External Magnetic Field Fluctuations Research Articles

On Monitoring Tearing Modes Stability in Toroidally Rotating Tokamak Equilibria

In tokamak operation, the control of dangerous MHD instabilities, possibly in real-time scenarios, must rely on prompt robust diagnostics of the state and stability of the system. The set of magnetic signals measured on the outside of the plasma boundary, based on the Zakharov–Shafranov, Shkarowsky, Wootton (ZSSW) current moments, has been always used for reliable monitoring of key characteristics of the instantaneous equilibrium condition, such as the quantities $\Delta _{\mathrm{ Sh}}$ , the Shafranov centroid shift, $\beta _{p} $ related to the thermal energy content, and $l_{i}$ related to the current profile peakedness. In addition, the fast pickup coils monitor the external magnetic field fluctuations due to internal MHD activity, however, without the possibility of radial localization of the source. Here, we explore the potential usefulness of more complete use of ZSSW moments in association with the information from fast B perturbation signals to detect tearing stability conditions. For clarity, we set up an analysis of the measurable response to tearing perturbations based on an exact equilibrium model, which is an extension of the Solov’ev case with the addition of an equilibrium, nonuniform plasma rotation $\Omega (\psi)$ . The relation of the selected (externally measurable) ZSSW moments to the calculated stability index is mapped for different rotation values. The footprint of the stability condition $\Delta ' on some current moments on the outer surface can then identify stability boundaries for different rotation conditions. This first discussion on an idealized exact model is proposed for testing the concept for application to realistic equilibria since it relies on a few externally monitorable quantities and very basic assumptions on the tearing modes physics.

''DOUBLE-HUMPED EFFECT'' IN THE TURBULENT COLLISION MAGNETIZED PLASMA

Statistical moments of the spatial power spectrum of multiple scattered ordinary and extraordinary waves in the turbulent collision magnetized plasma with aligned anisotropic electron density irregularities are investigated using modify smooth perturbation method taking into account diffraction effects. Correlation function and variances of the phase fluctuations are obtained for arbitrary correlation function of the electron density fluctuations. Double-humped Effect is investigated analytically and numerically using the anisotropic Gaussian spectral function of electron density irregularities for the polar ionospheric F-region applying the experimental data. Investigation of the anisotropy of the F layer irregularities is of great interest in ionospheric physics. It is well known that the irregularities are elongated in the direction of the geomagnetic field of lines, but especially at high latitudes they are also found to be anisotropic in the plane perpendicular to the external magnetic field vector. The anisotropy is usually investigated by correlation analysis of radio signals from satellites, observed by space receiver on the ground. The fluctuations in amplitude and phase (scintillations) of radio waves passing through the ionosphere are caused by spatial irregularities in the electron density. The spatial fluctuations in phase cause fluctuations of the angle of arrival at the observation points. Broadening of the spatial power spectrum (SPS) of scattered electromagnetic (EM) waves in the turbulent collision magnetized plasma for both power-law and anisotropic Gaussian correlation functions of electron density fluctuations was analyzed in (1) using the complex ray (-optics) approximation. Double-humped Effect, the features of the SPS, spectral width and shift of its maximum of multiple scattered EM waves in the turbulent collisionless magnetized plasma were considered in (2, 3). The influence of the collision frequency between plasma particles on the statistical characteristics of scattered EM waves in the turbulent magnetized plasma with both electron density and external magnetic field fluctuations was investigated in (4). The present paper reports the results of an analysis of the SPS, which is related to fluctuations of the radio refractive index in the F region. Analytical expressions of the correlation function of phase fluctuations of scattered both ordinary and extraordinary waves are obtained for the arbitrary correlation functions of electron density fluctuation using modify smooth perturbation method taking into account the diffraction effects. The Double-humped Effect in the collision magnetized plasma with elongated electron density irregularities is considered for the first time. Formation of a gap in the SPS of scattered radiation is analyzed numerically for the polar ionospheric F -region using the anisotropic Gaussian spectral function of electron density fluctuations. This spectrum contains angle of aligned plasma irregularities to the direction of an external magnetic field and anisotropy factor. The numerical calculation is computed based on experimental data. Finally, paper concludes the obtained results and their significance.

PECULIARITIES OF THE SPATIAL POWER SPECTRUM OF SCATTERED ELECTROMAGNETIC WAVES IN THE TURBULENT COLLISION MAGNETIZED PLASMA

General dispersion equation is obtained at arbitrary inclination angles of the external magnetic field and wave vector of an incident EM wave. Statistical characteristics of the phase fluctuations of scattered high frequency EM waves in the collision magnetized plasma caused by electron density and external magnetic field fluctuations taking into account polarization coefficients for both ordinary and extraordinary waves are calculated analytically. The influence of collision frequency, anisotropy factor and angle of inclination of prolate irregularities of electron density fluctuations with respect to the geomagnetic field of lines on the broadening of the spatial power spectrum is analyzed. Phase portraits of the phase fluctuations caused by the geomagnetic field fluctuations are constructed at different spatial parameters characterizing magnetic field and electron density fluctuations. Numerical calculations are carried out for the ionospheric F -region parameters using experimental data.

Statistical Characteristics of Scattered Radiation in Medium With Spatial-temporal Fluctuations of Electron Density and External Magnetic Field

Influence of temporal fluctuations of both electron density and external magnetic field fluctuations on scattered ordinary and extraordinary waves in magnetized plasma is investigated using the ray-(optics) method. Transport equation for frequency fluctuations of scattered radiation has been derived. Broadening of the spatial power spectrum and amplification of the intensity of frequency fluctuation taking into account geometry of the task and the features of turbulent magnetized plasma is analyzed for the anisotropic Gaussian correlation function using the remote sensing data. It is shown that spatial-temporal fluctuations of electron density and external magnetic field, anisotropy and angle of inclination of prolate irregularities relative to the external magnetic field may lead to the exponential amplification of the intensity of frequency fluctuations of scattered electromagnetic waves in the collisional magnetized plasma.

Diamagnetic flux measurement without a compensation coil in the Hanbit mirror

A diamagnetic loop receives the external magnetic field fluctuations distorted by vacuum vessel eddy currents. Without installing a compensation coil in vacuum, the fluctuation is compensated from the circuit model of the vacuum vessel with only a Rogowski coil measurement of the external magnetic coil current. The vacuum vessel is modeled as a mixture of several inductively linked conductors. By solving the circuit equations, it is shown that the distortion is given as a convolution of exponentially decaying functions and the Rogowski coil signal. The characteristic time is obtained by a least-squares fitting algorithm. The convolution is calculated by using the fast Fourier transform technique. The external magnetic field fluctuations of the diamagnetic loop are reduced to 0.005% of the external magnetic field intensity.

Penetration of spatially nonuniform alternating magnetic field into type-II superconductors

Spatially nonuniform fluctuations of external magnetic field are typically present in applications of superconductors as magnetic bearings and shields. We use the Bean critical-state model to analyze penetration of such alternating fields into type-II superconductors. Simple asymptotic solutions are found for infinite slab configuration and low penetration depth of the magnetic field. To calculate AC losses, we use a vector potential formulation. The solutions obtained are tested by numerical simulations, based on a variational reformulation of the critical-state problem, and by experiments. A BSCCO superconducting bulk specimen with power law voltage–current characteristic was used in experiments.

AC Losses in Type-II Superconductors Induced by Nonuniform Fluctuations of External Magnetic Field

Magnetic field fluctuations are inevitable in practical applications of superconductors and it is often necessary to estimate the AC losses these fluctuations induce. If the fluctuation wavelength is greater than the size of a superconductor, known estimates for an alternating uniform external magnetic field can be employed. Here we consider the opposite case and analyze, using a model critical-state problem, penetration of spatially nonuniform fluctuations into type-II superconductors. Numerical simulation is based on a variational formulation of the Bean model. The analytical solutions, found in a weak penetration limit, are used to evaluate AC losses for two types of fluctuations: the running and standing waves. It is shown that for spatially nonuniform fluctuations the losses are better characterized by the fluctuation penetration depth than by the fluctuation amplitude. The results can be used to estimate the AC losses in flywheels, electric motors, magnetic shields, etc.

Effect of fluctuations on the forced motion and interactions of domain walls in one-dimensional magnetic systems

Forced motion of a domain wall in the presence of fluctuations of external magnetic field and those of the parameters of the magnetic medium is studied. Calculations for the models of magnetic systems described by the sine-Gordon and Landau-Lifshitz equations are presented. It is shown that the driven motion of domain walls is characterized by the time-independent velocity distribution function which is used to calculate various statistical characteristics of the domain wall. Analysis of the mean velocity of the steady motion of the domain wall leads to the conclusion that the presence of a fluctuating magnetic field results in an increase of the effective relaxation constant of the magnetic system. In case of the sine-Gordon model the mean radiation power accompanying the forced motion of the domain wall is calculated. Inelastic interactions of two domain walls of opposite polarities are described.