Transport barrier as a bifurcation of the equilibrium of a tokamak plasma

The phenomenon of the internal transport barrier in a tokamak plasma is interpreted as a bifurcation of the plasma equilibrium. An expression describing the change in the plasma pressure due to the buildup of the barrier is derived as a functional dependent on the parameters of the original plasma equilibrium and the plasma rotation velocity within the barrier. This expression is applied to a circular cross section tokamak, specifically, the T-10 device.     

Tearing instability in a tokamak with a noncircular cross section

Using a straight-column model to describe tokamak plasma with a noncircular cross section, it is shown how to (i) find the boundary of tearing instability from the condition of existence of a magnetohydrodynamic plasma equilibrium different from that of a straight cylinder by solving a two-dimensional linear boundary-value problem with a second-order equation with respect to the flux coordinate and (ii) find the spatial structure of the tearing mode and the corresponding effective Δ' when there is only one resonance magnetic surface in the plasma for a given axial wavenumber by solving some kind of a boundary-value problem for the perturbation. The proposed approach is illustrated by numerical calculations for the case of an elliptical cross section as an example.     

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.     

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.     

Analytical Solution to External Equilibrium Problem for Plasma with Elliptic Cross Section in a Tokamak

Plasma Physics Reports - Expressions are obtained for the magnetic field created by the currents flowing in the tokamak plasma with elliptic cross section. The analytical approach is based on the...     

ECE measurements via B-X-O mode conversion: A proposal to diagnose the q profile in spherical tokamaks

Generation of electron Bernstein waves by the ordinary-extraordinary-Bernstein (O-X-B) mode conversion process has been successfully demonstrated on W7-AS. According to Kirchoff’s law, the inverse process of plasma EC emission by B-X-O mode conversion at particular angles must take place in tokamak plasmas. The optical depth at electron cyclotron harmonics is generally very high for electron Bernstein waves in tokamak plasmas. Consequently the O-mode ECE spectrum measured below the plasma frequency will show steps in the emitted power when each EC harmonic coincides with the upper hybrid resonance zone, where the mode conversion occurs, giving a local measurement of the relationship between the total magnetic field and plasma density. In a spherical tokamak, there are several EC harmonics below the plasma frequency, so several such steps can be observed via the B-X-O mode conversion mechanism. This is a very promising way to get information about the q profile in ST plasmas.     

Application of the canonical profile theory to the problems of heat transport in tokamaks

Abstrac A transport model for describing electron and ion plasmatemperatures is developed on the basis of the canonical profile theory for a tokamak with an arbitrary cross section. A comparison with the data from experiments on eight different tokamaks shows that the model is capable of adequately simulating plasma discharges. A scaling for the behavior of the relative temperature gradient at half the plasma minor radius is constructed based on both an analysis of the experimental data and the results of numerical calculations. __________ Translated from Fizika Plazmy, Vol. 30, No. 1, 2004, pp. 3–10. Original Russian Text Copyright ? 2004 by Dnestrovskij, Dnestrovskij, Lysenko, Cherkasov, Walsh.     

A study of low-frequency microturbulence by CO2-laser collective scattering in the FT-2 tokamak

Results are presented from studies of small-scale plasma density fluctuations in the FT-2 tokamak by the method of far-forward CO₂-laser collective scattering. The frequency and wavenumber spectra of fluctuations are measured using parallel k analysis at various positions of the scattering volume in the plane of the minor cross section of the torus. The data obtained are interpreted using numerical simulations. In phenomenological models, plasma fluctuations are substituted by a superposition of two-dimensional noninteracting cells with Gaussian profiles. A comparison of the calculated and experimental spectra shows that plasma fluctuations should be described based on the concept of strong microturbulence. The poloidal rotation velocity and the characteristic scale length of the scattering fluctuations, as well as the radial position of the region where they are located, are determined. The diffusion coefficient of the cells introduced in the model turns out to be close to the thermal diffusivity determined from the electron energy balance in the ohmic phase of the discharge.     

Numerical analysis of the safety factor and effective ion mass in a tokamak plasma with the help of the discrete alfvén wave spectrum

Numerical aspects of the method for diagnosing a tokamak plasma with the help of the discrete Alfvén wave spectrum are considered. It is shown that this diagnostics should be supported with highly accurate computational tools. A code suitable for implementing the relevant calculation scheme is developed, which makes it possible to identify the eigenmodes numerically with the desired accuracy. The code can also provide recommendations for performing tokamak experiments and can be used to study the possibility of auxiliary plasma heating by Alfvén waves. The discrete Alfvén wave spectrum, radial profiles of the energy deposited in the plasma, and the dependence of the Alfvén mode frequencies on the damping rate and on the class of the current-density profiles chosen are calculated for the first time for the T-10 tokamak. It is also shown that the diagnostic method proposed makes it possible to obtain reliable information about the plasma parameters.     

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.     

Jump in transport coefficients in discharges with ECR heating in the T-10 tokamak

Abstrac Transient processes after off-axis ECR heating in the T-10 tokamak is switched on or off are analyzed. It is found that the transient processes have the following two characteristic features. First, transport coefficients undergo a jump, thereby driving the evolution of the initial steady-state distributions of the plasma parameters. Second, the evolution of the original configuration is accompanied by ECR heating of the plasma. A mathematical model is proposed that takes into account the jump in transport coefficients over the entire cross section of the plasma column and adequately describes this transient process. An analysis of the experimental data confirms the validity of the model equations formulated here. It is shown that, without invoking the jump in transport coefficients after off-axis ECR heating is switched on or off, it is impossible to describe the experimentally observed opposite-sign changes in the electron temperature at the center of the plasma column and in the ECR heating region. __________ Translated from Fizika Plazmy, Vol. 28, No. 5, 2002, pp. 403–418. Original Russian Text Copyright ? 2002 by Andreev, Dnestrovskij, Razumova, Sushkov.     

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.     

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.     

A van der Pol coupled-oscillator model as a basis for developing a system for suppressing MHD instabilities in a tokamak

The main parameters of tokamak discharges are known to be limited by large-scale MHD instabilities. Sometimes, the instabilities lead to a rapid (on time scales of tens of microseconds) disruption of the discharge current and to the release of all the energy stored in the plasma column at the discharge chamber wall. This process, which is called the disruptive instability, may have irreversible catastrophic consequences for the operation of a fusion reactor. In the present paper, a study is made of the dynamics of self-oscillations in systems of two and six van der Pol coupled oscillators. A van der Pol coupled-oscillator model is used to develop a multivariable feedback controller based on the combined principle of compensating for internal cross feedbacks within the object and introducing damping feedbacks in each control channel. By using mathematical simulation methods, it is shown that the controller designed guarantees the suppression of self-oscillations in a system of van der Pol oscillators over a fairly broad range of parameters of the object under control (and thereby provides the structural stability of the object). The nonlinear control system model makes it possible to suppress coupled MHD perturbations developing in a tokamak plasma.     

Effect of helical magnetic fields on plasma stability in tokamaks

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

Charge-exchange recombination spectroscopy of the plasma ion temperature at the T-10 tokamak

Charge-exchange recombination spectroscopy (CXRS) based on a diagnostic neutral beam has been developed at the T-10 tokamak. The diagnostics allows one to measure the ion temperature profile in the cross section of the plasma column. In T-10 experiments, the measurement technique was adjusted and the elements of the CXRS diagnostics for ITER were tested. The used spectroscopic equipment makes it possible to reliably determine the ion temperature from the Doppler broadening of impurity lines (helium, carbon), as well as of the spectral lines of the working gas. The profiles of the plasma ion temperature in deuterium and helium discharges were measured at different plasma currents and densities, including with the use of active Doppler measurements of lines of different elements. The validity and reliability of ion temperature measurements performed by means of the developed CXRS diagnostics are analyzed.     

CXSFIT Code Application to Process Charge-Exchange Recombination Spectroscopy Data at the T-10 Tokamak

The applicability of the CXSFIT code to process experimental data from Charge-eXchange Recombination Spectroscopy (CXRS) diagnostics at the T-10 tokamak is studied with a view to its further use for processing experimental data at the ITER facility. The design and operating principle of the CXRS diagnostics are described. The main methods for processing the CXRS spectra of the 5291-Å line of C⁵⁺ ions at the T-10 tokamak (with and without subtraction of parasitic emission from the edge plasma) are analyzed. The method of averaging the CXRS spectra over several shots, which is used at the T-10 tokamak to increase the signal-to-noise ratio, is described. The approximation of the spectrum by a set of Gaussian components is used to identify the active CXRS line in the measured spectrum. Using the CXSFIT code, the ion temperature in ohmic discharges and discharges with auxiliary electron cyclotron resonance heating (ECRH) at the T-10 tokamak is calculated from the CXRS spectra of the 5291-Å line. The time behavior of the ion temperature profile in different ohmic heating modes is studied. The temperature profile dependence on the ECRH power is measured, and the dynamics of ECR removal of carbon nuclei from the T-10 plasma is described. Experimental data from the CXRS diagnostics at T-10 substantially contribute to the implementation of physical programs of studies on heat and particle transport in tokamak plasmas and investigation of geodesic acoustic mode properties.     

Reconfigurable RCS Reduction from Curved Structures Using Plasma Based FSS

Plasmonics - The radar cross section (RCS) reduction from curved surfaces using plasma based frequency selective surfaces (FSS) is investigated. A frequency reconfigurable plasma based FSS...     

Onset condition of the subcritical geodesic acoustic mode instability in the presence of energetic-particle-driven geodesic acoustic mode

An analytic model is developed for understanding the abrupt onset of geodesic acoustic mode (GAM) in the presence of chirping energetic-particle-driven GAM (EGAM). This abrupt excitation phenomenon has been observed on LHD plasma. Threshold conditions for the onset of abrupt growth of GAM are derived, and the period doubling phenomenon is explained. The phase relation between the mother mode (EGAM) and the daughter mode (GAM) is also discussed. This result contributes to the understanding of “trigger problems” of laboratory and nature plasmas.