Toroidal Magnetic Confinement Systems Research Articles

Modeling of the mode dynamics generated by Madison Symmetric Torus machine utilizing a modified sine-Gordon equation

In this paper, a new dynamic model is presented for the experimental data generated by the Madison Symmetric Torus (MST) machine. The model is based on a modified sine-Gordon (SG) dynamic equation. The modified sine-Gordon equation model effectively captures the behavior of the slinky mode in reversed-field pinch experiments. In addition, this paper demonstrates how the derived model accurately describes the behavior of the localized magnetohydrodynamic mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The modified SG equation model is solved analytically by using the perturbation method. The resulting model is fit to match a variety of experimental results in the MST reversed-field pinch experiment. The efficacy of the newly developed model in effectively representing the slinky mode is verified by comparing obtained analytical solution to experimentally measured data.

Evolution of views on the structure of the ambipolar electric field in toroidal magnetic confinement systems

Various methods of determining the ambipolar electric field in toroidal magnetic systems (predominantly, in stellarators) and the evolution of views on this problem are discussed. Paradoxes encountered in solving this problem are analyzed, and ways of resolving them are proposed.

Determination of broken KAM surfaces for particle orbits in toroidal confinement systems

The destruction of Kolmogorov–Arnold–Moser surfaces in a Hamiltonian system is an important topic in nonlinear dynamics, and in particular in the theory of particle orbits in toroidal magnetic confinement systems. Analytic models for transport due to mode-particle resonances are not sufficiently correct to give the effect of these resonances on transport. In this paper we compare three different methods for the detection of the loss of stability of orbits in the dynamics of charged particles in a toroidal magnetic confinement device in the presence of time dependent magnetic perturbations.

Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.

Calculation of the charged particle source in a toroidal magnetic confinement system (hydrodynamic approach)

In order to model transport processes in magnetic confinement systems, it is necessary to have information on the charged particle source. This in turn requires calculation of the inward flux of neutral particles. In this paper, a method for solving this problem in the hydrodynamic approach for the neutral gas is proposed. The average velocity of neutral particles and the spatial distribution of their density are determined. The obtained expression for the neutral density almost completely coincides with that calculated previously by solving the kinetic equation. However, the computational time required to solve the problem in the proposed hydrodynamic approach is much shorter than that in the kinetic approach.

Isodynamic axisymmetric equilibrium near the magnetic axis

Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration).

10.1007/s11452-008-3006-0

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.

The role of plasma elongation on the linear damping of zonal flows

Drift wave turbulence is known to self-organize to form axisymmetric macroscopic flows. The basic mechanism for macroscopic flow generation is called inverse energy cascade. Essentially, it is an energy transfer from the short wavelengths to the long wavelengths in the turbulent spectrum due to nonlinear interactions. A class of macroscopic flows, the poloidally symmetric zonal flows, is widely recognized as a key constituent in nearly all cases and regimes of microturbulence, also because of the realization that zonal flows are a critical agent of self-regulation for turbulent transport. In tokamaks and other toroidal magnetic confinement systems, axisymmetric flows exist in two branches, a zero frequency branch and a finite frequency branch, named Geodesic Acoustic Modes (GAMs). The finite frequency is due to the geodesic curvature of the magnetic field. There is a growing body of evidence that suggests strong GAM activity in most devices. Theoretical investigation of the GAMs is still an open field of research. Part of the difficulty of modelling the GAMs stems from the requirement of running global codes. Another issue is that one cannot determine a simple one to one relation between turbulence stabilization and GAM activity. This paper focuses on the study of ion temperature gradient turbulence in realistic tokamak magnetohydrodynamic equilibria. Analytical and numerical analyses are applied to the study of geometrical effects on zonal flows oscillations. Results are shown on the effects of the plasma elongation on the GAM amplitude and frequency and on the zonal flow residual amplitude.

Measurements of the load resistance of a poloidal antenna and the phase velocity of fast magnetosonic waves during ICR plasma heating in the L-2M stellarator

The propagation and damping of waves excited by a poloidal antenna in a hydrogen plasma at the ion cyclotron resonance (ICR) frequency were investigated. The longitudinal wavenumber and damping length of waves excited in the ohmically heated plasma of the L-2M stellarator, the dependence of the damping length of fast magnetosonic waves on the magnetic field strength, and the dependence of the antenna load resistance on the plasma density were measured. It is the first time that such complex measurements were performed in experiments on ICR heating of a hydrogen plasma at the fundamental harmonic of the ion gyrofrequency in toroidal magnetic confinement systems.

Overview of confinement and MHD stability in the Large Helical Device

The Large Helical Device is a heliotron device with L = 2 and M = 10 continuous helical coils with a major radius of 3.5–4.1 m, a minor radius of 0.6 m and a toroidal field of 0.5–3 T, which is a candidate among toroidal magnetic confinement systems for a steady state thermonuclear fusion reactor. There has been significant progress in extending the plasma operational regime in various plasma parameters by neutral beam injection with a power of 13 MW and electron cyclotron heating (ECH) with a power of 2 MW. The electron and ion temperatures have reached up to 10 keV in the collisionless regime, and the maximum electron density, the volume averaged beta value and stored energy are 2.4 × 1020 m−3, 4.1% and 1.3 MJ, respectively. In the last two years, intensive studies of the magnetohydrodynamics stability providing access to the high beta regime and of healing of the magnetic island in comparison with the neoclassical tearing mode in tokamaks have been conducted. Local island divertor experiments have also been performed to control the edge plasma aimed at confinement improvement. As for transport study, transient transport analysis was executed for a plasma with an internal transport barrier and a magnetic island. The high ion temperature plasma was obtained by adding impurities to the plasma to keep the power deposition to the ions reasonably high even at a very low density. By injecting 72 kW of ECH power, the plasma was sustained for 756 s without serious problems of impurities or recycling.

Feature Article: The Accelerator Laboratory at the Weizmann Institute

Controlled thermonuclear fusion remains one of the principle candidates for meeting the world's long-term energy needs in a sustainable and environmentally friendly way. The international fusion community is presently on the threshold of a major advance with negotiations to agree to the construction of the ITER project. ITER is an international collaboration between China, Europe, Japan, Korea, Russia, and the United States and its exploitation will represent a truly global effort to address this aspect of the energy problem. ITER is a toroidal magnetic confinement system known as a tokamak, a Russian idea that has since become the predominant system in all of the world's major fusion programs.

Quasilinear modification of the spectra of cyclotron emission from a toroidal plasma near the ECRH frequency

A study is made of the modification of the spectra of electron cyclotron emission from an ECR heated plasma in a toroidal magnetic confinement system into which the heating radiation is launched from the low-field side. It is shown that, at frequencies close to the heating frequency, cyclotron emission can become more intense because of the deformation of the distribution function of the resonant electrons. This effect can be used to diagnose the slightly pronounced quasilinear perturbations of the electron distribution in the thermal energy range, which are typical of experiments on ECR plasma heating. Results of a qualitative analysis carried out for model electron distribution functions are presented, and examples of three-dimensional numerical simulations of a circular tokamak are described.

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U0. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2vT/R (where vT is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ɛ of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.

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.

Some theoretical problems of the toroidal plasma equilibrium

Two problems of toroidal magnetic plasma confinement systems are considered. The first one is connected with advanced helical systems. The peculiarity of geometry of these stellarator systems with the improved confinement is discussed. Some additional ways for further optimization are marked too. The second problem is concerned with the island structure in toroidal systems. From the very beginning, the theoretical research on plasma equilibrium in stellarators was based mainly on the assumption that the toroidal magnetic surfaces are nested. It means that there is a unique magnetic axis which serves as the edge of the azimuthal coordinate surface θ = const. To avoid the difficulties with such a coordinate in the case of many magnetic axes that result from islands, the tokamak-like representation of the magnetic field B which does not use the coordinate θ is proposed.

Empirical Similarity of Frequency Spectra of the Edge-Plasma Fluctuations in Toroidal Magnetic-Confinement Systems

Frequency spectra of fluctuations of the ion saturation current, floating potential, and turbulent transport measured in the plasma edge of different fusion devices (tokamaks and stellarators) have been compared. All of the spectra show the same behavior over the whole frequency range investigated, which supports universality of plasma turbulence or turbulent transport. The results obtained are an indication of edge-plasma turbulence evolving into a critical state, independent of the size and plasma characteristics of the device.

ASH Pumping from Mirror and Toroidal Magnetic Confinement Systems

Induced selective stochastical transversal diffusion coefficients for ions in axisymmetric open and closed magnetic systems are presented. Single particle dynamics in complex field is described. The possibility of setting the radial losses time level of 0.02 s is shown both for mirror trap and for tokamak. 9 refs., 1 fig.

An experimental study of magnetic islands as Hamiltonian systems

Magnetic islands play an important role in determining plasma transport in toroidal magnetic confinement systems. The magnetic error fields and the associated islands can be theoretically described by a Hamiltonian approach. Experiments have been conducted on the Compact Auburn Torsatron [Fusion Technol. 18, 281 (1990)] to test the applicability and limits of the first-order Hamiltonian theory to magnetic islands. A novel set of helical trim coils with the same spatial periodicity as an ι– = 1/2 magnetic island were used to create a perturbation field of variable magnitude and phase. Extensive experimental parametric studies of the magnetic island were conducted and compared with theory. It was found that the first-order Hamiltonian theory is applicable for the complete range of experimental error fields.

Impurity transport in tokamaks in the plateau to Pfirsch–Schlüter regimes

Neoclassical transport coefficients for ion and impurity species are computed in a large aspect ratio toroidal magnetic confinement system for intermediate-to-high collision frequencies. A large range of values of the relevant density and charge parameters is explored and terms of order (mi/mI)1/2 are retained. The behavior of the transport coefficients is found to depend on the collisionality of both the ions and the impurities. A simple approximate analytic representation of these results which incorporates the correct asymptotic plateau and Pfirsch–Schlüter behavior is presented. In the plateau regime, when (nI/ni)(mI/mi)1/2≪1, the inward impurity flux is found to be suppressed for experimentally obtainable plasma parameters, implying that the time scale for impurity concentration could be too long to be observable.

Transport properties of a toroidal plasma at intermediate-to-high collision frequencies

Neoclassical transport coefficients are computed in a large aspect ratio toroidal magnetic confinement system in order to examine the transition between the plateau and Pfirsch–Schlüter regimes. The calculation employs a hybrid collision operator combining Krook and pitch angle scattering terms with the identical particle collision frequency taken to be a function of velocity which is determined from a fit to known exact results for classical transport. A simple approximate analytic form is presented which incorporates both these results and the results of Hinton and Rosenbluth for lower collision frequencies.