Analytical solutions for global geodesic acoustic modes in tokamak plasmas

Analytical solutions for global geodesic acoustic modes in the plasma of a tokamak with circular concentric magnetic surfaces are obtained. In the framework of ideal magnetohydrodynamics, an integral equation for eigenvalues (dispersion relation) taking into account toroidal coupling between electrostatic perturbations and electromagnetic perturbations with the poloidal mode number |m| = 2 is derived. In the absence of such coupling, the dispersion relation yields only the standard continuous spectrum. The existence of a global geodesic acoustic mode is analyzed for equilibria with both on-axis and off-axis maxima of the local geodesic acoustic frequency. The analytical results are compared with results of numerical calculations.     

Canonical profiles in tokamak plasmas with an arbitrary cross section

Two principles are used to determine a canonical profile: the principle of the minimum of free plasma energy with the constraint that the total current is conserved and the principle of profile consistency. A second-order differential equation for the canonical profile of the function μ=1/q is deduced in the natural coordinate system. Soft and hard boundary conditions are proposed to find an unambiguous solution to this equation. The range of their applicability is discussed. Numerical calculations show that the half-width of the canonical profile increases with decreasing aspect ratio, increasing plasma elongation, and decreasing q _a value. The canonical profiles obtained make it possible to determine the critical gradients for the heat and particle fluxes in transport models.     

Recombination kinetics of impurities during a major disruption in tokamak plasmas

The investigations of major disruptions in the TVD and DAMAVAND tokamaks showed that, in the rapid phase of disruption, accelerated (～1 keV) ions and charge-exchange neutrals are generated near the rational magnetic surfaces; this is accompanied by the bursts of line emission from light impurities (C, O). In the present paper, an analysis is made of the bursts of the CV triplet emission (2271–2278 Å) observed over all of the viewing chords in high-current discharges and also of a decrease in the spectral line emission below its initial (predisruption) level both in the plasma core and at the plasma edge in low-current discharges. The data from measurements of the spatial and temporal parameters of the CV line emission from the central and peripheral plasma regions in the rapid phase of disruption in the DAMAVAND tokamak are compared to the results from model calculations of the kinetics of the charge-state distribution of carbon impurity ions (during the disruption, their kinetics is governed by the increase in the effective recombination rate). A key result of the kinetic model is an increase in the effective rate of charge exchange of impurity ions by two orders of magnitude. Numerical simulations show that the dispersion of the charge-state distribution increases substantially; this is attributed to the rapid phase of disruption being dominated by the recombination of impurity ions through charge exchange with neutrals rather than by the anomalous transport. In this case, carbon impurities in the plasma are transported to the region of increased radiative losses on a time scale of 50 μs.     

Formation of self-consistent pressure profiles in simulation of turbulent convection in tokamak plasmas

The formation of pressure profiles in turbulent tokamak plasmas in ohmic heating regimes and transient regimes induced by turning-on of electron-cyclotron resonance (ECR) heating is investigated. The study is based on self-consistent modeling of low-frequency turbulent plasma convection described by an adiabatically reduced set of hydrodynamic-type equations. The simulations show that, in the ohmic heating stage, turbulence forms and maintains profiles of the total plasma pressure corresponding to turbulentrelaxed states. These profiles are close to self-consistent profiles of the total plasma pressure experimentally observed on the T-10 tokamak in ohmic regimes with different values of the safety factor q _L at the limiter. Simulations of nonstationary regimes induced by turning-on of on- and off-axis ECR heating show that the total plasma pressure profiles in the transient regimes remain close to those in the turbulent-relaxed state, as well as to the profiles experimentally observed on T-10.     

Drift and geodesic effects on the ion sound eigenmode in tokamak plasmas

A kinetic treatment of geodesic acoustic modes (GAMs), taking into account ion parallel dynamics, drift and the second poloidal harmonic effects is presented. It is shown that first and second harmonics of the ion sound modes, which have respectively positive and negative radial dispersion, can be coupled due to the geodesic and drift effects. This coupling results in the drift geodesic ion sound eigenmode with a frequency below the standard GAM continuum frequency. Such eigenmode may be able to explain the split modes observed in some experiments.     

Study of discharge quenching in the T-10 tokamak by injecting high-Z impurity pellets

The problem of the fast quenching of a discharge in tokamaks by injecting high-Z impurity pellets is considered. Results are presented from experiments in the T-10 tokamak, in which a substantial decrease (up to 70%) in the thermal plasma energy was observed. A one-dimensional transport code is developed to describe tokamak-discharge quenching. The code is used to simulate the experiments on quenching the T-10 discharge. It is shown that the injection of a high-Z pellet into the T-10 plasma changes the transport coefficients as compared to their steady-state values derived from the energy balance or scalings.     

Effect of flux surface curvature on the linear coupling of electron cyclotron waves in tokamak plasmas

Specific features of the linear interaction of ordinary and extraordinary electromagnetic waves in the electron cyclotron frequency range in a nonuniform plasma confined in a toroidal magnetic trap are considered. Reduced wave equations taking into account the curvature of the cut-off surfaces in toroidal geometry are formulated. Using these equations, the distributions of the wave fields in the coupling region are analyzed. A method for calculating quasi-optical beams passed through the region of linear wave interaction is proposed.     

The two and three most representative ionization state approximations for impurity description in coronal plasmas

Based on the analytical study of the solutions to the coronal balance equations, as well as on the numerical results, it is shown that, in many cases of practical interest, it is possible to describe the impurity ionization state with acceptable accuracy by only the two or three most representative ionization states. Reduced models for light impurities and strongly ionized heavy impurities in coronal hydrogen plasmas are proposed. The models make it possible to obtain analytical results for many cases as well as to significantly reduce computation time. In these approximations, simple equations determining the dynamics of impurity distributions over ionization states are derived.     

A possible way to reverse the impurity influx by alfvén heating in a tokamak plasma

A study is made of the effect of local heating on impurity fluxes in the Pfirsch-Schlüter regime. When the effect of the thermoforce on impurity ions is taken into consideration, the impurity flux can be reversed by heating the impurities. This concept may be implemented in experiments on Alfvén heating of plasmas in tokamaks. The RF heating power required to reverse the impurity influx is estimated.     

The charge-state model of protein polymorphism in natural populations

Routine electrophoretic surveys for genetic variation in natural populations depend primarily upon detecting differences in the net charge carried by a protein. We have calculated the proportion of base substitutions which would yield an electrophoretically detectable mutant protein, and the relative mutation rates among different chare classes, under a variety of simplifying assumptions. These calculations indicate that: (i) only 25 per cent of all single base mutations would lead to a charge change on a protein molecule. (ii) five distinct classes of electrophoretic variants can be generated from a specified protein by single base substitutions. (iii) the relative mutation rates differ markedly among the different charge classes which can be generated by single base substitutions. The estimates of the proportion of electrophoretically detectable mutant proteins and relative mutation rates among charge classes were relatively robust to changes in assumptions concerned with the kind and site of base substitutions and the amino acid composition of the protein.     

Energy distributions of superthermal ions in regime with sawtooth oscillations during neutral beam injection at the Globus-M tokamak

Specific features of the energy distributions of fast ions during neutral beam injection at the Globus-М tokamak are considered. Different loss mechanisms that can lead to the formation of a specific shape of the energy spectrum of superthermal ions are analyzed. The effect of sawtooth oscillations on the loss of fast ions is discussed.     

Kinetics of formation of fibrin oligomers. II. Size distributions of ligated oligomers

Human fibrinogen was treated with thrombin in the presence of fibrinoligase (Factor XIIIa) and calcium ion at pH 8.5, ionic strength 0.45, and the ensuing polymerization was interrupted at various time intervals (t) both before and after the clotting time (t_c) by solubilization with a solution of sodium dodecylsulfate and urea. Aliquots of the solubilized protein were subjected to gel electrophoresis on polyacrylamide gels after disulfide reduction by dithiothreitol and on agarose gels without reduction. The degree of γ-γ ligation was determined from the former and the size distribution of ligated oligomers, for degree of polymerization x from 1 to 10, from the latter. In some experiments, thrombin was inhibited, after partial polymerization, by p-nitrophenyl-p′-guanidinobenzoate. From these, it was concluded that for thrombin concentration ?0.013 units/mL and fibrinoligase ?30 mg/L, oligomer assembly is rapid compared with peptide A release and ligation is rapid compared with assembly. Under these conditions, the theory of the first paper of this series describes rather well the time dependences of the degree of γ-γ ligation, the weight fractions of monomer and small oligomers, and the number- and weight-average degrees of polymerization after solubilization of the staggered overlapped assemblies, each of which splits to give two strands of end-to-end ligated oligomers. The theory assumes that the second A peptide is released by thrombin more rapidly than the first by a factor q, which, from the experimental data, is determined to be 16. The subsequent assembly into staggered overlapped oligomers follows the statistics of linear polycondesation taking into account the presence of both difunctional and monofunctional combining units. For higher thrombin or lower fibrinoligase concentrations, ligation fails to keep pace with oligomer assembly, and the size distributions after solubilization show a higher proportion of very small and a lower proportion of larger ligated oligomers, owing to separation of the staggered overlapped assemblies into smaller fragments.     

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.     

Structure of global tokamak scalings

In empirical tokamak scalings, not all of the standard engineering parameters are independent. Thus, the larger the tokamak, the higher the required plasma current and input power. Also, by using higher magnetic fields, it is possible to raise the plasma density. Instead of the plasma density, plasma current, and input power, it is proposed to use such combinations of engineering parameters whose values are essentially the same for different tokamaks. With this approach, the number of free scaling parameters can be reduced from six to three, thereby improving the reliability of the scaling.     

Studies of runaway electrons in the Globus-M tokamak

Results are presented from experimental studies of runaway electrons in the ohmic heating regime in the Globus-M tokamak. The periodical hard X-ray bursts observed with the help of two hard X-ray spectrometers with high time resolution are attributed to MHD oscillations in the plasma core and at the periphery.     

Reversed-shear experiments in the T-10 tokamak

Results from T-10 experiments in regimes with nonmonotonic plasma current profiles are presented. The possibility of controlling the current profile j(r) by electron-cyclotron current drive is demonstrated experimentally. Nonmonotonic q profiles with the reversed shear are obtained in which the q _min value varies in a wide range, q _min=1–2.3. It is shown that the current profiles with q _min～2 (in this case, there are two resonant magnetic surfaces q=2 in the plasma) can cause the onset of MHD instabilities. The possibility of the formation of an internal transport barrier in reversed-shear discharges in the T-10 tokamak is analyzed. In T-10, electron transport is governed by short-wavelength electron turbulence. As a result, there is no clear evidence of the formation of an inner transport barrier in these experiments.     

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.