Diamagnetic Loop Research Articles

RETRACTED ARTICLE: Theoretical and Experimental Approach in Poloidal Beta and Internal Inductance Measurement on IR-T1 Tokamak

Measurements of poloidal beta βp and internal inductance li are essential in tokamak plasma research. Much more plasma parameters such as the plasma current density profile, magnetohydrodynamics instability, and plasma energy confinement time are determined by using these parameters. Discrete poloidal magnetic probes along with the diamagnetic loop can be utilized in measurement of the plasma poloidal beta βp and internal inductance li. In this paper, theoretical and experimental results in determining βp and li are presented and discussed.

Diamagnetic loop for the first plasma in the KSTAR machine

The diamagnetic loop (DL) is installed for the plasma diamagnetic measurement at the first plasma in the Korea superconducting tokamak advanced research (KSTAR) machine. Experimental results from the position measurement of the DL inside the KSTAR vacuum vessel and the vacuum flux measurement by using the DL for the evaluation of the geometrical data and the balance coefficient of the DL for the compensation of the vacuum flux in the diamagnetic measurement are described. In addition, a preliminary work of an instrument for a hardware compensation of the vacuum flux is presented.

Magnetic diagnostics for the lithium tokamak experiment

The lithium tokamak experiment (LTX) is a spherical tokamak with R(0)=0.4 m, a=0.26 m, B(TF) approximately 3.4 kG, I(P) approximately 400 kA, and pulse length approximately 0.25 s. The focus of LTX is to investigate the novel low-recycling lithium wall operating regime for magnetically confined plasmas. This regime is reached by placing an in-vessel shell conformal to the plasma last closed flux surface. The shell is heated and then coated with liquid lithium. An extensive array of magnetic diagnostics is available to characterize the experiment, including 80 Mirnov coils (single and double axis, internal and external to the shell), 34 flux loops, 3 Rogowskii coils, and a diamagnetic loop. Diagnostics are specifically located to account for the presence of a secondary conducting surface and engineered to withstand both high temperatures and incidental contact with liquid lithium. The diagnostic set is therefore fabricated from robust materials with heat and lithium resistance and is designed for electrical isolation from the shell and to provide the data required for highly constrained equilibrium reconstructions.

Poloidal beta and internal inductance measurement on HT-7 superconducting tokamak

Poloidal beta beta(theta) and internal inductance l(i) measurements are very important for tokamak operation. Much more plasma parameters can be inferred from the two parameters, such as the plasma energy confinement time, the plasma toroidal current profile, and magnetohydrodynamics instability. Using diamagnetic and compensation loop, combining with poloidal magnetic probe array signals, poloidal beta beta(theta) and internal inductance l(i) are measured. In this article, the measurement system and arithmetic are introduced. Different experimental results are given in different plasma discharges on HT-7 superconducting tokamak.

W7-X magnetic diagnostics: Performance of the digital integrator

In long pulse magnetic fusion experiments the use of conventional magnetic diagnostics is a challenge due to the so-called integrator problem. Magnetic sensors based on pickup coils and flux loops measure the time derivative of magnetic fluxes, and therefore, such signals have to be integrated in time to obtain flux signals. Although alternative methods of magnetic field measurement exist, magnetic flux measurements cannot be substituted due to the required measure of the vector potential integral along the area boundary. In addition, many of the alternative methods are not suited for usage in the harsh environment of a burning plasma experiment. An integrator for 1800s pulse operation in Wendelstein 7-X has been developed based on a chopper input stage and digital integration. Tests have been performed using a 25 turn diamagnetic loop at the WEGA stellarator, which has the capability of running long discharges. An important integrator property, in particular, for coping with radiation induced effects as they will occur in ITER, is the common mode rejection. At present, the integrator appears to be stable within 100μVs∕1000s when the common mode input voltage varies within ±1V.

Temperature and magnetic field dependencies in a model of diamagnetic hysteresis in beryllium

A model of a diamagnetic hysteresis loop of strongly correlated electron gas in dHvA effect conditions is developed. It is shown that in the framework of Rayleigh theory for magnetization loop, the coercive force and remnant magnetization at every stage of the dHvA oscillations are characterized by strong dependencies on temperature, magnetic field and Dingle temperature.

Modelling and Comparison with Experiment of Radial Profiles in a Tokamak with Magnetic Field Stochastization

A deliberate stochastization of the magnetic field in tokamaks with Ergodic Divertors (ED) modifies essentially the transport properties at the plasma edge by permitting a radial transfer of particles and heat along stochastic field lines and affecting anomalous transport perpendicular to them. A model for the effective transport coefficients in a stochastic magnetic field, taking into account both parallel flows and perpendicular transfer of anomalous nature, has been incorporated into the 1.5D transport code RITM for self-consistent calculations of the radial profiles of plasma parameters. Computations have been performed for the tokamak TEXTOR to simulate phases in an ohmic shot without and with the Dynamic Ergodic Divertor (DED). Results show that the increase of the outward convective transport in the stochastic boundary layer leads to a drop of the line average density. The experimentally observed density variation is reproduced by adjusting the amplitude of the stochastization characteristics with their radial dependence predicted by the field line mapping. The decrease of the diamagnetic energy after DED activation is in qualitative agreement with the experimental data from the diamagnetic loop measurements.

Timescale and magnitude of plasma thermal energy loss before and during disruptions in JET

In this paper we analyse and discuss the thermal energy loss dynamics before and during JET disruptions that occurred between 2002 and 2004 in discharges which reached >4.5 MJ of thermal energy. We observe the slow thermal energy transients with diamagnetic loops and the fast ones with electron cyclotron emission and soft x-ray diagnostics. For most disruption types in JET, the plasma thermal energy at the time of the thermal quench is substantially less than that of the full performance plasma, typically in the range of 10–50% depending on plasma conditions and disruption type. The exceptions to this observation are disruptions in plasmas with a strong internal transport barrier (ITB) and in discharges terminating in a pure vertical displacement event, in which the plasma conserves a very high energy content up to the thermal quench. These disruption types are very sudden, leaving little scope for the combined action of soft plasma landing strategies and intrinsic performance degradation, both requiring >500 ms to be effective, to decrease the available thermal energy. The characteristic time for the loss of energy from the main plasma towards the PFCs in the thermal quench of JET disruptions is in the range 0.05–3.0 ms. The shortest timescales are typical of disruptions caused by excessive pressure peaking in ITB discharges. The available thermal energy fraction and thermal quench duration observed in JET can be processed (with due caution) into estimates for the projected PFC lifetime of the ITER target.

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.

Continued Hot-Electron Plasma Production Studies in the Hanbit Plug

Continuing the experiments reported previously, additional microwave power has been applied to the plug region of Hanbit in order to increase the stored energy and beta of the hot-electron plasma created there. Two new 1.5-kW VA-806 klystrons at 7.67 GHz and 7.87 GHz have been used in conjunction with the existing 2-kW CPI klystron at 14 GHz. The plasma is created in order to provide a high-beta ring to stabilize the Hanbit central cell plasma against ballooning instabilities. An array of Hall probes mounted on the outside of the Hanbit plug cavity was installed to measure the axial profile of the Bz fields. The total stored energy was measured by diamagnetic loops and the radial location of the plasma was determined by a Si-PIN diode detector measuring the energetic electron end loss. All three measurements were to be used to determine the radial and axial location of the plasma, the plasma volume, the stored energy, and hence the plasma beta. However, the Bz signal was too small to measure and the diamagnetic signal was smaller than previously found. The ring was found to be very wide and not adequate to stabilize the central cell plasma.

The role of high frequency oscillations in the penetration of plasma clouds across magnetic boundaries

Experiments are reported where a collissionfree plasma cloud penetrates a magnetic barrier by self-polarization. Three closely related effects, all fundamental for the penetration mechanism, are studied quantitatively: (1) anomalous fast magnetic field penetration (two orders of magnitude faster than classical), (2) anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion), and (3) the ion energy budget as ions enter the potential structure set up by the self-polarized plasma cloud. It is concluded that all three phenomena are closely related and that they are mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process. The fast magnetic field penetration occurs as a consequence of the anomalous resistivity caused by the wave field and the fast electron transport across magnetic field lines is caused by the correlation between electric field and density oscillations in the wave field. It is also found that ions do not lose energy in proportion to the potential “hill” they have to climb, rather they are transported against the dc potential structure by the same correlation that is responsible for the electron transport. The results obtained through direct measurements are compared to particle in cell simulations that reproduce most aspects of the high frequency wave field.

On the Theory of Diamagnetic Measurements in Open Traps

A formula for the plasma pressure as a functional of the diamagnetic loop voltage is derived for a general case when the time for the magnetic flux to percolate through conducting wall of vacuum chamber is not small as compared to the plasma confinement time. An arbitrary shape of the conducting chamber and the plasma column are allowed in contrast to earlier theories based on axial symmetry of the system.

Integrating diagnostic data analysis for W7-AS using Bayesian graphical models

Analysis of diagnostic data in fusion experiments is usually dealt with separately for each diagnostic, in spite of the existence of a large number of interdependencies between global physics parameters and measurements from different diagnostics. In this article, we demonstrate an integrated data analysis model, applied to the W7-AS stellarator, where diagnostic interdependencies have been modeled in a novel way by using so called Bayesian graphical models. A Thomson scattering system, interferometer, diamagnetic loop, and neutral particle analyzer are combined with an equilibrium reconstruction, forming together one single model for the determination of quantities such as density and temperature profiles, directly in magnetic coordinates. The magnetic coordinate transformation is itself inferred from the measurements. Influence of both statistical and systematic uncertainties on quantities from equilibrium calculations, such as position of flux surfaces, can therefore be readily estimated together with uncertainties of profile estimates. The model allows for modular addition of further diagnostics. A software architecture for such integrated analysis where possibly large number of diagnostic and theoretical codes need to be combined, will also be discussed.

ASTRA Modeling of Electron Cyclotron Heating in the Helically Symmetric Experiment

Thomson scattering and diamagnetic loop measurements in a hot electron plasma in the Helically Symmetric Experiment (HSX) indicate that the central electron temperature and stored energy increase linearly with power. Experimentally it is found that the central electron temperature is roughly independent of plasma density. The ASTRA code is used to model electron cyclotron heating for a magnetic configuration that is quasi-symmetric as well as for a configuration in which the symmetry is broken. The experimental results are consistent with an anomalous thermal conductivity that scales inversely with the density. However, the experimental scaling of the stored energy against density is not usually in agreement with the model. From the measured X-ray flux and the high absorbed power, as well as from the calculated low single-pass absorption efficiency, it is concluded that at low densities, a nonthermal electron population accounts for a significant fraction of the stored energy. With the ASTRA code, it is also possible to model under what conditions the central electron temperature in the quasi-symmetric configuration will be measurably greater than the temperature in the nonsymmetric configuration. These calculations depend greatly on the radial electric field of the nonsymmetric plasma but suggest that at somewhat higher density and higher power than achieved to date, differences in the central electron temperature may be observed.

The penetration of plasma clouds across magnetic boundaries: The role of high frequency oscillations

Experiments are reported where a collision-free plasma cloud penetrates a magnetic barrier by self-polarization. Two closely related effects, both fundamental for the penetration mechanism, are studied quantitatively: anomalous fast magnetic field penetration (two orders of magnitude faster than classical), and anomalous fast electron transport (three orders of magnitude faster than classical and two orders of magnitude faster than Bohm diffusion). It is concluded that they are both mediated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop which is set up in the plasma in the penetration process.

Hot-Electron Plasma Studies in the Plug Section of the Hanbit Tandem Mirror

Hot electrons have been created in the plug section of the Hanbit tandem mirror in order to allow a test of high-in ballooning stability provided by a high-β hot-electron plasma in a tandem mirror. A rectangular microwave cavity was built to confine the energy from a 2-kW 14-GHz klystron. The cavity was equipped with a diamagnetic loop, a skimmer probe, and bremsstrahlung windows. An end-loss probe has been added in the cusp section in order to study the hot-electron mirror losses from the plug. The end-loss probe contains a Silicon PIN diode that is used to detect the x-rays from fast electrons striking a tantalum radiator. The end-loss probe was scanned radially to determine the radius and radial width of the hot-electron distribution ring for two different magnetic fields. A clear ring is observed for both magnetic fields. Bremsstrahlung measurements have shown the presence of a hot-electron plasma in the plug with an electron temperature in the range of 60 to 120 keV. The temperature with the optimum magnetic field is ~ 100 keV. Diamagnetic measurements give the total stored energy. Stored-energy measurements combined with the radial dimensions determined by the end-loss detector were used to give the value of beta with assumptions on the plasma length. The average beta value is much less than 1% due to the low power and short heating time.

Diamagnetic Loop Measurement in the Central Cell of The Hanbit Magnetic Mirror Device

Diamagnetic flux is measured by using diamagnetic loops in the central cell of the Hanbit magnetic mirror device. Diamagnetic loop measurements are carried out during rf discharges with a frequency of 3.5 MHz or 3.75MHz. In the measurement, the rf power is varied from 60 kW to 200kW, and the vacuum magnetic field of 0.130 T – 0.242 T is applied in the central cell. The present status of the diamagnetic loop measurements is described and experimental results from diamagnetic flux measurements under several Hanbit operational conditions are presented. The purpose of this work is preparation of a database (such as the dependence of the diamagnetic flux upon the applied vacuum magnetic field and rf power) for physics studies in the Hanbit device.

Observation of room-temperature spontaneous chemical phase segregation in overdopedBi2Sr2CaCu2O8+xsingle crystals

The occurrence and development of phase inhomogeneity in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ single crystals have been investigated by measuring their superconducting transition patterns using a high-sensitivity ac magnetometer. We find that the overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ single crystals, even if they were single-phased immediately after a high-temperature annealing process, show progressively pronounced multiple superconducting transitions with time as they were kept at room temperature in a dry air atmosphere. The results reveal that the oxygen dopants in the crystal are still mobile at room temperature. These dopants tend to rearrange and thus form different phases, at a characteristic time scale of one or two weeks or so. Moreover, the diamagnetic loops in the newly segregated phase are very weak, presumably due to the existence of additional inhomogeneity down to a nanometer scale. Our results also show that the optimally doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+x}$ crystals seem capable to remain in a single transition with storage time.

Measurement of Shafranov shift with soft x-ray CCD camera on large helical device

The Shafranov shift is derived from the two-dimensional profile of x-ray intensity measured with a soft x-ray CCD camera in large helical device. The accuracy of the measurement of the magnetic axis is 3% of the Shafranov shift at high β. The measured Shafranov shift increases linearly up to 280±3 mm, which is 47% of the minor radius as the volume averaged β ⟨βdia⟩ measured with a diamagnetic loop is increased up to 2.6%. The Shafranov shift measured with a soft x-ray CCD camera agrees with that calculated with the three-dimensional equilibrium code VMEC. The reduction of the Shafranov shift due to the higher harmonics of the Fourier components of the magnetic field is also observed.

Differential method for the real time measurement of the diamagnetic β and internal inductance in Tore Supra

A differential method for real time measurements of the diamagnetic energy and poloidal β has been successfully installed on the Tore Supra tokamak. This diagnostic makes use of concentric diamagnetic loops compensated by precise measurements of toroidal current variations. This diamagnetic measurement is now routinely used in the feedback system to control the internal inductance of the Tore Supra plasma using non-inductive current drive generated by lower hybrid waves.