour of the central nervous system (CNS) in controlling the musculature. One avenue for gaining a better understanding of this behaviour is to seek a quantitative characterisation of these phasic and tonic components. We propose that these signal characteristics can range between unvarying, tonic and intermittent, phasic activation through a continuum of EMG amplitude modulation. In this paper, we present two new algorithms for quantifying amplitude modulation: a linear-envelope approach, and a mathematical morphology approach. In addition we present an algorithm for synthesising EMG signals with known amplitude modulation. The efficacy of the synthesis algorithm is demonstrated using real EMG data. We present an evaluation and comparison of the two algorithms for quantifying amplitude modulation based on synthetic data generated by the proposed synthesis algorithm. The results demonstrate that the EMG synthesis parameters represent 91.9% and 96.2% of the variance of linear-envelopes extracted from lumbo-pelvic muscle EMG signals collected from subjects performing a repetitive-movement task. This depended, however, on the muscle and movement-speed considered (F = 4.02, p < 0.001). Coefficients of determination between input and output amplitude modulation variables were used to quantify the accuracy of the linear-envelope and morphological signal processing algorithms. The linear-envelope algorithm exhibited higher coefficients of determination than the most accurate morphological approach (and hence greater accuracy, T = 8.16, p < 0.001). Similarly, the standard deviation of the coefficients of determination was 1.691 times smaller (p < 0.001). This signal processing algorithm represents a novel tool for the quantification of amplitude modulation in continuous EMG signals and can be used in the study of CNS motor control of the musculature in repetitive-movement tasks.     

MHD limits in the T-15M tokamak

Abstrac The problem of plasma MHD stability in the T-15M tokamak is considered in realistic geometry. Stability of the external kink modes with the toroidal wavenumbers n=1, 2, and 3 is numerically investigated in equilibrium configurations similar to the systematically analyzed steady-state configurations with reversed shear in ITER. The stability limits in T-15M are found with and without account taken of the stabilizing influence of the first wall. The results of the calculations are used to compare T-15M with ITER. The stabilizing effect resulting from reducing the distance between the first wall and the plasma in T-15M is evaluated. __________ Translated from Fizika Plazmy, Vol. 29, No. 12, 2003, pp. 1088–1098. Original Russian Text Copyright ? 2003 by Medvedev, Pustovitov.     

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I _p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P _RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.