Characteristics of discharge disruptions in the T-10 tokamak

The results of experimental studies of discharge disruptions in the T-10 tokamak at the limiting plasma density are presented. On the basis of measurements of the generated soft X-ray emission, for a group of “slow” disruptions, the dynamics of the magnetic configuration of the central part of the plasma column is studied and the possible role of the m/n = 1/1 mode in the excitation of predisruptions or the final stage of disruption is analyzed. It is shown that the characteristics of plasma electron cooling in predisruptions correspond to those of electron cooling upon pellet injection into T-10 and in discharge predisruptions occurring in regimes with the “quiet mode.” It is found that, in the latter case, the reason for predisruptions and fast electron cooling in the plasma core is the instability of the m/n = 2/1 mode, its spontaneous spatial reconstruction, and the generation of a “cooling wave” during this process. Measurements of the electron temperature (determined from the plasma radiation intensity at the second electron cyclotron harmonic) in the zone of the m/n = 2/1 mode have shown that the transformation of the m/n = 2/1 mode leads to the excitation of predisruptions and the final phase of disruption not only in regimes with the “quiet mode,” but also in disruptions of ordinary ohmic discharges. The experimental results obtained in this work make it possible to determine the scenario of the development of “slow” discharge disruptions in the T-10 tokamak at the limiting plasma density.     

Stiffness and rigidity of the temperature profile in a tokamak

The notions of “stiffness” and “rigidity” of the temperature profile in a tokamak are introduced and formalized. By stiffness is meant the consistency of the profile when the plasma density, boundary temperature, and heating power change. By rigidity is meant the strong dependence of the central temperature on the boundary temperature. Analytical and numerical estimates carried out in a transport model with critical temperature gradients show that, at a low boundary temperature (the L-mode), the profiles are, as a rule, stiff but are not rigid. For a sufficiently high temperature pedestal in the H-mode, there exists a parameter range in which the profiles are stiff and at the same time rigid. However, when the pedestal temperature is too high and the deposited power profile is flat, the temperature profile may be neither stiff nor rigid. This behavior of the electron temperature profile was observed in a number of H-mode discharges with high plasma densities in the DIII-D and JET tokamaks. An analysis is also made of the stiffness and rigidity of the temperature profiles in the MAST and T-10 tokamaks.     

Parameters of turbulent structures at the periphery of the FT-2 tokamak

Results are presented from probe measurements carried out in the scrape-off layer of the FT-2 tokamak in the course of additional lower hybrid heating, during which an L-H transition was observed. The objective of this study was to obtain information on the parameters of blobs-turbulent structures with enhanced plasma density. The measurements were performed not only on the low-field side of the torus, but also on the high-field side, which is still poorly studied. Coherent structures with radial velocities directed both toward the vessel wall and into the plasma column were revealed at the tokamak periphery. Blobs propagating toward the vessel wall were found to prevail both before and after the L-H transition. The average radial velocity of blobs in the L- and H-modes was determined experimentally. The dependence of the radial blob velocity on the transverse size and density of the structure agrees with the ballooning mode model. It is found that the average value of the poloidal blob velocity is four to five times higher than the average radial velocity. The results of measurements carried out on both sides of the torus indicate the presence of internal poloidal polarization of blobs. The average drift velocity of such polarized structures is directed toward the vessel wall. The L-H transition is accompanied by a reduction in the radial velocity. At the same time, the average plasma density inside the structures observed on the low-field side increases appreciably during the transition. The obtained dependences of the radial blob velocity on the plasma density inside the structure generally agree with predictions of the ballooning mode model.     

Model magnetic field configurations with islands

Helical perturbations of the tokamak magnetic field can give rise to magnetic islands in the vicinity of the rational magnetic surfaces at which the pitch of the magnetic field lines coincides with that of the perturbation. The widely known relationship between the magnetic island width and the perturbation amplitude is valid under the assumptions that the island width is small in comparison to the radius of the rational surface and that the perturbation amplitude is constant in the radial direction. The latter assumption indicates that the island width is small in comparison to the radial size of the region where the perturbation current is localized. The calculations carried out for four model magnetic field configurations show that the geometry of the magnetic islands depends on the extent to which the perturbation current is localize and that the width of the magnetic islands is smaller than that calculated from the familiar relationship. The larger the perturbation amplitude, the greater this difference: it may be as large as 25% for the strong perturbations arising during disruptions. The calculations are based on the solution of the geometric problem of constructing the lines of the magnetic field determined by the given distributions of the initial current and perturbation current; the equilibrium equation is not considered. The question of the direction of the perturbation current within the island relative to the direction of the initial unperturbed current is discussed. The perturbation current flowing in an island is directed opposite to the initial current with a radially decreasing density; for this reason, such an island can naturally be called a “negative” island. Together with the formation of negative islands, the formation of “positive” ones is also considered. The latter are shown to form under the following conditions: the perturbation current density should be higher than the density of the current that produces the unperturbed field and the perturbation current itself should be localized in a sufficiently narrow radial layer. The positive islands are smaller in size than negative ones.     

Current filaments in plasmas

Possible configurations of current filaments in Z-pinch and tokamak plasmas are analyzed. A thin current-carrying beam injected in a plasma should be surrounded by a halo of countercurrents, in which case the resulting configuration may resemble a tubular structure. A.B. Kukushkin and V.A. Rantsev-Kartinov pointed out the existence of specific plasma structures of the squirrel-cage type and interpreted them as “wild cables of solid-state nanotubes.” It is shown that these structures can also be attributed to the fundamental mode of the conventional magnetic filamentation in the form of a “hexagonal parquet.” Also, a study is made of the phenomena governing the pattern of plasma structures, namely, tearing filamentation, two types of longitudinal beam bunching, and self-organization of the filaments.     

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.     

Study of runaway electrons using the conditional average sampling method in the Damavand tokamak

Some experiments for studying the runaway electron (RE) effects have been performed using the poloidal magnetic probes system installed around the plasma column in the Damavand tokamak. In these experiments, the so-called runaway-dominated discharges were considered in which the main part of the plasma current is carried by REs. The induced magnetic effects on the poloidal pickup coils signals are observed simultaneously with the Parail–Pogutse instability moments for REs and hard X-ray bursts. The output signals of all diagnostic systems enter the data acquisition system with 2 Msample/(s channel) sampling rate. The temporal evolution of the diagnostic signals is analyzed by the conditional average sampling (CAS) technique. The CASed profiles indicate RE collisions with the high-field-side plasma facing components at the instability moments. The investigation has been carried out for two discharge modes—low-toroidal-field (LTF) and high-toroidal-field (HTF) ones—related to both up and down limits of the toroidal magnetic field in the Damavand tokamak and their comparison has shown that the RE confinement is better in HTF discharges.     

Pulsed time-of-flight refractometry measurements of the electron density in the T-11M tokamak

A new method for measuring the plasma density in magnetic confinement systems—pulsed time-of-flight refractometry—is developed and tested experimentally in the T-11M tokamak. The method is based on the measurements of the time delay of short (with a duration of several nanoseconds) microwave pulses propagating through the plasma. When the probing frequency is much higher than the plasma frequency, the measured delay in the propagation time is proportional to the line-averaged electron density regardless of the density profile. A key problem in such measurements is the short time delay of the pulse in the plasma (～1 ns or less for small devices) and, consequently, low accuracy of the measurements of the average density. Various methods for improving the accuracy of such measurements are proposed and implemented in the T-11M experiments. The measurements of the line-averaged density in the T-11M tokamak in the low-density plasma regime are performed. The results obtained agree satisfactorily with interferometric data. The measurement errors are analyzed, and the possibility of using this technique to measure the electron density profile and the position of the plasma column is discussed.     

Electrostatic plasma turbulence and spitzer longitudinal conductivity in tokamaks

An analysis has revealed that there may be three radically different steady states of a tokamak plasma: (i) discharges in which the electron and ion transport can be described by neoclassical theory; (ii) discharges with the Spitzer longitudinal conductivity, neoclassical ion transport, and “anomalous” electron transport; and (iii) discharges in which the electron transport and ion transport are both “anomalous.” The dimensionless parameters responsible for the occurrence of the three types of discharges are determined. In accordance with the criteria derived for the achievement of different steady states, discharges of the second type are most typical of modern tokamaks and discharges of the third type can occur only if the turbulence is sufficiently strong. Discharges of the first type cannot occur in the range of the working parameters of present-day tokamaks and future tokamak reactors, but they can be ignited in a large class of magnetic confinement systems. The physical reason for the onset of different types of discharges is associated with the fact that turbulent fluctuations play very different roles in the dynamics of the ion and electron components of a finite-size magnetized plasma. The question of the self-consistency between the profiles is considered. A law is derived according to which the thermal diffusivity increases toward the plasma edge.     

Effect of helical magnetic fields on plasma stability in tokamaks

Physical mechanisms for destabilization of MHD perturbations by external quasistatic magnetic fields and rotating helical magnetic fields in a tokamak plasma are identified using a numerical model of tearing modes in a viscous high-temperature plasma. The critical conditions for the onset of MHD perturbations and their dynamic model are compared with the experimental results from the JET tokamak. The model is used to predict how the stray magnetic fields will influence plasma stability in a tokamak reactor (ITER). __________ Translated from Fizika Plazmy, Vol. 26, No. 8, 2000, pp. 675–682. Original Russian Text Copyright ￠ 2000 by Savrukhin.     

Analysis of quasistatic MHD perturbations and stray magnetic fields in a tokamak plasma

Mechanisms for the development of quasistatic MHD perturbations in a viscous rotating tokamak plasma are considered. The influence of stray magnetic fields on the stability of MHD modes in the plasma of the TFTR tokamak is analyzed.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

Inhomogeneous stationary states in reaction-diffusion systems.

Inhomogeneous stationary solutions for reaction—diffusion equations are of interest with regard to the chemical basis of morphogenesis. Numerical means of determining such solutions and of testing their stability to small perturbations are examined, and applied to shape formation in three systems: the “Brusselator” and “Lotka—Volterra” mechanisms, and a simple model for slimemould aggregation.     

Response to “Different measures of ‘genome-wide’ DNA methylation exhibit unique properties in placental and somatic tissues”

I found the research paper “Different measures of ‘genome-wide’ DNA methylation exhibit unique properties in placental and somatic tissues” by Price ME and colleagues in the June 2012 issue of Epigenetics to be an interesting read, but it contains errors in regards to the use of the MethylFlash Methylated DNA Quantification Kit. The text contained in the “Global DNA Methylation” paragraph under the “Methods” section of the paper claims that the kit was used by “following the manufacturer’s protocol.” I find that this is quite misleading to the reader as we have identified, based on the original electronic publication ahead of print, that the steps had not been correctly carried out.

The original text was the following: “DNA was hybridized to wells treated to have a high affinity for DNA. The wells were washed with a 5-mC-specific capture antibody followed by a detection antibody. The absorbance (or optical density) of each well was measured using a microplate spectrophotometer. Correlation of technical replicates was poor (r = 0.09, p = 0.72) using this kit.” However, the user guide of this kit clearly states that DNA is bound, not hybridized, to the strip wells and that the wells should be washed with the included Wash Buffer rather than a “5-mC-specific capture antibody.”

Therefore, it is not surprising that the result or correlation of replicates was poor and that the authors’ “results were variable” due to improper use of the kit. Based on our quality control tests and feedback from the vast amount of users of this popular kit, the variation between replicates should be less than 10% with R value > 0.9 (p < 0.01), assuming proper user performance according to the product manual.

I hope this helps to correct the misinformation presented in the paper as I feel that it is important to promote accuracy on behalf of the epigenetic research community. I also kindly encourage any users of an Epigentek product to work with our very knowledgeable technical support team should they have any difficulties.     

Generation of zonal flows and large-scale magnetic fields by drift-Alfvén turbulence

The possibility of generating zonal perturbations by drift-Alfvén turbulence in a plasma with a finite pressure (1>β>m_e/m_i) is investigated. A set of coupled equations is derived that includes the equation for the spectral function of the turbulence and the averaged equations for zonal perturbations. It is shown that, in particular cases, the equation for the spectral function possesses action invariants; i.e., it takes the form of a conservation law for some quantities that are proportional to the spectral function of turbulence. Two types of instability of the zonal perturbations are revealed. The first type of instability generates only a zonal flow. Two regimes of this instability—resonant and hydrodynamic regimes—are examined, and the corresponding instability growth rates are determined. The second type of instability takes place when the resonant interaction of drift-Alfvén waves with electrons is taken into account. Because of this instability, the generation of a zonal magnetic field is inevitably accompanied by the generation of a zonal flow. It is found that the growth rate of the second type of instability is slower than that of the first type.     

Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.     

Emission spectroscopy diagnostics of rare gases in the PNX-U facility

Results are presented from measurements of the electron temperature and neutral atom density in a low-temperature microwave plasma by the method of emission spectroscopy. The measurements were conducted in the PNX-U facility—a magnetic confinement system with a “magnetic wall.” Multichord measurements of plasma radiation at a wavelength of 750.37 nm were performed with the help of an absolutely calibrated monochromator. The neutral atom density was calculated using the collisional-radiative model. The degree of plasma ionization near the axis of the facility was found to be close to unity. The electron temperature of the argon plasma was measured from the relative intensities of the spectral lines of neutral helium injected in small amounts into the plasma (the so-called helium thermometer method). At a low microwave heating power, the results of these measurements agree well with the results of probe measurements.     

Aspects of the Phænogamic Vegetation of Rodriguez,with Descriptions of new Plants from the Island.

As regards the history of its flora, the island of Rodriguez bears a striking resemblance to St. Helena. We read of the latter island that fire, goats, and finally introduced foreign plants well nigh exterminated the indigenous flora; and the same causes have operated and, I regret to say, are still operating in Rodriguez. The result is that the primitive vegetation has been in great part destroyed, leaving the island a field for the rank and rapid growth of common tropical weeds. The old and luxuriant vegetation of two hundred years ago—thus quaintly described by Leguat*, “We could hardly take our eyes off from the little mountains of which the island entirely consists; they are so richly spread with great and tall trees,” and, again, “‘Tis as I have hinted, composed of lovely hills covered all with fine trees whose perpetual verdure is entirely charming”—has now, to a large extent, disappeared, and is represented by only a few species, many of which are confined to the more unfrequented and less accessible places. It is indeed difficult to recognize in the barren and arid Rodriguez of the present day the “little Eden,”“lovely isle,”“earthly paradise” of Leguat. The flora, as it now exists, is an exceedingly fragmentary one; it is therefore a matter of some difficulty to determine its exact limits and to draw conclusions as to its affinities with the floras of other oceanic islands and of adjacent continents. This is the more to be regretted, as, from the geographical position of the island and the physical condition of climate to which it is subject, its flora might be expected, whether taken singly or as part of that of the Mascarene group, to contribute very important data towards the solution of the problem of the distribution of plant‐life in that region. The following general statements may, however, be made:—     

Bifurcations of axisymmetric plasma equilibrium in a tokamak

Bifurcation of solutions to the Grad–Shafranov-type equation for helically symmetric plasma near the threshold for tearing instability are analyzed. Quadratic and cubic nonlinearities were added to the linear dependence of the current density on the helical flux. Depending on the character of nonlinearity, two types of bifurcation can be observed, the “small” and the “large” ones. The small bifurcation is typical of cubic nonlinearity and reveals itself in the growth of the magnetic island from zero as the profile parameter increases above the instability threshold. The large bifurcation is typical of quadratic nonlinearity and causes jumplike formation of a large-scale magnetic island upon exceeding the instability threshold. As the profile parameter decreases below the instability threshold, the large-scale island continues to persist for some time (the hysteresis effect) and then suddenly disappears.     

Time evolution of the exponential wavenumber spectra of turbulence upon helium injection into a hydrogen discharge at the FT-2 tokamak

The effect of variations in the key parameter of short-wavelength turbulence—the ion-acoustic Larmor radius ρ _s , which determines the position of the maximum of the drift instability growth rate over poloidal wavenumbers—was studied experimentally at the FT-2 tokamak. For this purpose, helium was injected to hydrogen plasma, which resulted in a change in the electron temperature at the plasma edge. The universality of the exponential shape of the turbulence spectra over radial wavenumbers q and a substantial excess of the characteristic turbulence scale L over the ion-acoustic Larmor radius was confirmed with the help of correlative diagnostics of enhanced scattering. This excess at the discharge periphery reaches a value of 3–5 at a low electron temperature, apparently, due to an increase in the dissipation of drift waves upon their cascade transfer toward short scale-lengths.