New approach to the probabilistic-statistical analysis of turbulent transport processes in plasma

It is proposed to apply the statistical analysis of the increments of fluctuating particle fluxes to examine the probability characteristics of turbulent transport processes in plasma. Such an approach makes it possible to pass over to the analysis of the dynamical probability characteristics of the process under study. It is shown that, in the plasmas of the L-2M stellarator and the TAU-1 linear device, the increments of local fluctuating particle fluxes are stochastic in character and their distributions are scale mixtures of Gaussians. In particular, in TAU-1, the increments obey a Laplacian distribution (which is a scale mixture of Gaussians with an exponential mixing distribution). A mathematical model is proposed to explain such distributions. Possible physical mechanisms responsible for the random character of the increments of fluctuating particle fluxes are discussed.     

Effect of vacuum chamber boronization on the plasma parameters in the L-2M stellarator

After boronization of the vacuum chamber of the L-2M stellarator, radiative losses from ohmically and ECR heated plasmas were reduced by a factor of 3–4. Under these conditions, radiative losses in the ECRH regime comprise only 10–15% of the input microwave power. Some effects have been detected that were not observed previously: a substantial increase in the gradient of the electron temperature near the separatrix, a preferentially outward-directed radial turbulent particle flux (both throughout the discharge phase and from shot to shot), and a longer (by a factor of 2–3) duration of the plasma cooling phase.     

Mechanisms governing radial heat fluxes in tokamak plasma

A method for analyzing the characteristics of turbulence responsible for radial heat transport is proposed. The method is based on the previously proposed hypotheses (to a great extent, confirmed experimentally) concerning the consistency of normalized pressure profiles in tokamak plasmas and the mechanism of internal transport barrier formation. Using the proposed approach, it is shown that, under an external action on the plasma, when the plasma heat flux onto the wall grows, the spectrum of turbulent modes broadens due to the excitation of modes with lower poloidal numbers m. Thus, in contrast to the conventional diffusion approach, the transport coefficient depends on the flux intensity. A mechanism of formation of internal transport barriers is proposed.     

Studies of fluctuations in the high-temperature plasma of modern stellarators by the microwave scattering technique

Microwave scattering diagnostics are described that allow direct measurements of the turbulent processes in the high-temperature plasma of magnetic confinement systems. The first physical results are presented from fluctuation measurements carried out in 2000–2001 in three stellarators: L-2M (Institute of General Physics, Moscow), LHD (National Institute of Fusion Science, Toki), and TJ-II (CIEMAT, Madrid). Plasma density fluctuations in the axial (heating) regions of the L-2M and LHD stellarators were measured from microwave scattering at the fundamental harmonic of the heating gyrotron radiation. In the TJ-II stellarator, a separate 2-mm microwave source was used to produce a probing beam; the measurements were performed at the middle of the plasma radius. Characteristic features of fluctuations, common for all three devices, are revealed by the methods of statistical and spectral analysis. These features are the wide frequency Fourier and wavelet spectra, autocorrelation functions with slowly decreasing tails, and non-Gaussian probability distributions of the magnitudes and the increments in the magnitude of fluctuations. Observations showed the high level of coherence between turbulent fluctuations in the central region and at the edge of the L-2M plasma. The drift-dissipative instability and the instability driven by trapped electrons are examined as possible sources of turbulence in a high-temperature plasma.     

Is it possible that MHD instability triggers a transition into the improved confinement regime of toroidal plasmas?

Analyzing the experimental data from L-2M stellarator and performing appropriate theoretical analysis, the authors affirmatively answer the question raised in the title of the article. The external peeling mode is proposed as the instability triggering the transition. Peeling mode stability in magnetic-hill Mercierstable plasmas is analyzed analytically. It is shown that correctly taking into account vacuum region forbids internal peeling modes, while the external peeling mode has a threshold with respect to the plasma pressure gradient. Calculations and experimental data are in reasonable agreement.     

Description of turbulent convection in a plasma with the help of interacting Lorentz oscillators

A four-field model is proposed that describes turbulent plasma convection inside the separatrix during the L-H transition. It is shown that the Braginskii four-field hydrodynamic equations, which describe fluctuations of the electron and ion temperatures, plasma density, and electrostatic potential in tokamak edge plasmas, can be reduced to three Lorentz-like systems of equations coupled through the equation for the kinetic energy of the fluctuations, i.e., to a four-field edge turbulent layer model describing the nonlinear dynamics of convective cells in the presence of a sheared flow. For three coupled oscillators, the critical pressure gradient corresponding to transitions to both L-and H-modes is found to be much lower than that for an individual oscillator, which describes turbulent convection driven by fluctuations of one type. The edge turbulent layer model makes it possible to describe the formation of a transport barrier inside the separatrix during the L-H transition; calculate heat and particle fluxes via ion and electron channels; and, in combination with the transport code for a core plasma, compute the auxiliary heating power required for a transition to the H-mode.     

Second harmonic of gyrotron radiation: New potentialities of plasma diagnostics

It is shown that the relative intensity of the second harmonic of gyrotron radiation on the axis of a microwave beam after quasi-optical filtering in a four-mirror quasi-optical transmission line is about ?50 dB of the total radiation intensity. The second-harmonic radiation is used in collective-scattering diagnostics of turbulent density fluctuations in the plasma column of the L-2M stellarator. At an electron temperature of 0.8–1.0 keV and average plasma density of 2.0–2.5×10¹³ cm^?3 (a plasma energy of about 0.6 kJ), which was achieved after the boronization of the vacuum chamber, spatiotemporal structures in plasma density fluctuations were observed in the central region of the plasma column. The correlation time between the structures was found to be on the order of 1 ms. It is shown that the spectrum of the signal from the second-harmonic scattering extends to higher frequencies compared to that from the fundamental-harmonic scattering.     

One-dimensional nonlinear self-organized structures in dusty plasmas

Dusty plasmas, which are open systems, can form stable one-dimensional self-organized structures. Absorption of plasma by dust particles results in the plasma flux from the plasma regions where the dust is absent. It is found that, in a one-dimensional dust layer, this flux is completely determined by the number of dust particles per unit area of the layer surface. This number determines all of the other parameters of the steady-state dust structure; in particular, it determines the spatial distributions of the dust density, dust charge, electron and ion densities, and ion drift velocity. In these structures, a force and electrostatic balance is established that ensures the necessary conditions for confining the dust and plasma particles in the structure. The equilibrium structures exist only for subthermal ion flow velocities. This criterion determines the maximum possible number of dust particles per unit area in the steady-state structure. The structures have a universal thickness, and the dust density changes sharply at the edge of the structure. The structures with a size either less than or larger than the ion mean free path with respect to ion-neutral collisions, quasi-neutral and charged structures, and soliton-and anti-soliton-like structures are investigated. Laboratory experiments and observations in extraterrestrial plasma formation are discussed in relation to dust structures.     

Apoptotic cell death and related gene expression in metastatic tumors of AKR lymphomas of varying malignancy

Resistance to apoptosis may be related to tumor progression, due to the implications it might have on both tumor mass and genetic instability. We compared the tendency to spontaneous apoptosis and the proliferative capacity of metastatic growths of several AKR lymphoma variants (TAU-45, TAU-47, TAU-44, TAU-33, TAU-42 and TAU-46, in the order of increasing metastatic potential). We further compared the expression of several apoptosis-related genes. Cell proliferative capacity did not appear to determine malignant behavior since, on the whole, a decrease in S + G2M fraction was observed with increasing malignancy. Sensitivity to apoptotic cell death decreased with increasing malignancy when comparing the TAU-45, TAU-47, TAU-44 and TAU-33 variants, suggesting a role of reduced apoptosis in this T-cell lymphoma. An increase in Bcl-2 content with increasing aggressiveness among these variants, implicates this protein in this tumor progression-related resistance to apoptosis. However, the two variants of highest malignancy, TAU-42 and TAU-46, did not follow the same trend, since they displayed a relatively high content in apoptotic cells and a low Bcl-2 content. Fas receptor expression did not correlate with tendency to apoptosis, indicating that malignant behavior in the AKR lymphoma does not depend on CD95/Fas/APO1 downregulation. Overexpression of p53 was observed only in one of the variants of lowest malignancy.     

Stability of global magnetohydrodynamic modes in the L-5 compact torsatron

Global magnetohydrodynamic (MHD) modes in free-boundary plasma equilibrium configurations of the L-5 six-period compact torsatron (project of the Prokhorov General Physics Institute, Russian Academy of Sciences; G. M. Batanov et al., Plasma Dev. Operat. 11, 161 (2003)) have been investigated using the CAS3D code. It is shown that global internal ideal MHD modes can be found reliably only in Mercier unstable plasmas. In all cases under study, they are intrinsically ballooning in nature, i.e., the disturbance at the inner side of the torus is significantly lower in value than that at the outer side. Besides internal modes localized near low-order rational magnetic surfaces, external modes that are localized near the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) have been found. In contrast to a tokamak with the same aspect ratio, in which pressure-gradient edge-localized modes are ballooning in nature, the peeling modes in the 3D currentless magnetic configuration investigated in the present work are quasi-cylindrical in the flux coordinate system. The problem of plasma boundary destruction under the action of magnetic fields generated by plasma currents is also briefly discussed.     

Thin current sheets in collisionless plasma: Equilibrium structure,plasma instabilities,and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.     

Investigation of the possibility of using correlation reflectometry to determine the parameters of small-scale turbulence in the core of a tokamak plasma

Results are reported from investigating the possibility of using reflectometry to determine the parameters of small-scale turbulence in the core of a tokamak plasma. In particular, the extent to which the reflectometric measurements are local is estimated. Experimental data from reflectometric measurements in the gradient zone, as well as the cross spectra and radial correlation functions, are presented. A turbulence model is constructed that yields spectral, statistical, and correlation turbulent plasma properties close to the measured ones. The model is used to simulate the propagation of electromagnetic radiation in a turbulent plasma.     

Formation of vortex dust structures in inhomogeneous gas-discharge plasmas

A generalized analytical model of instabilities in a dusty plasma with a nonzero grain charge gradient in a field of nonelectrostatic forces is considered. A review is given of different experimental observations of the dust self-oscillations that occur in the plasmas of an rf capacitive discharge and a dc glow discharge and whose appearance can be explained in terms of the proposed model. It is shown that the change in the grain charge gives rise to dynamic dust structures in laboratory gas-discharge plasmas. Attention is focused on the analysis of the onset of vortex motion of the dust grains.     

Scattering of polarized radio waves by Langmuir turbulence in a plasma in a magnetic field

A study is made of radio-wave scattering by Langmuir turbulent pulsations in a plasma in a magnetic field. The effect of this process on the polarization of radio waves at frequencies far above or close to the electron plasma frequency is investigated. The wave scattering by Langmuir turbulence is shown to strongly affect the polarization characteristics. When the optical thickness typical of the scattering process is on the order of unity, the degree of wave polarization can change by 30% both at high frequencies and at frequencies close to the plasma frequency, in which case the circular polarization can reverse direction. It is shown that, as a result of wave scattering by Langmuir turbulence, the degree of circular polarization of radio waves depends on the wavelength even in a uniform magnetic field.     

Markov model plus k-word distributions: a synergy that produces novel statistical measures for sequence comparison

MOTIVATION: Many proposed statistical measures can efficiently compare biological sequences to further infer their structures, functions and evolutionary information. They are related in spirit because all the ideas for sequence comparison try to use the information on the k-word distributions, Markov model or both. Motivated by adding k-word distributions to Markov model directly, we investigated two novel statistical measures for sequence comparison, called wre.k.r and S2.k.r. RESULTS: The proposed measures were tested by similarity search, evaluation on functionally related regulatory sequences and phylogenetic analysis. This offers the systematic and quantitative experimental assessment of our measures. Moreover, we compared our achievements with these based on alignment or alignment-free. We grouped our experiments into two sets. The first one, performed via ROC (receiver operating curve) analysis, aims at assessing the intrinsic ability of our statistical measures to search for similar sequences from a database and discriminate functionally related regulatory sequences from unrelated sequences. The second one aims at assessing how well our statistical measure is used for phylogenetic analysis. The experimental assessment demonstrates that our similarity measures intending to incorporate k-word distributions into Markov model are more efficient.     

Kinetics of impurity charge-state distributions in tokamak plasmas

An analysis of impurity behavior in tokamak plasmas with the use of the observation results on impurity emission shows that it is necessary to distinguish between the ion dynamics (for example, ion transport) and ion kinetics, i.e., the processes related to the motion of ions on the charge states and/or excited states due to atomic processes in plasma. This paper presents a systematic analysis of the kinetics of impurity chargestate distributions and the related effects, as well as their typical scales and conditions for their observation. The quantitative analysis is performed in terms of the lowest moments of charge-state distributions such as the average charge m and dispersion D. Analytic approaches to solving charge-state kinetic equations are considered. An approach based on the symmetry properties of the kinetic matrix is proposed for the first time. The simplest types of impurity charge-state kinetics and the most important limiting cases are considered. A detailed analysis of the nonstationary behavior of the function of the moments D(m) of the charge-state distribution is presented. A quantitative analysis of the available experimental and model charge-state distributions of C, O, Ne, and Ar impurities in the JET, DIII-D, TORE SUPRA, ALCATOR-C, TEXTOR, PLT, TFR, and DAMAVAND tokamaks is performed in terms of the moments D(m). It is shown that the moments D(m)of the model charge-state distributions of the above impurities in the plasma core are essentially insensitive to the empirical diffusion coefficient. The equivalent curves D(m) obtained for the plasma periphery can be attributed to the convective fluxes of ionizing and/or recombining impurity ions.     

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.     

Study of the termination phase of plasma production and the formation of magnetic flux breakthroughs during wire array implosion

The phenomenon of magnetic flux breakthrough into a wire array during its implosion was studied experimentally at the Angara-5-1 facility. It is shown that breakthroughs develop in the final stage of plasma production from the wire material and occur near the initial wire position. The spatial distributions of the azimuthal magnetic field within tungsten, molybdenum, copper, and aluminum wire arrays were studied using magnetic probes. The distributions of the azimuthal magnetic field B _φ(z, t) along the array height in different stages of implosion were measured, and the characteristic dimensions of regions with a nonuniform magnetic field that appear during magnetic flux breakthroughs at the outer boundary of the wire array plasma were determined. The dimensions of these regions are compared with those of the regions with depressed plasma radiation observed in frame and time-integrated X-ray images. The dynamics of the distribution B _φ(z, t) in regions with a nonuniform magnetic field during breakthroughs of the azimuthal magnetic flux is compared with that of the spatial distribution of pinch radiation in the frame X-ray images in different stages of implosion. The experimental data on the characteristics of spatially nonuniform breakthroughs of the magnetic flux into the wire array are analyzed using the plasma rainstorm model proposed by V.V. Aleksandrov et al. (JETP 97, 745 (2003)). The plasma density in the region of magnetic flux breakthrough is estimated.     

Nonlinear equilibrium spherical dust structures I: Basic equations and criterion for the existence of self-organized structures

Basic equations for dust structures are formulated that account for the balance of the forces, plasma fluxes, and grain charges with allowance for nonlinearity in the screening of individual grains and possible violation of quasineutrality due to the interaction of collective fields with plasma fluxes. A theory of non-linear drag forces exerted by plasma fluxes on dust grains is developed for moderate drift flux velocities, higher than the mean ion thermal velocity but much lower than the acoustic speed. It is shown that equilibrium dust structures have finite sizes and negative charges and that they can exist only in a certain range of intensities of external fluxes on their surfaces. When there is no additional volume ionization, the size of the structures is determined by the intensity of the external flux. A study is made of a weakly ionized dusty plasma in which the interaction of its components with neutral gas atoms plays a major role. The ion, electron, and dust density distributions, as well as the distributions of the dust grain charges and plasma fluxes, are calculated self-consistently as functions of the distance from the center of a structure.