Poloidal Beta Research Articles

Synchronous oscillation prior to disruption caused by kink modes in HL-2A tokamak plasmas

A class of evident MHD activities prior to major disruption has been observed during recent radiation induced disruptions of the HL-2A tokamak discharges. It can be named SOD, synchronous oscillations prior to disruption, characterized by synchronous oscillation of electron cyclotron emission (ECE), core soft x-ray, Mirnov coil, and radiation signals at the divertor plate. The SOD activity is mostly observed in a parametric regime where the poloidal beta is low enough before disruption, typically corresponding to those radiation-induced disruptions. It has been found that the m/n = 2/1 mode is dominant during the SODs, and consequently it is the drop of the mode frequency and the final mode locking that lead to thermal quench. The mode frequency before the mode locking corresponds to the toroidal rotation frequency of the edge plasma. It is also found that during SODs, the location of the q = 2 surface is moving outward, and most of the plasma current is enclosed within the surface. This demonstrates that the current channel lies inside the rational surface during SOD, and thus the resistive kink mode is unstable. Further analysis of the electron temperature perturbation structure shows that the plasma is indeed dominated by the resistive kink mode, with kink-like perturbation in the core plasma region. It suggests that it is the nonlinear growth of the m/n = 2/1 resistive kink mode and its higher order harmonics, rather than the spontaneous overlapping of multiple neighboring islands, that ultimately triggered the disruption.

Sensitivity of the diamagnetic sensor measurements of ITER to error sources and their compensation

The present paper is focused on the sensitivity analysis of the diamagnetic sensor measurements of ITER against several kinds of error sources, with the aim of compensating them for improving the accuracy in the evaluation of the energy confinement time and poloidal beta, via Shafranov formula.The virtual values of measurements at the diamagnetic sensors were simulated by the COMPFLUX code, a numerical code able to compute the field and flux values generated in a prescribed set of output points from massive conductors and generalized filamentary currents (with an arbitrary 3D shape and a negligible cross section) in the presence of magnetic materials. The major issue to face with has been to determine the possible deformations of sensors and electromagnetic sources. The analysis has been carried out considering the following cases:-deformed sensors and ideal EM (electromagnetic) sources;-ideal sensors and perturbed EM sources;-both sensors and EM sources perturbed.As regards the compensation, several formulas have been proposed, based on the measurements carried out by the compensation coils; they basically use the value of the flux density measured to compensate the effects of the poloidal eddy currents induced in the conducting structures surrounding the plasma.The static deviation due to sensor manufacturing and positioning errors has been evaluated, and most of the pollution of the diamagnetic flux has been compensated, meeting the prescribed specifications and tolerances.

Demonstration of real-time control for poloidal beta in KSTAR

Sustaining the plasma in a stable and a high performance condition is one of the important control issues for future steady state tokamaks. In the 2014 KSTAR campaign, we have developed a real-time poloidal beta (βp) control technique and carried out preliminary experiments to identify its feasibility. In the control system, the βp is calculated in real time using the measured diamagnetic loop signal, and compared with the target value leading to the change of the neutral beam (NB) heating power using a feedback PID control algorithm. To match the requested power of NB which is operated with constant voltage, the on-time periods of the intervals were adjusted as the ratio of the required power to the maximum achievable one. This paper will present the overall procedures of the βp control, the βp estimation process and NB operation scheme implemented in the plasma control system (PCS), and the analysis on the preliminary experimental results.

Highβpplasma formation using off-axis ECCD in Ohmic heated plasma in the spherical tokamak QUEST

High poloidal beta (ɛβp ~ 1) operation in steady state condition in tokamaks is of great interest and has previously been demonstrated using NBI, LHCD and low current (Ip ) plasma for a short time ( in tokamak plasma. In this work we report the first result of high βp production and its sustainment though an off axis ECCD at two different frequencies (fundamental and second harmonic) in Ohmic (OH) target plasma. With application of ECCD, plasma βp increased to encounter an equilibrium limit and the standard limiter configuration is transformed to an Inboard Poloidal field Null (IPN) configuration. Both off-axis and on-axis ECCD is studied and found to have some distinctive features, which are discussed in this paper.

Study of the poloidal beta and internal inductance by solving the simplest Grad-Shafranov equation for a tokamak with a circular cross section

In this work, we present the poloidal beta βp and internal inductance li by solving the simplest Grad-Shafranov equation (GSE), using the Solov’ev assumption for an HT-7 tokamak with a circular cross section. The poloidal beta and internal inductance are measured by using diamagnetic and compensation loops, combined with poloidal magnetic probe array signals. In this paper, theoretical and experimental results of determining βp and li are presented. The calculated poloidal beta and internal inductance are demonstrated to depend on the kind of the discharge or plasma current.

A semi-analytical solver for the Grad-Shafranov equation

In toroidally confined plasmas, the Grad-Shafranov equation, in general, a non-linear partial differential equation, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic flux and the squared poloidal current is a quadratic function of it. In this work, the eigenvalue of the associated homogeneous equation is related with the safety factor on the magnetic axis, the plasma beta, and the Shafranov shift; then, the adjustable parameters of the particular solution are bounded through physical constrains. The poloidal magnetic flux becomes a linear superposition of independent solutions and its parameters are adjusted with a non-linear fitting algorithm. This method is used to find hydromagnetic equilibria with normal and reversed magnetic shear and defined values of the elongation, triangularity, aspect-ratio, and X-point(s). The resultant toroidal and poloidal beta, the safety factor at the 95% flux surface, and the plasma current are in agreement with usual experimental values for high beta discharges and the model can be used locally to describe reversed magnetic shear equilibria.

Impact of plasma core profiles on MHD stability at tokamak edge pedestal

Impact of plasma core profiles on magnetohydrodynamics (MHD) stability at tokamak edge pedestal is investigated numerically to extend an operation regime for small amplitude grassy edge localized mode (ELM). With the hypotheses that pedestal pressure profile can be predicted with the EPED1 model and the trigger of grassy ELM is an ideal ballooning mode, the impacts of plasma poloidal beta and plasma internal inductance on edge MHD stability are investigated, the parameters of which are related to plasma core profiles and are important parameters for grassy ELMy H-modes in JET quasi-double null plasma. The numerical results indicate that a ballooning mode can be destabilized by decreasing poloidal beta and/or internal inductance. In contrast, it is confirmed that pedestal density, which is also an important parameter for realizing grassy ELMy H-mode, can stabilize a ballooning mode. In combination with these trends, it is possible to relax the necessary conditions for grassy ELMy H-mode by adjusting the parameters carefully, though this relaxation destabilizes type-I ELM more easily due to the increase in edge current density.

Pedestal structure in H-mode plasmas

The present understanding of edge pedestal structure is reviewed. Pedestal plasma strongly affects fusion power and divertor heat load, and as such, characterization of the pedestal structure has significantly progressed. In high-confinement mode (H-mode) plasmas, the pedestal component plays the role of a boundary condition in determining the core heat transport through profile stiffness. On the other hand, a higher global poloidal beta or Shafranov shift improves the stability of the plasma edge in the low magnetic field side particularly at high triangularity. Toroidal rotation also influences the edge stability boundary. While toroidal flow stabilizes high-n ballooning modes, it destabilizes low-n kink/peeling modes. On the basis of this background, characterization of the pedestal pressure profile has been attempted from a geometrical viewpoint of width, gradient and height. While the pressure gradient is given mainly by the peeling–ballooning stability limit, many experimental results indicate the pedestal width scales approximately as the square root of the poloidal beta at the pedestal. Some supportive experimental results were observed where the kinetic ballooning mode (KBM) was seen as a turbulent transport that exists in the pedestal region and explained the empirical scaling of the pedestal width. A predictive model of the pedestal height (EPED1) has been developed, in which the pedestal height can be consequently estimated by knowledge of the edge magneto-hydrodynamic (MHD) stability on the pressure gradient and the KBM transport characterizing the pedestal width.The influence of the metal wall on the pedestal and confinement has intensively been studied in accordance with the decision of the installation of a full beryllium first wall and a full tungsten divertor in ITER. A common pattern among the existing metal wall tokamaks has been found that the pedestal and global confinement are affected by a requirement for increased gas fuelling (to screen high-Z impurity influxes) as well as a change in pedestal characteristics due to a decrease of the low-Z impurity concentration in the pedestal region. The pedestal pressure or temperature, and thus the energy confinement, can be raised by seeding low-Z extrinsic impurities.

Improved confinement region without large magnetohydrodynamic activity in TPE-RX reversed-field pinch plasma

We found that spontaneous improved confinement was brought about depending on the operating region in the Toroidal Pinch Experiment-Reversed eXperiment (TPE-RX) reversed-field pinch plasma [Y. Yagi et al., Fusion Eng. Des. 45, 421 (1999)]. Gradual decay of the toroidal magnetic field at plasma surface Btw reversal makes it possible to realize a prolonged discharge, and the poloidal beta value and energy confinement time increase in the latter half of the discharge, where reversal and pinch parameters become shallow and low, respectively. In the latter half of the discharge, the plasma current and volume-averaged toroidal magnetic field 〈Bt〉 increase again, the electron density slowly decays, the electron temperature and soft X-ray radiation intensity increase, and the magnetic fluctuations are markedly reduced. In this period of improved confinement, the value of (〈Bt〉-Btw)/Bpw, where Bpw is the poloidal magnetic field at the plasma surface, stays almost constant, which indicates that the dynamo action occurs without large magnetohydrodynamic activities.

Tokamak Plasma Parameters in the Presence of Resonant Field and Biased Electrode

Plasma energy, poloidal beta, plasma pressure, plasma temperature, plasma resistance, and plasma effective atomic number are important parameters in tokamak plasma experiments. In this paper, we present a theoretical and experimental approach especially based on diamagnetic loop for measurement of these parameters in the presence of resonant helical field (RHF) and biased electrode in IR-T1 tokamak. For this purpose, an electrode biasing system and a diamagnetic loop with its compensation coil designed, constructed, and installed on the IR-T1. In addition, we measured the plasma current, plasma voltage, and the plasma density from the Rogowski coil, the poloidal flux loop, and the Langmuir probe measurements, respectively. Experimental results show that the addition of a relatively small amount of RHF with L = 2 and L = 3 modes could be effective for improving the quality of tokamak plasma discharge by creating the steady-state plasma.

Plasma Internal Inductance in the Presence of External Resonant Fields in IR-T1 Tokamak

In this paper we presented experimental investigation of effects of local limiter biasing (Vbiasing = +200 v, Vbiasing = +320 v) on the plasma parameters as plasma current, loop voltage, poloidal beta, plasma pressure, plasma energy, plasma resistance, plasma temperature, plasma displacement, Shafranov parameter and plasma internal inductance in IR-T1 tokamak. For these purposes, array of magnetic probes and also a diamagnetic loop have been used. The results show that applied biased voltage Vbiasing = +200 v causes to decrease of about 40 % in plasma internal inductance. The plasma resistance and the plasma displacement have been decreased by Vbiasing = +200 v. The main result of the application of Vbiasing = +200 v is flatting the plasma parameters profiles. In other words, the addition of biasing voltage Vbiasing = +200 v to plasma could be effective for improving the quality of tokamak plasma discharge by creating the steady state plasma. The plasma current, plasma pressure, plasma energy, plasma temperature and shift parameter have increased after the application of limiter biasing with Vbiasing = +320 v but they decrease rapidly.

Edge-localized mode avoidance and pedestal structure in I-mode plasmas

I-mode is a high-performance tokamak regime characterized by the formation of a temperature pedestal and enhanced energy confinement, without an accompanying density pedestal or drop in particle and impurity transport. I-mode operation appears to have naturally occurring suppression of large Edge-Localized Modes (ELMs) in addition to its highly favorable scalings of pedestal structure and overall performance. Extensive study of the ELMy H-mode has led to the development of the EPED model, which utilizes calculations of coupled peeling-ballooning MHD modes and kinetic-ballooning mode (KBM) stability limits to predict the pedestal structure preceding an ELM crash. We apply similar tools to the structure and ELM stability of I-mode pedestals. Analysis of I-mode discharges prepared with high-resolution pedestal data from the most recent C-Mod campaign reveals favorable pedestal scalings for extrapolation to large machines—pedestal temperature scales strongly with power per particle Pnet/n¯e, and likewise pedestal pressure scales as the net heating power (consistent with weak degradation of confinement with heating power). Matched discharges in current, field, and shaping demonstrate the decoupling of energy and particle transport in I-mode, increasing fueling to span nearly a factor of two in density while maintaining matched temperature pedestals with consistent levels of Pnet/n¯e. This is consistent with targets for increased performance in I-mode, elevating pedestal βp and global performance with matched increases in density and heating power. MHD calculations using the ELITE code indicate that I-mode pedestals are strongly stable to edge peeling-ballooning instabilities. Likewise, numerical modeling of the KBM turbulence onset, as well as scalings of the pedestal width with poloidal beta, indicates that I-mode pedestals are not limited by KBM turbulence—both features identified with the trigger for large ELMs, consistent with the observed suppression of large ELMs in I-mode.

Study of Energy Confinement Time by the Analytical Solution of Grad–Shafranov Equation with Lithium Limiter for Circular Cross-Section Tokamak

In this work we calculated the energy confinement time by analytical solution of Grad–Shafranov equation (GSE) with Lithium limiter for circular cross-section HT-7 tokamak. A generalized Grad–Shafranov-type equation has been used. Specific functional forms of plasma internal energy and current are used. For this, the Shafranov parameter (asymmetry factor) and poloidal beta were obtained from by analytical solution of GSE. Than we can find the plasma energy confinement time. It is observed, the energy confinement time obtained from the analytical solution of GSE by using liquid lithium limiter is longer than that using graphite limiter, which shows that the plasma performance was improved.

Role of energetic electrons during current ramp-up and production of high poloidal beta plasma in non-inductive current drive on QUEST

A scenario for non-inductive current ramp-up has been demonstrated using electron cyclotron waves in the spherical tokamak QUEST. The configuration was characterized by a high toroidal magnetic mirror ratio of 2 and a steady vertical magnetic field of more than 10% of the toroidal magnetic field. The generation and confinement of energetic electrons having energy greater than 10 keV were studied using hard x-rays. Because of the energetic electron pressure, a natural divertor formed with an inboard poloidal field null at the high poloidal beta (approximately 3–4).

Progress and improvement of KSTAR plasma control using model-based control simulators

Superconducting tokamaks like KSTAR, EAST and ITER need elaborate magnetic controls mainly due to either the demanding experiment schedule or tighter hardware limitations caused by the superconducting coils. In order to reduce the operation runtime requirements, two types of plasma simulators for the KSTAR plasma control system (PCS) have been developed for improving axisymmetric magnetic controls. The first one is an open-loop type, which can reproduce the control done in an old shot by loading the corresponding diagnostics data and PCS setup. The other one, a closed-loop simulator based on a linear nonrigid plasma model, is designed to simulate dynamic responses of the plasma equilibrium and plasma current (Ip) due to changes of the axisymmetric poloidal field (PF) coil currents, poloidal beta, and internal inductance. The closed-loop simulator is the one that actually can test and enable alteration of the feedback control setup for the next shot. The simulators have been used routinely in 2012 plasma campaign, and the experimental performances of the axisymmetric shape control algorithm are enhanced. Quality of the real-time EFIT has been enhanced by utilizations of the open-loop type. Using the closed-loop type, the decoupling scheme of the plasma current control and axisymmetric shape controls are verified through both the simulations and experiments. By combining with the relay feedback tuning algorithm, the improved controls helped to maintain the shape suitable for longer H-mode (10–16s) with the number of required commissioning shots largely reduced.

RETRACTED ARTICLE: Plasma Stability Evaluation Based on MHD Activity and Hard X-Ray Emission in the IR-T1 Tokamak

Determinations of the poloidal beta, internal inductance, plasma energy, plasma pressure, plasma temperature, plasma resistance, plasma effective atomic number, magneto-hydrodynamics (MHD) activity, Runaway electrons energy and energy confinement time are essential for tokamak experiments and optimized operation. Also some of the plasma information can be deduced from these parameters, such as plasma toroidal current profile, and MHD instabilities. In this contribution we investigated about measurements of some plasma parameters as well as MHD activity and Runaway electrons energy. For this purpose we used the magnetic diagnostics and a hard X-ray spectroscopy in IR-T1 tokamak. A hard X-ray emission is produced by collision of the Runaway electrons with the plasma particles or limiters. The mean energy was calculated from the slope of the energy spectrum of hard X-ray photons. In this paper in order to measure energy of the Runaway electrons, we obtained hard X-ray energy in every 5 ms intervals, from the beginning to the end of plasma. Results indicated mean energy of Runaway electrons is maximum during the 0–5 ms interval.

Measurements and simulations of low-wavenumber pedestal turbulence in the National Spherical Torus Experiment

Previous pedestal turbulence measurements in the National Spherical Torus Experiment assessed the spatial and temporal properties of turbulence in the steep gradient region of H-mode pedestals during edge localized mode (ELM)-free, MHD-quiescent periods. Here, we extend the analysis to fluctuation amplitudes and compare observations to pedestal turbulence simulations. Measurements indicate normalized fluctuation amplitudes are about 1–5% in the steep gradient region. Regression analysis indicates fluctuation amplitudes scale positively with electron density gradient, collisionality, and poloidal beta, and scale negatively with magnetic shear, electron density, ion temperature gradient (ITG), toroidal flow and radial electric field. The scalings are most consistent with trapped electron mode, kinetic ballooning mode, or microtearing instabilities, but, notably, least consistent with ITG turbulence. Gyrokinetic simulations of pedestal turbulence with realistic pedestal profiles show collisional instabilities with growth rates that increase at higher density gradient and decrease at higher ITG, in qualitative agreement with observed scalings. Finally, Braginskii fluid simulations of pedestal turbulence do not reproduce scalings from measurements and gyrokinetic simulations, and suggest electron dynamics can be a critical factor for accurate pedestal turbulence simulations.

RETRACTED ARTICLE: Evolution of the IR-T1 Tokamak Plasma Local and Global Parameters

In this contribution, an attempt is made to investigate of evolution of some local and global plasma parameters in IR-T1 tokamak. For this purpose, four magnetic pickup coils were designed, constructed and installed on outer surface of the tokamak and then asymmetry factor is obtained from them. On the other hand, diamagnetic loop were designed and installed on IR-T1 and poloidal beta is determined from it. Therefore, the internal inductance and effective edge safety factor measured. Also, time evolution of the energy confinement time is measured using the diamagnetic loop. Experimental results show that maximum energy confinement time (which correspond to minimum collisions, minimum microinstabilities and minimum transport), relate to the low values of effective edge safety factor and also relate to the low values of internal inductance.

Static current profile control and RFP confinement

Static current profile control (CPC) is shown numerically to substantially enhance plasma confinement in the reversed-field pinch (RFP). By suitable application of an auxiliary electric field and adjustment of its internal location, width and amplitude, strongly decreased levels of dynamo fluctuations are obtained. The simulations are performed using a fully non-linear, resistive magnetohydrodynamic model, including the effects of ohmic heating as well as parallel and perpendicular heat conduction along stochastic field lines. The importance of controlling the parallel current profile in the core plasma to minimize the effects of tearing modes on confinement is thus confirmed. A near three-fold increase in energy confinement is found and poloidal plasma beta increases by 30% from 0.20 to 0.27. The edge heat flux is reduced to a third of that of the conventional RFP. The high-confinement phase is interrupted here by a crash, characterized by a rapid decrease in confinement. A detailed study of the crash phase is carried out by the standard Δ′ theory and a fully resistive linearized time-spectral method; the generalized weighted residual method. The analysis suggests that the instability is caused by pressure-driven, resistive g-modes. Inclusion of anisotropic thermal conduction reduces the linear growth rates. As compared with our earlier numerical studies of CPC in the RFP, employing feedback control, the present static control scheme should be more easily implemented experimentally.

Low MHD activity using resonant helical field and limiter biasing in IR-T1 tokamak

AbstractIn this paper, the effect of resonant helical magnetic field (RHF) and cold biased local limiter on plasma current, loop voltage, confinement time energy, poloidal beta, line emission intensity Hα, and magnetohydrodynamic (MHD) behavior based on Mirnov oscillations in the IR-T1 tokamak has been investigated. The experiments have been done in different regimes as cold biased local limiter, magnetic perturbation application, and both of these. At first the effect of the positive and negative bias voltage on plasma parameters and magnetic fluctuations detected by Mirnov coils has been investigated. Also, the effects of RHF on plasma parameters have been investigated in the edge region. Then the effects of applied biasing and RHF at the same time are analyzed. The bias voltage has been restricted to (−320 ≤ Vbias ≤ +320) and it has been applied with the limiter biasing that is fixed at r = 11.25 cm. These parameters have been measured using a diamagnetic loop, spectrometer, which is a visible light spectrometer for H-alpha, and Mirnov coils. The time-resolved frequency component analysis has been performed using short-time Fourier transforms. Fourier-based techniques and auto-correlation have been employed to analyze the frequency of MHD fluctuations. The results show that applied radial electric field at the plasma edge could control electromagnetic instabilities in the tokamak. In the positive biased regime, the amplitude of low-frequency Mirnov oscillations (<30 kHz) decreases after the application of biasing. Confinement time increases and line emission intensity decreases in all situations. The results are reversed when negative biasing has been applied. When RHF and biasing are applied to the plasma at the same time, the plasma parameters do not change any more compared to corresponding discharges with only RHF (L = 3). In other words, the amplitude of MHD activity can be totally controlled when a convenient biasing is applied to the limiter in the phases of current flat-top.