Magnetic Island Width Research Articles

Simulation of neoclassical tearing modes in the DIII-D tokamak. II. Suppression by radially localized electron cyclotron current drive

The problem of neoclassical tearing mode (NTM) suppression by a radially localized toroidal current from electron cyclotron current drive (ECCD) is considered. Simulation of NTM stabilization by ECCD is performed with the Nonlinear Fully Toroidal Code (NFTC) [Phys. Plasmas 8, 3605 (2001)] for DIII-D discharges. The optimal parameters are determined for the radially localized ECCD current required to reduce the NTM instability. The time response and nonlinear evolution of the magnetic island width for ECCD and the required modulation phasing, the current drive location with respect to the rational surface, and the width of the spatial distribution are determined for both monotonic q-profile and negative central shear discharges.

Neoclassical tearing modes for a finite ratio of ion gyroradius tomagnetic island width

A model of neoclassical tearing modes (NTMs) allowing for a finite width ofthe transition layer near the island separatrix, where perturbed plasmaparameters vary significantly, is proposed. In contrast to traditionalmodels of NTMs, this model includes the parameter ρi/w properly,where ρi is the ion Larmor radius, and w is the magnetic islandwidth. It is shown that both the polarization current and bootstrap currenteffects on these modes prove to be weakened compared with those predicted bytraditional theories of NTMs. The competition of these effects results in acritical beta for NTM onset which is lower than that usually used forinterpretation of experimental observations and predictions for reactor-gradetokamaks.

Electron temperature perturbations measured by electron cyclotron emission diagnostic systems in JT-60U

Electron cyclotron emission (ECE) diagnostic systems in JT-60U for the measurement of electron temperature perturbations and the results of the measurement are described. In 1999, the heterodyne radiometer system was upgraded, and the number of the channels was doubled to 24. It can now measure ECE ranging from 176 to 200 GHz. The heterodyne system enables the measurement of the location and structure of the magnetic island, which is observed in the steady state high β p H-mode discharges. Behavior of an m/ n=1/1 mode and sawtooth oscillations during electron cyclotron heating and electron cyclotron current drive is investigated by using the grating polychromator. Here, m and n are poloidal and toroidal mode numbers, respectively. It is found that magnetic island width with m/ n=1/1 is decreased during electron cyclotron (EC) wave injection. It is also found that sawtooth period is significantly expanded by EC wave injection near the q=1 surface. The obtained maximum sawtooth-free period was about four times longer than the theoretically predicted one.

Regularized magnetic islands. II. The role of polarization current

The role of polarization current in the problem of rotating magnetic islands in the absence of drift effects is discussed for the case of nonregularized and regularized velocity profiles governed by the perpendicular viscosity. The polarization current is calculated taking into account the finite ion Larmor radius effects. It is shown that, in correspondence with the general rule by Waelbroeck and Fitzpatrick [Phys. Rev. Lett. 78, 1703 (1997)], this current is destabilizing. The destabilizing contribution of the polarization current into the generalized Rutherford equation for the magnetic island width does not depend on whether the profile function is regularized or not. It is shown that the Larmor corrections to the current consist of the sum of two oppositely directed currents and do not contribute into the generalized Rutherford equation.

Modeling of the stabilization of neoclassical tearing modes by localized radio frequency current drive

Numerical modeling of the stabilization of neoclassical tearing modes by localized radio frequency (rf) current drive is presented. The bootstrap current is self-consistently calculated from the pressure evolution equation, the rf current source is obtained from the ray-tracing code and the Fokker–Planck code, and the change of the driven current profile due to the change of the magnetic island width has also been taken into account by modeling the two-dimensional transport of the fast electrons induced by the rf wave. It is found that both parallel and the perpendicular transport of the fast electrons play important roles in the stabilization, and modulated and nonmodulated rf current drive have approximately the same stabilizing effect. The neoclassical tearing modes is shown to be stabilized by a continuous rf current drive. The simulation results essentially agree with experimental observations.

Hamiltonian magnetic reconnection

Magnetic reconnection in two dimensional (2D), collisionless, non-dissipative regimes is investigated analytically and numerically by means of a finite difference code in the nonlinear regime where the island size becomes macroscopic. The cross-shaped structure of the reconnection region, originally reported by Cafaro et al (1998 Phys. Rev. Lett. 80 20) is analysed as a function of the ratio between the ion sound Larmor radius and the inertial skin depth. This cross shape structure is found to survive in the presence of weak dissipation. Further insight on the quasi-explosive behaviour of the magnetic island width as a function of time and on the spatial structure of the perturbed current density is provided. We confirm that the amount of reconnected flux becomes of order unity on the time scale of the inverse linear growth rate. Results in the collisionless limit are interpreted on the basis of the Hamiltonian properties of the adopted collisionless, 2D, fluid model. Thus, collisionless reconnection is a fast, non-steady-state process, fundamentally different from 2D resistive magnetic reconnection, of which the Sweet-Parker model is the classic paradigm.

Analysis of perturbed magnetic fields via construction of nearby integrable fields

For a given nonintegrable toroidal magnetic field, a nearby integrable magnetic field is constructed from quadratic-flux minimizing surfaces. A new mathematical definition and derivation of quadratic-flux minimizing surfaces, which directly exploits the analogy between toroidal magnetic fields and 112 degree of freedom Hamiltonian systems, is given. The width and phase of magnetic islands (calculated from the shear of the integrable field and the magnitude and phase of the perturbation harmonics) are in excellent agreement with detailed Poincaré plots.

Measurement of magnetic island width in long-pulse, high- discharges in JT-60U

The magnetic island width during long-pulse, high- discharges was evaluated by measuring oscillations of electron cyclotron emission using a heterodyne radiometer. Because of its high spatial resolution of about 2 cm, evolution of the magnetic island structure can be measured in detail. The island width increases with the amplitude of the magnetic fluctuations. The saturated island width was about 7 cm when the m/n = 3/2 mode appeared. The resistive modes which limit the sustainable have typical mode numbers of m/n = 3/2 and 2/1. The relationship between the observed magnetic island and the neoclassical tearing mode is discussed.

High precision pick-up (Mirnov) coils for disruption studies in the T-11M and TCABR tokamaks

Newly developed methods of visualization and determination of widths of internal magnetic islands are based on measurements of the perturbed magnetic fields near the plasma border. Reliable analysis of pick-up (Mirnov) coils data is rather complicated and measurement errors have to be minimized. Plasma wall interaction, electrical sparks in the discharge chamber, and resonances in the measurement systems could be main sources of errors but, also, the design of coils should take into account that the typical frequency band of the disruptive processes is in the range of ∼100 kHz–1.5 MHz. A double Faraday coaxial screening with a symmetrically input system of pick-up coils was developed for disruption studies in the TCABR tokamak in São Paulo. The main design features of this high precision pick-up coil system are discussed.

Nonlinear growth and motion of magnetic islands in regimes with a high fraction of bootstrap current density

The nonlinear evolution of magnetic islands is investigated in regimes with a high fraction of bootstrap current density, which are of great interest for advanced tokamak scenarios. For a sufficiently large fraction of the equilibrium bootstrap current density (measured against the local magnetic shear and the poloidal magnetic fields), the nonlinear island growth and the saturated magnetic island width are found to depend neither on the original local equilibrium magnetic shear nor on the fraction of the bootstrap current density. In addition, in the positive magnetic shear region the magnetic islands together with its rational surface move inwards. The results of corresponding numerical simulations agree well with analytical predictions.

On the stabilization of neoclassical tearing modes by phased electron cyclotron waves

The stabilization of neoclassical tearing modes by phased electron cyclotron current drive (ECCD) and electron cyclotron resonance heating (ECRH) is studied numerically. The dependence of the saturated magnetic island width on the magnitude, width and location of the driven current and the corresponding resistivity perturbation are investigated. Since the saturated island size cannot become much smaller than the width of the driven current layer, this width is one of the most important parameters. Assuming usual heat transport coefficients, the stabilization by ECRH is found to be more effective than that by ECCD for a large island in a middle-size tokamak, while the stabilization by ECCD should be more effective for a tokamak reactor.

Magnetic Island in Helically Perturbed Force-Free Equilibrium

An analytical formula has been derived for the magnetic island width in a helically perturbed force-free equilibrium with uniform force-free parameters. In this calculation, the effect of the nonlinear plasma response to the resultant field configuration has been self-consistently taken into account up to the first order. The radial magnetic field at the resonant surface is amplified as a result of the nonlinear plasma response, or, the magnetohydrodynamic (MHD) relaxation. Typical width of the core island is 10% of the plasma radius for the perturbation level of 1% at the edge, and the inner island is larger than the outer one when compared at the same perturbation level at the edge. Usefulness of the formula is demonstrated by comparing the experimental results with the theoretical calculation.

Neoclassical tearing modes in Tokamak Fusion Test Reactor experiments. I. Measurements of magnetic islands and Δ′

Tearing-type modes are observed in most high confinement operation regimes in the Tokamak Fusion Test Reactor (TFTR) [Nucl. Fusion 35, 1429 (1995)]. Three different methods are used to measure the magnetic island widths: external magnetic coils, internal temperature fluctuation from electron cyclotron emission (ECE) diagnostics and an experiment where the plasma major radius is rapidly shifted (“Jog” experiments). A good agreement between the three methods is observed. Numerical and analytic calculations of Δ′ (the tearing instability index) are compared with an experimental measurement of Δ′ using the tearing mode eigenfunction mapped from the jog data. The obtained negative Δ′ indicates that the observed tearing modes cannot be explained by the classical current-gradient-driven tearing theory.

Chaotic Approach to Evaluation of Disturbed Magnetic Surfaces

A circle mapping can approximately reproduce the cross section of magnetic surfaces and the value of the periodic driving force ( K ) at a magnetic island varies with the width of the magnetic island, which suggests the value of K is one of measures for the degradation of magnetic surfaces. The profile of a rotational transform has flat regions at the magnetic islands. The width of the flat region is proportional to the width of the magnetic island. Therefore it may be another measure of the degradation of magnetic surfaces. This method requires less data for the estimation than the usual method of calculating the width of magnetic islands. For collapsed magnetic surfaces that are produced by overlapping of two magnetic islands, the fractal dimension can effectively estimate the degradation of them. The fractal dimensions of cross sections of regular magnetic surfaces and clear magnetic islands are nearly 1, while that of a collapsed magnetic surface is about 1.2 in the present study.

Characteristic parameters of the magnetic field due to the dynamic ergodic divertor

Resonant perturbations of sufficient amplitude impose an ergodic structure on the field line trajectories. In the standard theory, these features are related to the amplitude of the resonant Fourier components of the Br-field. The characteristic parameters of an ergodized field are the width of magnetic islands, the Chirikov parameter (amount of overlapping of islands) and the coherence length (Kolmogorov length). The perturbation current amplitude allows for Chirikov parameters of up to 1.6 for the pure 12/4 excitation mode. The Chirikov value is very sensitive to a possible mixing of 12/4 and 6/2 modes and can considerably be enhanced.

Structure instability and nonlinear evolution of magnetic islands at the magnetopause

Structure instability and nonlinear evolution of magnetic islands produced by time‐dependent magnetic reconnection at the magnetopause are studied. The analytic expression for the width of magnetic islands and critical conditions for the occurrence of bifurcation and chaos axe derived. It is shown that the magnetic islands are unstable against the interference from external disturbances. Their structure can be destroyed by medium and small‐scale solar wind turbulences, leading to stochastic magnetic reconnection and the formation of irregular small‐scale structures in magnetospheric boundary regions.

Helical temperature perturbations associated with tearing modes in tokamak plasmas

An investigation is made into the electron temperature perturbations associated with tearing modes in tokamak plasmas. It is found that there is a critical magnetic island width below which the conventional picture where the temperature is flattened inside the separatrix is invalid. This effect comes about because of the stagnation of magnetic field lines in the vicinity of the rational surface and the finite parallel thermal conductivity of the plasma. Islands whose widths lie below the critical value are not destabilized by the perturbed bootstrap current, unlike conventional magnetic islands. This effect may provide an explanation for some puzzling experimental results regarding error field-induced magnetic reconnection. The critical island width is found to be fairly substantial in conventional tokamak plasmas, provided that the long mean-free path nature of parallel heat transport and the anomalous nature of perpendicular heat transport are taken into account in the calculation.

On the possibility of determining the sawtooth location from impurity ion density profiles

A new method is proposed for determination of the magnetic island location from the density profiles of multiply charged impurity ions. The method is based on (1) measuring the impurity ion’s emissivity profiles in T-10 tokamak experiments and (2) a theoretical model for the behavior of the impurities under conditions of sawtooth oscillations. The main physical basis of the method is the fact that the impurity is forced out from the sawtooth region in such a way that the profile of impurity ions appears to be a composition of two different profiles. These two profiles are determined by the Braginskii mechanism of impurity diffusion sustained in the regions r≳rs and r<(rs−Δ), whereas in the transient region (rs−Δ)≤r≤rs the impurity density has a sharp drop with decreasing minor radius. Interpretation of T-10 tokamak experimental data within the frame of a theoretical model allows one to determine the location of the surface q=1 and the width of magnetic islands. The method appears to be very sensitive to the level of large-scale MHD activity of the plasma.

Transport effects of low (m,n) MHD modes on TFTR supershots

Supershots in TFTR often suffer a performance deterioration characterized by a gradual decrease of the DD fusion neutron yield and plasma stored energy after several hundred milliseconds of auxiliary heating. The correlation between this performance deterioration and the development of low m (the poloidal mode number), n (the toroidal mode number) MHD modes is studied through shot-to-shot comparisons and statistical data analyses. A good correlation is observed between performance deterioration and the appearance of strong 3/2 and 4/3 macroscopic modes. The magnetic island structures are observed using Mirnov and ECE diagnostics. The measured Te, Ti and ne profiles show that development of the islands corresponds to a nearly constant decrement of these quantities over the core region r < rs, where rs is the mode rational surface, on a transport time-scale (t > τE). The observed energy deterioration scaling, δW/W varies as w/a, where w is the magnetic island width and a is the plasma minor radius, agrees with a local transport model. Numerical simulations based on the local transport model reveal many features consistent with the experiments. Besides the MHD effect, it is found that a continuous increase of edge recycling rate during the neutral beam injection phase also has a large effect on the performance deterioration

Interaction between resonant magnetic perturbation and the rotating magnetic island

Nonlinear interaction between an external static resonant magnetic perturbation (RMP) and the corresponding rotating saturated magnetic island in tokamak plasma has been numerically simulated. The influence of flow shear driven by this nonlinear interaction is considered. It is found that applied resonant magnetic perturbations can effectively reduce the width of spontaneous magnetic island so that the amplitude of Mirnov signal is suppressed and the velocity profile is changed as well.