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Studying stationary regimes with high plasma confinement in a tokamak with reactor technologies (TRT) [1] involves calculating the plasma stability taking into account the influence of the current density profiles and pressure gradient in the pedestal near the boundary. At the same time, the operating limits should be determined by the parameters of the pedestal, which, in particular, are set by the stability limit of the peeling–ballooning modes that trigger the peripheral disruption of edge localized modes (ELM). Using simulation of the quasi-equilibrium evolution of the plasma by the ASTRA and DINA codes, as well as a simulator of magnetohydrodynamic (MHD) modes localized at the boundary of the plasma torus based on the KINX code, stability calculations are performed for different plasma scenarios in the TRT with varying plasma density and temperature profiles, as well as the corresponding bootstrap current density in the pedestal region. At the same time, experimental scalings for the width of the pedestal are used. The obtained pressure values are below the limits for an ITER-like plasma due to the lower triangularity and higher aspect ratio of TRT plasma. For the same reason, the reversal of magnetic field shear in the pedestal occurs at a lower current density, which causes the instability of modes with low toroidal wave numbers and reduces the effect of diamagnetic stabilization.

Results of experimental studies of toroidal Alfven eigenmodes (TAEs) in the Globus-M spherical tokamak (R = 36 cm, a = 24 cm) are reported. The experiments were carried out in a wide range of plasma parameters at a magnetic field of up to 0.5 T and plasma current of up to 250 kA. Auxiliary plasma heating was performed by tangential injection of a deuterium beam with a power of Pb= 0.75 MW and particle energy of Eb = 28 keV into deuterium plasma. The experiments have shown that the TAE-induced loss of fast particles decreases with increasing plasma current and magnetic field. Using multifrequency Doppler backscattering diagnostics, it is established that the TAEs are localized at the plasma periphery. Results of simulations of the Alfven continuum and TAE structure by means of the modified KINX and CAXE codes agree satisfactory with the experimental data on the TAE frequencies and localization.

Abandoning the assumption of nested magnetic surfaces in tokamak plasma expands the field of research and opens up new approaches for both theoretical and experimental plasma physics. The computer code KINX for calculations of the ideal MHD stability was developed for studies of doublet plasmas with two magnetic axes and using block-structured grids in each subdomain with nested magnetic surfaces. Then, the MHD_NX code on unstructured grids was developed to calculate the stability of two-dimensional equilibria with an arbitrary topology of magnetic surfaces. The study of equilibrium and stability of equilibrium configurations with toroidal current density reversal and axisymmetric n = 0 islands, which are associated with internal transport barrier and low current density at the magnetic axis, as well as with the operation of tokamaks in the alternating current regime, leads to more general issues of MHD stability of two-dimensional solutions of the Grad−Shafranov equations with islands under other types of symmetry—chain of islands in helical symmetry and cylindrically symmetric m = 0 islands in configurations with the longitudinal field reversal. New ideal MHD unstable modes have been discovered for various types of two-dimensional island configurations. The energy principle with MHD-compatible boundary conditions at open magnetic field lines is necessary for the self-consistent stability analysis of divertor configurations in tokamaks with a finite current density at the separatrix, taking into account the plasma outside the separatrix. Several codes have been developed for calculations of plasma equilibrium and stability, taking into account the influence of currents outside the separatrix, which are ready for integration with other codes for edge plasma modeling.

The features of a multichannel modem that has been developed for transmission of frequency and time reference signals on a fiber-optic communication line with phase instability compensation are examined. Its capabilities for transmitting signals of reference frequencies of active hydrogen masers (such as the Ch1-1003M), we well as a 1 PPS signal with an error of synchronization no greater than 250 psec over 100 km without the use of optical amplifiers are assessed. The results of experimental verification of the metrological characteristics of the modem are given.

Issues in the output signal generation of an atomic clock ensemble and the smooth management of the time scale are considered. Special algorithms are proposed to solve the objectives, making it possible to improve the stability of the output signals against possible reference frequency signal jumps. The operation of the algorithms is demonstrated by means of numerical modeling.

One of the three goals of the ITER project is to demonstrate fusion gain Q ≥ 5 in steady-state operation (SSO). A reassessment of the necessary conditions for Q ≥ 5 SSO in ITER has been carried out for steady-state scenarios assuming no internal transport barrier in the core plasma and with the sole use of neutral beam injection (NBI) and electron cyclotron heating and current drive (EC H&CD) as heating and current drive sources in these scenarios. The parametric operational space for SSO in ITER has been reassessed utilizing an inverse evaluation approach that takes into account the baseline design of the NBI and EC H&CD systems with PNBI = 33 MW, PEC = 20 MW and their possible upgrade capabilities included in their design, PNBI ≤ 49.5 MW, and PEC ≤ 30 MW. The optimal operational points from this evaluation approach have been chosen for detailed 1.5-D transport modelling by ASTRA and followed-up by magnetohydrodynamic (MHD) stability analysis to demonstrate the conditions in which the Q = 5 SS goal can be achieved in ITER where the plasma current is fully accounted for by the driven current by NBI and EC H&CD and the self-driven bootstrap current. The ideal MHD stability of plasma configurations with self-consistently simulated plasma profiles and equilibrium for the chosen OPs has been analysed by the KINX code. Using this analysis, the possibility to control the MHD stability of these steady-state plasmas by tailoring the current profile with the flexibility provided by design of the systems for electron cyclotron current drive and neutral beam current drive in ITER has been demonstrated. Issues related to the realization of such scenarios from the point of view of plasma physics, experimental demonstration and design limits of the ITER systems and components is discussed.

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 Alfven 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.

The level of knowledge accumulated to date in the physics and technologies of controlled thermonuclear fusion (CTF) makes it possible to begin designing fusion—fission hybrid systems that would involve a fusion neutron source (FNS) and which would admit employment for the production of fissile materials and for the transmutation of spent nuclear fuel. Modern Russian strategies for CTF development plan the construction to 2023 of tokamak-based demonstration hybrid FNS for implementing steady-state plasma burning, testing hybrid blankets, and evolving nuclear technologies. Work on designing the DEMO-FNS facility is still in its infancy. The Efremov Institute began designing its magnet system and vacuum chamber, while the Kurchatov Institute developed plasma-physics design aspects and determined basic parameters of the facility. The major radius of the plasma in the DEMO-FNS facility is R = 2.75 m, while its minor radius is a = 1 m; the plasma elongation is k 95 = 2. The fusion power is P FUS = 40 MW. The toroidal magnetic field on the plasma-filament axis is B t0 = 5 T. The plasma current is I p = 5 MA. The application of superconductors in the magnet system permits drastically reducing the power consumed by its magnets but requires arranging a thick radiation shield between the plasma and magnet system. The central solenoid, toroidal-field coils, and poloidal-field coils are manufactured from, respectively, Nb3Sn, NbTi and Nb3Sn, and NbTi. The vacuum chamber is a double-wall vessel. The space between the walls manufactured from 316L austenitic steel is filled with an iron—water radiation shield (70% of stainless steel and 30% of water).

Conditions of the excitation of toroidal Alfven eigenmodes (TAEs) and their inf luence on the confinement of fast particles into the Globus-M spherical tokamak have been studied by KINX code calculations of the magnetohydrodynamic spectra of reconstructed divertor equilibrium configurations with stability margin q0 > 1 on the magnetic axis. The sensitivity of the frequencies of TAE modes with toroidal wavenumber n = 1 to the type of boundary conditions and choice of boundary surface has been studied. It has been established that the frequencies of modes with dominating poloidal harmonics m = 1 and 2 in the gap of continuum are significantly higher than those observed in the spectra of signals measured in the Mirnov coil probes, especially under the assumption of free plasma boundary with allowance for its compressibility. The TAE modes with lower frequencies and higher poloidal wavenumbers localized near the plasma boundary may be responsible for the oscillations observed in the experiment. However, these modes are characterized by the interaction with continuum and, probably, exhibit related damping.

Ideal magnetohydrodynamic (MHD) properties depending on the plasma pressure are considered for axisymmetric equilibrium magnetoplasma configurations in the Galatea trap with three ring current-carrying conductors embedded in plasma. The study of ideal MHD modes with different toroidal wave numbers takes into account the plasma compressibility with an adiabatic index of 5/3 in the perturbed potential energy functional in the framework of the energy principle. The stability calculations are performed in the presence of a vacuum layer between the plasma and the vacuum chamber. The limiting pressure values corresponding to stable multiply connected plasma configurations without an assumption of nested magnetic surfaces are estimated.

This paper finalizes the self-consistent study of the sideways force acting on the resistive wall due to eddy currents induced by n = 1 kink instability under variations of the external poloidal field and its impact on the force peaking factor as outlined in A. A. Martynov and S. Yu. Medvedev, Phys. Plasmas 27, 012508 (2020). A proper analytical treatment of the sideways forces for a large aspect ratio circular tokamak is limited to the case q 1 at the plasma boundary, the sideways force is generated by a sideband m/n = 1/1 harmonic, which gives lower net force as compared to the q

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.

This paper presents the results of analytical and numerical calculations of the sideways force acting on the resistive wall due to eddy currents induced by n = 1 kink instability. The inertia-less ideal MHD model for resistive wall mode is explicitly shown to be compatible with the condition of vanishing sideways force in the ideal wall limit. In the frame of standard high aspect ratio approximation, assuming that tokamak plasma is separated from the coaxial resistive wall by a vacuum layer, we calculate analytically the sideways force as a function of the growth rate γ taking into account the known relation between γ and the value of the safety factor q. It is noted that this dependence is determined by the single mode m / n = 1 / 1 instability in the range of q-values q 1 is smaller because the sideways force is generated by toroidally coupled satellite harmonic m / n = 1 / 1. The forces due to resistive wall mode with conformal and one-sided wall proximity to the plasma boundary are compared.

ELM mitigation to avoid melting of the tungsten (W) divertor is one of the main factors affecting plasma fuelling and detachment control at full current for high Q operation in ITER. Here we derive the ITER operational space, where ELM mitigation to avoid melting of the W divertor monoblocks top surface is not required and appropriate control of W sources and radiation in the main plasma can be ensured through ELM control by pellet pacing. We apply the experimental scaling that relates the maximum ELM energy density deposited at the divertor with the pedestal parameters and this eliminates the uncertainty related with the ELM wetted area for energy deposition at the divertor and enables the definition of the ITER operating space through global plasma parameters. Our evaluation is thus based on this empirical scaling for ELM power loads together with the scaling for the pedestal pressure limit based on predictions from stability codes. In particular, our analysis has revealed that for the pedestal pressure predicted by the EPED1 + SOLPS scaling, ELM mitigation to avoid melting of the W divertor monoblocks top surface may not be required for 2.65 T H-modes with normalized pedestal densities (to the Greenwald limit) larger than 0.5 to a level of current of 6.5–7.5 MA, which depends on assumptions on the divertor power flux during ELMs and between ELMs that expand the range of experimental uncertainties. The pellet and gas fuelling requirements compatible with control of plasma detachment, core plasma tungsten accumulation and H-mode operation (including post-ELM W transient radiation) have been assessed by 1.5D transport simulations for a range of assumptions regarding W re-deposition at the divertor including the most conservative assumption of zero prompt re-deposition. With such conservative assumptions, the post-ELM W transient radiation imposes a very stringent limit on ELM energy losses and the associated minimum required ELM frequency. Depending on W transport assumptions during the ELM, a maximum ELM frequency is also identified above which core tungsten accumulation takes place.

A new algorithm is presented for the formation of an analytical time scale that takes into account the fluctuations of atomic clock signal frequencies over several time scales. Numerical simulation shows that the algorithm can obtain a group time scale for an ensemble of atomic clocks with rather high frequency stability characteristics. The proposed algorithm is compared with the algorithm for calculating a time scale based on the Kalman filter.

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (with arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.

An algorithm for generating the output signal of a group frequency standard using control of the frequency of an auxiliary crystal oscillator based on two time scales is proposed. The algorithm may be used in back-up systems of the output signal of the reference that are based on synchronization of the auxiliary oscillator relative to several time and frequency standards.

Active control of the ideal external kink mode and the resistive wall mode (RWM) is numerically investigated using the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), for a reactor relevant tokamak plasma shaped with negative triangularity (NTR). Magnetic coils are used as the actuators of the control system. An ideal feedback system (i.e. with no time delays), located inside the vacuum vessel, is shown to be capable of stabilizing the external kink mode and moderately increasing the ideal-wall beta limit by up to 10%. Despite the rather different plasma boundary shape as compared to the conventional D-shaped plasma, the optimal poloidal location of the active coils is still the low-field-side of the torus. The eddy currents in the wall may enhance or cancel the control field produced by active coils depending on the poloidal location of the active coils, thus improving or deteriorating the feedback performance. For a single row of active coils, the optimal poloidal width is about 50° for the RWM stabilization, for the NTR plasmas considered in this study. With two rows of coils, optimization of the feedback gain phasing helps to substantially improve the RWM control. The control performance experiences jumps as the radial location of the active coils is shifted across the poloidal sensor location, as shown in both MARS-F computations and by an analytic model.

Dealing with electromagnetic fields, in particular current and related magnetic fields, yields "natural" physical vector relations in 3-D. However, when it comes to choosing local coordinate systems, the "usual" right-handed systems are not necessarily the best choices, which means that there are several options being chosen. In the magnetic fusion community such a difficulty exists for the choices of the cylindrical and of the toroidal coordinate systems. In addition many codes depend on knowledge of an equilibrium. In particular, the Grad-Shafranov axisymmetric equilibrium solution for tokamak plasmas, psi, does not depend on the sign of the plasma current I-p nor that of the magnetic field B-0. This often results in ill-defined conventions. Moreover the sign, amplitude and offset of psi are of less importance, since the free sources in the equation depend on the normalized radial coordinate. The signs of the free sources, dp/d psi and dF(2)/d psi (p being the pressure, psi the poloidal magnetic flux and F = RB phi), must be consistent to generate the current density profile. For example, RF and CD calculations (Radio Frequency heating and Current Drive) require an exact sign convention in order to calculate a co- or counter-CD component. It is shown that there are over 16 different coordinate conventions. This paper proposes a unique identifier, the COCOS convention, to distinguish between the 16 most-commonly used options. Given the present worldwide efforts towards code integration, the proposed new index COCOS defining uniquely the COordinate COnventionS required as input by a given code or module is particularly useful. As codes use different conventions, it is useful to allow different sign conventions for equilibrium code input and output, equilibrium being at the core of any calculations in magnetic fusion. Additionally, given two different COCOS conventions, it becomes simple to transform between them. The relevant transformations are described in detail. (C) 2012 Elsevier B.V. All rights reserved.

The Russian Academy of Sciences and the Russian Federal Space Agency are planning to launch Radioastron in 2011, which is a unique space observatory with a 10-meter reflector antenna. In conjunction with the largest ground-based radio telescopes and tracking stations, it forms the first system that will be able to carry out studies with a resolution millions of times greater than that of eyesight.

The space interferometer Radioastron is working jointly with the largest radio telescopes of the world. Ground tracking stations provide for retrieving the information and determining the orbital parameters for data processing centers. The project is aimed at systematic studies of images of radio emitting regions, their coordinates, and time-dependent variations near super-massive black holes in galactic nuclei, stellarmass black holes, neutron and quark stars, regions of star and planet formation in our and other galaxies, the structure of interplanetary and interstellar plasma, and the Earth’s gravitational field.

A second order null divertor (snowflake) has been successfully created and controlled in the TCV Tokamak. The results of ideal MHD edge stability computations show an enhancement of the edge stability properties of the snowflake equilibria compared to standard X-point configurations....

An overview of the state of the art and of the MHD plasma equilibrium modeling is given in the paper. The statements of the problems, their mathematical properties, and numerical algorithms are considered.

Stability limits against external kink modes driven by large current density and pressure gradient values in the pedestal region are investigated for tokamak plasmas with separatrix. Stability diagrams for modes with different toroidal wave numbers under variations of pressure gradient and current density in the pedestal region are presented for several equilibrium configurations related to TCV. A scaling for the toroidal wave number of the most unstable mode is proposed. The influence of the plasma cross-section geometry on the stability limits is discussed.

The requirements for pellet injection parameters for plasma fuelling are assessed for ITER scenarios with enhanced particle confinement. The assessment is based on the integrated transport simulations including models of pedestal transport, reduction of helium transport and boundary conditions compatible with SOL/divertor simulations. The requirements for pellet injection for the inductive H-mode scenario (HH98y,2 = 1) are reconsidered taking account of a possible reduction of the particle loss obtained in some experiments at low collisionalities. The assessment of fuelling requirements is carried out for the hybrid and steady state (SS) scenarios with enhanced confinement with HH98y,2 > 1. A robustness of plasma performance to the variation of particle transport is demonstrated. A new type of SS scenario is considered with neutral beam current drive and electron cyclotron current drive instead of lower hybrid current drive (LHCD) to extend the range of stable operation and to avoid the reduction of the edge LHCD efficiency caused by pellet injection.

The problem of feedback stabilization of the resistive wall modes (RWMs) in a tokamak is discussed. An equilibrium configuration with the parameters accepted for the stationary ITER scenario 4A is considered as the main scenario. The effect of the vacuum chamber's shape on the plasma stability is studied. Ideal MHD stability is analyzed numerically by using the KINX code. It is shown that, in a tokamak with the parameters of the designed T-15M tokamak, RWMs can be stabilized by a conventional stabilizing system made of framelike coils. However, the maximum possible gain in β in such a tokamak is found to be smaller than that in ITER. It is shown that, in this case, a reduction in the plasma—wall gap width by 10 cm allows one to substantially increase the β limit, provided that RWMs are stabilized by active feedback.

The profile and dissipation of the field excited by dynamic ergodic divertor (DED) coils in tokamak plasmas are calculated, and an estimate is made of the poloidal/toroidal velocities driven by this field. The coils are idealized as an inboard sheet current composed of a toroidal sequence of helical line current segments expanded in Fourier series with poloidal/toroidal mode numbers M/N, and mode amplitudes depending on feeding. Numerical calculations with cylindrical and toroidal codes show maxima of field dissipation due to Alfven wave mode conversion effect taking place at the rational magnetic surfaces where q = M/N. The effects of toroidicity and ion collisions in the dielectric tensor in the upper DED frequency range described (f = 5-10 kHz) are found to be very important in absorption calculations. At the q = 3 resonant magnetic surface typical for DED coil design, it is estimated that ponderomotive forces produced by 20 kW of dissipation can drive local toroidal and poloidal flows of respective orders 8 km s(-1) and 10 km s(-1) in the TEXTOR tokamak.

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.

In view of the probabilistic nature and very wide uncertainty of internal exposure assessment, its deterministic ('precise') assessment does not protect against not exceeding established reference levels or even the dose limits for a particular individual. Minimising such potential risks can be achieved by setting up a sufficiently wide confidence interval for an expected dose distribution instead of its average ('best' estimate) value, and by setting the limit at the 99% fractile level. The ratio of the 99% level and the mean ('best' estimate) is referred to as the safety coefficient. It is shown for the typical radiological conditions inside the Chernobyl Sarcophagus that the safety coefficient corresponding to the 99% fractile of the expected internal dose distribution varies within the range from 5 to 10. The maintenance of minimum uncertainty and sufficient sensitivity of the indirect dosimetry method requires measurement of individual daily urinary excretion of 239 Pu at a level of at least 4 X 10 -5 Bq. For the purpose of reducing the uncertainty of individual internal dose assessment and making dosimetric methods workable, it is suggested that the results of workplace monitoring are combined with the results of periodic urinary and faecal bioassay measurements.

This paper presents experimental results on the accessibility and the properties of plasmas with improved confinement in TCV. First, the H-mode threshold power is measured in Ohmic plasmas. Above an Ohmic threshold density, the threshold power increases with the density. A lower threshold density is found when additional electron cyclotron heating (ECH) is applied. At these low densities, the threshold power increases dramatically with decreasing density. Only a small fraction of the wide operational domain leading to the Ohmic H-mode is found to lead to a stationary regime with edge localized modes (ELMs). The ELMs have an irregular frequency, but in TCV they can be triggered by an external magnetic perturbation that induces a rapid vertical movement of the plasma. With this perturbation, the ELM frequency can be increased. The ELM triggering mechanism is provided by the vertical movement of the plasma away from the X-point of a single null configuration. This movement induces a positive current at the plasma edge, and we deduce that the ELMs are being controlled by this modification of the plasma edge current.Electron internal transport barriers (eITBs) are produced deep in the plasma during the stationary phase of TCV discharges. Different scenarios of ECH or electron cyclotron current drive (ECCD) at different radial locations have been used to obtain eITBs with and without inductively driven current. The eITBs are characterized by steep electron temperature gradients, high confinement improvement and a large fraction of bootstrap current. In plasmas with fully non-inductively driven current the size and the strength of the eITB are controlled by the location of the power deposition and by the co- or counter-direction of the central ECCD. Finally, a small inductive perturbation of an otherwise non-inductively driven plasma current profile progressively shrinks the eITB, confirming the link between current profiles and eITBs.

Analytically described toroidal (axisymmetric and three-dimensional) equilibrium magnetic field configurations with a “flat” current density, j=λB (λ = const), are proposed. Such configurations are superpositions of several force-free two-dimensional configurations with plane, axial, or helical coordinate symmetry. Each of them is generated by an exact partial solution to the corresponding Grad-Shafranov equation. A variety of toroidal configurations thus obtained allows one to model topological changes of magnetic surfaces, such as magnetic axis splitting (doublets) in axisymmetric equilibrium configurations and the appearance and interaction of magnetic islands and ergodic lines in three-dimensional configurations.

The numerical method is developed for calculations of wave excitation and dissipation in Alfven and in Ion Cyclotron Range of Frequency (ICRF) in axisymmetric tokamaks. Multi-fluid magneto-hydrodynamic plasma model is used and two-dimensional inhomogeneity of plasma parameters with arbitrary cross section of magnetic surfaces is considered. The difference scheme for the wave equation is not connected to magnetic field geometry and is suitable for the method extensions to nonlinear and three-dimensional case. Special care is taken to avoid the spectrum distortion and pollution. Relevant benchmark cases are presented. Finally, the results of numerical calculations of Alfven wave absorption are presented for the experimental conditions foreseen for the Tokamak Chauffage Alfven wave experiment in Brazil (TCABR) [Nucl. Fusion 30 (1996) 503]. In particular, the effect of toroidal mode coupling on the power deposition of Global Alfven Wave (GAW) eigenmodes is demonstrated.

We analyze the accuracy of digital estimation of the signal spectrum. Quantization noise introduced by the analog-to-digital converter (ADC) and fast Fourier transform (FFT) is allowed for. The basic analysis is carried out using the example of a test harmonic signal. The characteristic of the signal-to-noise ratio, called the effective binary word size of a harmonic signal is introduced. Optimal combinations between the ADC word size and the FFT type used are discussed.

For integrated modeling of equilibrium, stability and dynamics of the divertor tokamak plasma with scrape-off layer (SOL) high resolution equilibrium calculations are needed. A new version of the CAXE equilibrium code computes the tokamak equilibrium on a numerical grid adaptive to magnetic surfaces both in the plasma region with closed flux surfaces and in the SOL region with open magnetic lines. The plasma profiles can be prescribed independently in each region with nested flux surfaces, and realistic SOL profiles with very short pressure drop off length can be accurately treated. The influence of the finite current density in SOL on the connection length is studied. From the point of view of the MHD equilibrium and stability modeling, self-consistent calculations of diverted tokamak configurations with finite current density at the separatrix require taking into account plasma outside the separatrix. Calculated high resolution equilibria provide an input to new versions of the ideal MHD stability codes treating tokamak plasma with SOL. The study of the influence of the pressure gradient profile in the pedestal plasma inside and outside the separatrix on the pedestal height limit set by external kink-ballooning mode stability is presented. Another possible application of the high resolution pedestal and SOL equilibrium code is a coupling to the SOLPS code with a purpose to increase equilibrium accuracy and support self-consistent plasma flow/equilibrium modeling.

We analyze the estimate of the correlation factor between noise intensities at the outputs of two bandpass filters as a parameter that allows us to obtain additional information on the nature of the 1/f noise. The confidence interval is calculated for the experimental evaluation of the correlation factor between readings of noise intensities. Data on noise in GaAs films and also for the numerical model of the 1/f noise as a superposition of telegraphic random processes are presented and discussed.

To study the nature of the 1/f noise phenomenon in conductors, we seek a tool for testing different hypotheses of 1/f noise origin. The method analyzing the noise intensity at the output of a bandpass filter is discussed for the case of non-Gaussian processes. Data on measurement error are presented for the 1/f noise intensity in GaAs films and the Gaussian white noise emulated by a computer. A numerical model of 1/f noise as the superposition of telegraph random processes has been created. This method requires further improvement to check the noise for stationarity. Some ideas of how to do that are proposed.

Linear magnetohydrodynamic (MHD) and equilibrium evolution approaches describe the linear and non-linear axisymmetric displacement dynamics of free boundary plasma equilibrium configurations surrounded by conductors in an external magnetic field. A comparison of the two different approaches was made using DIII-D-like free boundary equilibria. Good agreement was found for up-down symmetric configurations. However, a considerable difference in growth rates is found for up-down asymmetric equilibria. The difference can be explained by taking into account surface current perturbations in the MHD model. Common and specific features of the two approaches are discussed