Simulation of the Plasma Density Evolution during Electron Cyclotron Resonance Heating at the T-10 Tokamak

In ohmically heated (OH) plasma with low recycling, an improved particle confinement (IPC) mode is established during gas puffing. However, after gas puffing is switched off, this mode is retained only for about 100 ms, after which an abrupt phase transition into the low particle confinement (LPC) mode occurs in the entire plasma cross section. During such a transition, energy transport due to heat conduction does not change. The phase transition in OH plasma is similar to the effect of density pump-out from the plasma core, which occurs after electron cyclotron heating (ECH) is switched on. Analysis of the measured plasma pressure profiles in the T-10 tokamak shows that, after gas puffing in the OH mode is switched off, the plasma pressure profile in the IPC stage becomes more peaked and, after the peakedness exceeds a certain critical value, the IPC-LPC transition occurs. Similar processes are also observed during ECH. If the pressure profile is insufficiently peaked during ECH, then the density pump-out effect comes into play only after the critical peakedness of the pressure profile is reached. In the plasma core, the density and pressure profiles are close to the corresponding canonical profiles. This allows one to derive an expression for the particle flux within the canonical profile model and formulate a criterion for the IPC-LPC transition. The time evolution of the plasma density profile during phase transitions was simulated for a number of T-10 shots with ECH and high recycling. The particle transport coefficients in the IPC and LPC phases, as well as the dependences of these coefficients on the ECH power, are determined.     

Current density distribution during disruptions and sawteeth in a simple model of plasma current in a tokamak

The processes that are likely to accompany discharge disruptions and sawteeth in a tokamak are considered in a simple plasma current model. The redistribution of the current density in plasma is supposed to be primarily governed by the onset of the MHD-instability-driven turbulent plasma mixing in a finite region of the current column. For different disruption conditions, the variation in the total plasma current (the appearance of a characteristic spike) is also calculated. It is found that the numerical shape and amplitude of the total current spikes during disruptions approximately coincide with those measured in some tokamak experiments. Under the assumptions adopted in the model, the physical mechanism for the formation of the spikes is determined. The mechanism is attributed to the diffusion of the negative current density at the column edge into the zero-conductivity region. The numerical current density distributions in the plasma during the sawteeth differ from the literature data.     

Use of additional helium puffing for the diagnostics of plasma parameters at the FT-2 tokamak

The experiments carried out at the FT-2 tokamak in which additional pulsed puffing of helium into the hydrogen plasma was used for diagnostic purposes are considered. To estimate the necessary content of helium ions in the experiments on studying short-scale plasma oscillations, the ionization-recombination balance was simulated numerically under the assumption of a toroidally homogeneous influx of the working gas onto the boundary of the plasma column. In these simulations, the effective density of the neutral gas incident on the plasma boundary was determined by the iteration method, which made it possible to provide agreement between the obtained solution and the experimental discharge conditions. In particular, the correspondence of the determined admixture content to both the plasma quasineutrality condition and the value of the effective charge Z _eff, as well as agreement between the calculated and measured plasma density profiles, was ensured. The simulations were performed under the assumption of anomalous diffusion coefficients for all plasma components. The temporal variations of the ionization-recombination balance were checked by comparing them with the measured spectra of radiation in the HeI, HeII, and H_?? lines. In the current drive experiments, variations in n _e (r) at the discharge periphery were examined by the method based on the proportionality of the intensity ratio of the helium spectral lines, HeI(668 nm)/HeI(728 nm), to the plasma density. In these calculations, the factors relating the intensity ratio of these lines to the plasma density were taken from the literature on spectral diagnostics.     

Collisionless current generation in the center of the tokamak plasma by an isotropic source of α-particles

The density of the noninductive current generated due to collisionless motion of α-particles in the tokamak magnetic field is calculated. The analysis is based on fully three-dimensional calculations of charged particle trajectories without simplifying assumptions typical for drift and neoclassical approaches. The current is calculated over the entire cross section of the plasma column, including the magnetic axis. It is shown that the current density is not a function of a magnetic surface and is strongly polarized over the poloidal angle. The current density distribution in the tokamak poloidal cross section is obtained, and the current density as a function of the safety factor, the tokamak aspect ratio, and the ratio of the particle Larmor radius on the axis to the tokamak minor radius is determined. It is shown that, when the source of α-particles is spatially nonuniform, the current density in the center of the tokamak is nonzero due to asymmetry of the phase-space boundary between trapped and passing particles. The current density scaling in the tokamak center differs from the known approximations for the bootstrap current and is sensitive to the spatial distribution of α-particles.     

Study of plasma fluctuations in the TUMAN-3M tokamak during various types of L-H transitions

The reflectometer method is used to comparatively study plasma fluctuations in the edge plasma of the TUMAN-3M tokamak during L—H transitions initiated by different methods. It is shown that the width of the spectrum of backscattered microwave radiation is the most representative parameter when comparing the results obtained in different confinement regimes. The following methods for affecting the edge plasma were applied: gas puffing, a fast current ramp-up, a rapid increase in the toroidal magnetic field, and ion cyclotron heating. The studies were performed at different positions of the cutoff of O-and X-mode probing waves. A similar behavior of the spectral width was observed during transitions triggered by the fast current ramp-up and the rapid increase in the toroidal field. This provides evidence that the mechanism for transition to the H-mode is the same in both cases in spite of the different character of the evolution of the current density profiles. The fastest and strongest narrowing of the spectra was observed during the transition triggered by ion cyclotron heating. Possible reasons for similarities and differences in the behavior of the spectra during the transitions to the improved confinement regime are discussed.     

Influence of the safety factor inhomogeneity on collisionless current generation in tokamaks

An improved scaling for the current density generated due to collisionless motion of α-particles in a tokamak is proposed. The dependence of the current density on the radial profile of the safety factor q is investigated. Monotonically increasing q profiles are considered, as well as q profiles with a minimum in the axial region of the plasma column. It is shown that the current density depends on the variation in q along the charged particle trajectories, rather than on the q value at the starting magnetic surface. The dependence of the current density on the gradient of q is strongest in the plasma core because of the large deviation of the drift surfaces from the magnetic ones in this region. At the plasma edge, the larger the second derivative of the plasma density, the greater the contribution of the gradient of q. For conventional plasma density profiles, the poloidal-angle-averaged current density calculated for a varying safety factor q is always lower than that calculated for a constant q. The effect of the nonuniformity of the safety factor on the current generation at the magnetic axis of a tokamak is investigated.     

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

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

Real-time determination of the position and shape of the plasma column from external magnetic measurements in the GLOBUS-M tokamak

A fast algorithm is elaborated for determining the position and shape of the plasma column from measurements performed with magnetic probes located outside the vacuum vessel of the GLOBUS-M tokamak. The algorithm is based on the modeling of the plasma current by movable current filaments and allows one to take into account the effect of eddy currents induced in the vacuum vessel. The algorithm was tested in a series of model discharges under conditions characteristic of the GLOBUS-M tokamak and serves now as a software component of its magnetic diagnostic system. By employing a conventional PC (Pentium 1 GHz, 200-MHz data bus), the calculation time of the plasma column parameters at one instant in time does not exceed 3 ms, which offers the possibility of controlling the plasma parameters during a discharge.     

Topology of drift trajectories of charged particles in a tokamak

The topology of drift orbits in a tokamak is analyzed in the entire cross section of the device both near the magnetic axis and at the periphery of the plasma column. The use of invariants of the drift equations (the generalized momentum, magnetic moment, and total energy) as variables for the entire cross section of the plasma column and self-similar variables near the magnetic axis makes it possible to comprehensively classify closed drift orbits in a tokamak. When describing orbits of different types and domains of their existence, discriminant and locus curves obtained by the methods of differential geometry are used to determine the ranges in which the invariants vary. The influence of the nonuniformity of the longitudinal current on the drift trajectories of fast particles is studied. The works in which, together with known types of orbits, trajectories along which particles leave the plasma column and can fall on the chamber wall are analyzed.     

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 Plasma Flows Generated in Plasma Focus Discharge in Different Regimes of Working Gas Filling

Results are presented from experimental studies of the plasma flows generated in the KPF-4 Phoenix Mather-type plasma focus device (Sukhum Physical Technical Institute). In order to study how the formation and dynamics of the plasma flow depend on the initial distribution of the working gas, a system of pulsed gas puffing into the discharge volume was developed. The system allows one to create profiled gas distributions, including those with a reduced gas density in the region of plasma flow propagation. Results of measurements of the magnetic field, flow profile, and flow deceleration dynamics at different initial distributions of the gas pressure are presented.     

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.     

Analysis of electron thermal diffusivity and bootstrap current in ohmically heated discharges after boronization in the HT-7 tokamak

Significant improvements of plasma performance after ICRF boronization have been achieved in the full range of HT-7 operation parameters. Electron power balance is analyzed in the steady state ohmic discharges of the HT-7 tokamak. The ratio of the total radiation power to ohmic input power increases with increasing the central line-averaged electron density, but decreases with plasma current. It is obviously decreased after wall conditioning. Electron heat diffusivity χ_e deduced from the power balance analysis is reduced throughout the main plasma after boronization. χ_e decreases with increasing central line-averaged electron density in the parameter range of our study. After boronization, the plasma current profile is broadened and a higher current can be easily obtained on the HT-7 tokamak experiment. It is expected that the fact that the bootstrap current increases after boronization will explain these phenomena. After boronization, the plasma pressure gradient and the electron temperature near the boundary are larger than before, these factors influencing that the ratio of bootstrap current to total plasma current increases from several percent to above 10%.     

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.     

High-current plasma channel produced with a narrow gas column

A new method for creating high-current plasma channels is developed. The method uses a narrow gas column formed by the leading particles of a nonsteady gas jet outflowing into a vacuum. An electric discharge device with a system for the formation of a narrow gas column is experimentally studied. The parameters of emission from the plasma channel are measured.     

Physical nature of the electric current produced by the asymmetry of particle motion in toroidal magnetic confinement systems

A new type of longitudinal electric current is revealed by analyzing the drift trajectories of charged particles in a tokamak—the current that may be referred to as the asymmetry current because it is associated with the asymmetry of the boundary between trapped and transit particles in phase space. The generation of this current is explained by the fact that the motions of the particles that cross the magnetic surface at a given point in opposite directions are qualitatively different. The asymmetry current results from the toroidal variations of the magnetic field and is maintained by the radial momentum flux of transit particles. The contribution of the particles of different species to the asymmetry current density is proportional to their pressure, is independent of the gradients of the plasma parameters, is maximum at the magnetic axis, and decreases toward the plasma periphery. In contrast to standard neoclassical theory, the asymmetry current can be found only from exact particle trajectories. The asymmetry current is calculated for tokamaks with differently shaped magnetic surfaces and for a model stellarator. By exploiting the newly revealed asymmetry current, together with the bootstrap current, it may be possible to substantially simplify the problem of creating a tokamak reactor.     

Microwave measurements of the time evolution of electron density in the T-11M tokamak

Unambiguous diagnostics intended for measuring the time behavior of the electron density and monitoring the line-averaged plasma density in the T-11M tokamak are described. The time behavior of the plasma density in the T-11M tokamak is measured by a multichannel phase-jump-free microwave polarization interferometer based on the Cotton-Mouton effect. After increasing the number of simultaneously operating interferometer channels and enhancing the sensitivity of measurements, it became possible to measure the time evolution of the plasma density profile in the T-11M tokamak. The first results from such measurements in various operating regimes of the T-11M tokamak are presented. The measurement and data processing techniques are described, the measurement errors are analyzed, and the results obtained are discussed. We propose using a pulsed time-of-flight refractometer to monitor the average plasma density in the T-11M tokamak. The refractometer emits nanosecond microwave probing pulses with a carrier frequency that is higher than the plasma frequency and, thus, operates in the transmission mode. A version of the instrument has been developed with a carrier frequency of 140 GHz, which allows one to measure the average density in regimes with a nominal T-11M plasma density of (3–5)×10¹³ cm^?3. Results are presented from the first measurements of the average density in the T-11M tokamak with the help of a pulsed time-of-flight refractometer by probing the plasma in the equatorial plane in a regime with the reflection of the probing radiation from the inner wall of the vacuum chamber.     

Parameters of a tokamak reactor operating at a fixed fusion power as functions of the aspect ratio

Such parameters of a tokamak reactor as the major radius, plasma current, reactor volume, neutron load to the first wall, heat load to the divertor plates, and bootstrap current are studied as functions of the aspect ratio, assuming that the reactor operates at a fixed power. The conclusion is drawn that a demonstrative prototype reactor should be based on a large aspect ratio tokamak.     

MHD diagnostics in the T-11M tokamak

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

Nonisothermal theory of the positive column of an electric discharge in the axial magnetic field

A nonisothermal model of the positive column allowing for electron energy balance is analyzed. The influence of the axial magnetic field on the characteristics of the cylindrical positive column of a low-pressure discharge is investigated in the hydrodynamic approximation. It is shown that the magnetic field affects the plasma density distribution, plasma velocity, and electron energies. The radial dependences of the plasma density, electron energy, and plasma velocity, as well as the azimuthal velocities of electrons and ions, are calculated for helium at different values of the magnetic field strength. It is established that inertia should be taken into account in the equations for the azimuthal motion of electrons and ions. The results obtained in the hydrodynamic approximation differ significantly from those obtained in the framework of the common diffusion model of the positive column in the axial magnetic field. It is shown that the distributions of the plasma density and radial plasma velocity in the greater part of the positive column tend to those obtained in the diffusion approximation at higher values of the axial magnetic field and gas density, although substantial differences remain in the near-wall region.