Plasma Internal Inductance Research Articles

Effects of internal inductance on the Shafranov parameter by using the solution of equilibrium problem

In this work, the dependence of Shafranov parameter on plasma internal inductance has been studied by using the solution of Grad–Shafranov equation (GSE) for Hefei Tokamak-7. The Shafranov parameter was obtained from the solution of GSE, using the expansion of free functions, which is quadratic in flux function. Then, we can find the dependence of Shafranov parameter on plasma internal inductance.

Investigation of instabilities and rotation alteration in high beta KSTAR plasmas

H-mode plasma operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) device has been expanded to significantly surpass the ideal MHD no-wall beta limit. Plasmas with high normalized beta, βN, up to 4.3 have been achieved with reduced plasma internal inductance, li, to near 0.7, exceeding the computed n = 1 ideal no-wall limit by a factor of 1.6. Pulse lengths at maximum βN were extended to longer pulses by new, more rapid control. The stability of the observed m/n = 2/1 tearing mode that limited the achieved high βN is computed by the M3D-C1 code, and the effect of sheared toroidal rotation to tearing stability is examined. As a method to affect the mode stability in high βN plasmas, the non-resonant alteration of the rotation profile by non-axisymmetric magnetic fields has been used, enabling a study of the underlying neoclassical toroidal viscosity (NTV) physics and stability dependence on rotation. Non-axisymmetric field spectra were applied using in-vessel control coils (IVCCs) with varied n = 2 field configurations to alter the plasma toroidal rotation profile in high beta H-mode plasmas and to analyze their effects on the rotation. The rotation profile was significantly altered with rotation reduced by more than 60% without tearing activity or mode locking. To investigate the physical characteristics and scaling of the measured rotation braking by NTV, changes in the rotation profile are analytically examined in steady state. The expected NTV scaling with the square of the normalized applied field perturbation agrees with the measured profile change δB2.1–2.3. The NTV is also found to scale as Ti2.1–2.4, in general agreement with the low collisionality “1/ν” regime scaling of the NTV theory (TNTV-(1/ν) ∝ Ti2.5).

Statistical analysis of m/n = 2/1 locked and quasi-stationary modes with rotating precursors at DIII-D

A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance li divided by the safety factor at 95% of the poloidal flux, q95, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as dedge, performs comparably to in its ability to discriminate disruptive locked modes. Out of all parameters considered, dedge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between and q95 in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the response times necessary for disruption avoidance and mitigation. Observations of the evolution of during a locked mode, the effects of poloidal beta on the saturated width, and the reduction in Shafranov shift during locking are also presented.

Application of poloidal beta and plasma internal inductance in determination of input power time of Damavand tokamak

In this study, magnetic measurement of poloidal fields were used to determine poloidal beta and plasma internal inductance of Damavand tokamak combination of poloidal beta and plasma internal inductance ( $$\beta _p+\dfrac{l_i}{2}$$ ), known as Shafranov parameter, was obtained experimentally in terms of normal and tangential components of the magnetic field. Plasma internal inductance and poloidal beta were obtained using parametrization method based on analytical solution of Grad-Shafranov equation (GSE) and compared with parabolic-like profile of toroidal current density approach for determination of the plasma internal inductance. Finding evolution of $$\beta _p+\dfrac{l_i}{2}$$ and plasma internal inductance. Finding poloidal beta (Shafranov parameter and internal inductance) and using energy balance equation, thermal energy and energy confinement were determined qualitatively in terms of poloidal beta during a regular discharge of Damavand tokamak.

Modelling the Ohmic L-mode ramp-down phase of JET hybrid pulses using JETTO with Bohm–gyro-Bohm transport

The empirical Bohm–gyro-Bohm (BgB) transport model implemented in the JETTO code is used to predictively simulate the purely Ohmic (OH), L-mode current-ramp-down phase of three JET hybrid pulses, which combine two different ramp rates with two different electron densities (at the beginning of the ramp). The modelling is discussed, namely the strategy to reduce as much as possible the number of free parameters used to benchmark the model predictions against the experimental results. Hence, keeping the gas puffing rate as measured whilst controlling the line-averaged electron density via the recycling coefficient (which in the modelling is taken at the separatrix instead of the wall), one of the many possible ways to fix the total particle source, it is shown that the BgB model reproduces well the experimental data, as far as both average quantities (plasma internal inductance and volume-averaged electron temperature) and profiles (electron density and temperature) are concerned, with relative errors remaining mostly below . The sensitivenesses with respect to the recycling coefficient, the ion effective charge, the energy of neutrals entering the plasma through the separatrix and the need to introduce a particle pinch are assessed; the necessity for a proper sawtooth model if experimental results are to be reproduced is also shown. The strong non-linear coupling in a OH plasma between density, temperature and current (essentially via interplay between the power-balance equation, Joule’s heating with a temperature-dependent resistivity and the dependence of BgB transport coefficients on profile gradients) is put in evidence and analyzed in light of modelling results. It is still inferred from the modelling that the real value of the recycling coefficient at the separatrix (basically, the so-called fuelling efficiency times the actual recycling coefficient at the wall) must become close to one in the final stages of the discharges, when the gas puffing is switched off and so recycling comes to be the only source of particles. If the wall recycling remains close to one (as standard for tokamaks), this may indicate that the fuelling efficiency also approaches unity, apparently consistent with the observed fact that the plasma is pushed towards the machine wall at the end of the current ramps.

Effects of internal inductance on the energy confinement time by using the solution of equilibrium problem

In this work, dependence of energy confinement time on plasma internal inductance has been studied by using the solution of Grad–Shafranov equation (GSE) for circular cross-section HT-7 tokamak. For this, the Shafranov parameter (asymmetry factor) and poloidal beta were obtained from solution of GSE. Then we can find the dependence of energy confinement time, on plasma internal inductance. It is observed that the maximum energy confinement time is related to the low values of internal inductance [Formula: see text].

Magnetic measurement based methods in determination of plasma equilibrium parameters in Damavand tokamak

Determination of plasma equilibrium parameters such as poloidal beta (βp) with half of plasma internal inductance (li) known as Shafranov parameter (asymmetry factor) (βp+\U0001d521li2) and edge safety factor plays very important role in primary equilibrium and stability analysis and control of tokamak plasma. In this study, the well known Shafranov semi-empirical model, based on external magnetic measurements is used to extract Shafranov parameter and effective edge safety factor in low-β operating regime of Damavand tokamak. The well known integral representation of βp+\U0001d521li2 was modified for non-circular tokamaks with ellipse-like cross section. After calibration of magnetic pick-up coils, Shafranov parameter was estimated with respect to the first and second Fourier harmonic of radial and poloidal components of magnetic field. The results were compared with approximate, semi-analytical determination of Shafranov parameter which is based on analytical solution of Grad-Shafranov equation (GSE). Founding evolution of Shafranov parameter, effective edge safety factor was obtained in terms of Shafranov parameter and compared with semi-empirical description. It was found that between the ramp-up and ramp-down domain of the plasma current, the result from Shafranov model is approximately in good agreement with the semi-analytical and semi-empirical benchmarks and the integral model provides more reliable trace of the Shafranov parameter in out of ramp domains of the discharge.

Semi-analytic approach for determination of poloidal beta limits using plasma internal inductance in Damavand tokamak

The Grad–Shafranov equation plays a very important role in analysis of the plasma equilibrium in magnetic confinement configurations such as the tokamak. In tokamaks which are operating in Ohmic heating regime, the Grad–Shafranov equation can be expanded through the inverse aspect ratio parameter. Consequently, the first order of poloidal flux function and the poloidal/radial components of the magnetic field are obtained. In this study, by considering the effect of tokamak non-circularity, a semi-analytic model which is based on magnetic measurements was developed and highest and lowest values of plasma internal inductance and poloidal beta were estimated by means of the poloidal and radial magnetic field experimental data acquired from Damavand tokamak magnetic probes.

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.

Robustness and increased time resolution of JET Advanced Predictor of Disruptions

The impact of disruptions in JET is well-known not only with the carbon fiber composite (CFC) wall, but also with the metallic ITER-like wall (ILW). A disruption predictor, called APODIS, was developed and implemented for the JET real-time data network. This predictor uses seven plasma quantities (plasma current, mode lock amplitude, plasma internal inductance, plasma density, stored diamagnetic energy time derivative, radiated power and total input power) and it has been working during the ILW campaigns in JET. It has reached good results in terms of success rate, false alarm rate and prediction anticipation time. However, it is important to note that any signal could fail during any discharge. If an incorrect signal is used by APODIS, this can be an issue for the predictions. Therefore, the first purpose of this article is to determine the robustness of APODIS. Robustness is the predictor reliability when a signal fails. To determine the robustness, anomalous signals have been simulated and the quality of the APODIS predictions has been estimated. The results show that some signals, such as the mode lock and the plasma inductance, are essential for APODIS to provide a reasonable success rate. Under the failure of other signals, APODIS performance slightly decreases but remains acceptable. On the other hand, during the ILW campaigns, APODIS has missed some disruptions due to a lack of temporal resolution in the prediction. Owing to this reason, a second analysis has been carried out in this paper. The effect of increasing the prediction temporal resolution has been analyzed. The plasma signals are digitized at the same sampling frequency (1 ksample s−1) but a sliding window mechanism has been implemented to modify the prediction period from 32 to 1 ms.

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.

Soft real-time EPICS extensions for fast control: A case study applied to a TCV equilibrium algorithm

For new control systems development, ITER distributes CODAC Core System that is a software package based on Linux RedHat, and includes EPICS (Experimental Physics and Industrial Control System) as software control system solution. EPICS technology is being widely used for implementing control systems in research experiments and it is a very well tested technology, but presents important lacks to meet fast control requirements. To manage and process massive amounts of acquired data, EPICS requires additional functions such as: data block oriented transmissions, links with speed-optimized data buffers and synchronization mechanisms not based on system interruptions. This EPICS limitation turned out clearly during the development of the Fast Plant System Controller Prototype for ITER based on PXIe platform.In this work, we present a solution that, on the one hand, is completely compatible and based on EPCIS technology, and on the other hand, extends EPICS technology for implementing high performance fast control systems with soft-real time characteristics. This development includes components such as: data acquisition, processing, monitoring, data archiving, and data streaming (via network and shared memory). Additionally, it is important to remark that this system is compatible with multiple Graphics Processing Units (GPUs) and is able to integrate MatLab code through MatLab engine connections. It preserves EPICS modularity, enabling system modification or extension with a simple change of configuration, and finally it enables parallelization based on data distribution to different processing components.With the objective of illustrating the presented solution in an actual tokamak application, we have implemented fundamental tokamak equilibrium quantities such as plasma position, Shafranov shift or internal inductance. The algorithms have been parallelized and implemented for its execution on CPU, GPUs and Matlab, and have been tested using actual magnetic data from the TCV tokamak fast control system.

The effect of the electron temperature and current density profiles on the plasma current decay in JT-60U disruptions

The plasma current decay during the initial phase of the current quench in JT-60U disruption has been calculated by a disruption simulation code (DINA) using the measured electron temperature Te profile. In the case of fast plasma current decay, Te has a peaked profile immediately after a thermal quench and the Te profile does not change significantly during the initial phase of the current quench. On the other hand, in the case of a slow plasma current decay, the Te profile is broader immediately after the thermal quench, and the Te profile shrinks. The results of the DINA simulation show that the plasma internal inductance Li increases during the initial phase of the current quench, whereas the plasma external inductance Le does not change over time. If the plasma is represented by a simple electrical circuit, the time derivative of Li functions as a resistance on the plasma current decay. It was confirmed that the increase in Li is caused by current diffusion toward the core plasma due to the decrease in Te in the intermediate and edge regions.

Investigation of MHD instabilities and control in KSTAR preparing for high beta operation

Initial H-mode operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) is expanded to higher normalized beta and lower plasma internal inductance moving towards design target operation. As a key supporting device for ITER, an important goal for KSTAR is to produce physics understanding of MHD instabilities at long pulse with steady-state profiles, at high normalized beta, and over a wide range of plasma rotation profiles. An advance from initial plasma operation is a significant increase in plasma stored energy and normalized beta, with Wtot = 340 kJ, βN = 1.9, which is 75% of the level required to reach the computed ideal n = 1 no-wall stability limit. The internal inductance was lowered to 0.9 at sustained H-mode duration up to 5 s. In ohmically heated plasmas, the plasma current reached 1 MA with prolonged pulse length up to 12 s. Rotating MHD modes are observed in the device with perturbations having tearing rather than ideal parity. Modes with m/n = 3/2 are triggered during the H-mode phase but are relatively weak and do not substantially reduce Wtot. In contrast, 2/1 modes to date only appear when the plasma rotation profiles are lowered after H–L back-transition. Subsequent 2/1 mode locking creates a repetitive collapse of βN by more than 50%. Onset behaviour suggests the 3/2 mode is close to being neoclassically unstable. A correlation between the 2/1 mode amplitude and local rotation shear from an x-ray imaging crystal spectrometer suggests that the rotation shear at the mode rational surface is stabilizing. As a method to access the ITER-relevant low plasma rotation regime, plasma rotation alteration by n = 1, 2 applied fields and associated neoclassical toroidal viscosity (NTV) induced torque is presently investigated. The net rotation profile change measured by a charge exchange recombination diagnostic with proper compensation of plasma boundary movement shows initial evidence of non-resonant rotation damping by the n = 1, 2 applied field configurations. The result addresses perspective on access to low rotation regimes for MHD instability studies applicable to ITER. Computation of active RWM control using the VALEN-3D code examines control performance using midplane locked mode detection sensors. The LM sensors are found to be strongly affected by mode and control coil-induced vessel current, and consequently lead to limited control performance theoretically.

Approximate Methods for the Calculation of Plasma Internal Inductance for Circular Cross Section Tokamak

Calculation of Plasma internal inductance (li) is essential in Tokamak plasma research. Much more plasma parameters such as the plasma current density profile, magnetohydrodynamics instability, and plasma energy confinement time can be determined by using this parameter. Discrete poloidal magnetic probes along with the diamagnetic loop can be utilized in measurement of the Plasma internal inductance (li). In this paper Plasma internal inductance (li) is studied by theoretical and experimental approach for HT-7 Tokamak plasmas. The results of two methods are in good agreement with each other.

Development and validation of a tokamak skin effect transformer model

A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non-linear interaction of plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as a function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with random binary signals have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated under ohmic conditions between 200 and 300 kA with 30 ms rise time, several times faster than its time constant L/R ≈ 200 ms. A second-order linear differential equation for equilibrium loop voltage is sufficient to describe the plasma current and internal inductance modulation with 70% and 38% fit parameters, respectively. The model explains the most salient features of the plasma current transients, such as the inverse correlation between plasma current ramp rates and internal inductance changes, without requiring detailed or explicit information about resistivity profiles. This proves that a lumped parameter modelling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least under ohmic conditions without external heating and current drive sources.

Plasma internal inductance dynamics in a tokamak

A lumped parameter model for tokamak plasma current and inductance time evolution as a function of plasma resistance, non-inductive current drive sources and boundary voltage or poloidal field coil current drive is presented. The model includes a novel formulation leading to exact equations for internal inductance and plasma current dynamics. Having in mind its application in a tokamak inductive control system, the model is expressed in state space form, the preferred choice for the design of control systems using modern control systems theory. The choice of system states allows many interesting physical quantities such as plasma current, inductance, magnetic energy, and resistive and inductive fluxes be made available as output equations.The model is derived from energy conservation theorem, and flux balance theorems, together with a first order approximation for flux diffusion dynamics. The validity of this approximation has been checked using experimental data from JET showing an excellent agreement.

Equilibrium and global MHD stability study of KSTAR high beta plasmas under passive and active mode control

The Korea Superconducting Tokamak Advanced Research, KSTAR, is designed to operate a steady-state, high beta plasma while retaining global magnetohydrodynamic (MHD) stability to establish the scientific and technological basis of an economically attractive fusion reactor. An equilibrium model is established for stability analysis of KSTAR. Reconstructions were performed for the experimental start-up scenario and experimental first plasma operation using the EFIT code. The VALEN code was used to determine the vacuum vessel current distribution. Theoretical high beta equilibria spanning the expected operational range are computed for various profiles including generic L-mode and DIII-D experimental H-mode pressure profiles. Ideal MHD stability calculations of toroidal mode number of unity using the DCON code shows a factor of 2 improvement in the wall-stabilized plasma beta limit at moderate to low plasma internal inductance. The planned stabilization system in KSTAR comprises passive stabilizing plates and actively cooled in-vessel control coils (IVCCs) designed for non-axisymmetric field error correction and stabilization of slow timescale MHD modes including resistive wall modes (RWMs). VALEN analysis using standard proportional gain shows that active stabilization near the ideal wall limit can be reached with feedback using the midplane segment of the IVCC. The RMS power required for control using both white noise and noise taken from NSTX active stabilization experiments is computed for beta near the ideal wall limit. Advanced state-space control algorithms yield a factor of 2 power reduction assuming white noise while remaining robust with respect to variations in plasma beta.

Compatibility of ITER scenarios with full tungsten wall in ASDEX Upgrade

The transition of ASDEX Upgrade (AUG) from a graphite device to a full tungsten device is demonstrated with a reduction by an order of magnitude in both the carbon deposition and deuterium retention. The tungsten source is dominated by sputtering from intrinsic light impurities, and the tungsten influxes from the outboard limiters are the main source for the plasma. In H-mode discharges, central heating (neutral beams, ECRH) is used to increase turbulent outward transport avoiding tungsten accumulation. ICRH can only be used after boronization as its application otherwise results in large W influxes due to light impurities accelerated by electrical fields at the ICRH antennas. ELMs are important in reducing the inward transport of tungsten in the H-mode edge barrier and are controlled by gas puffing. Even without boronization, stationary, ITER baseline H-modes (confinement enhancement factor from ITER 98(y, 2) scaling H98 ∼ 1, normalized beta βN ∼ 2), with W concentrations below 3 × 10−5 were routinely achieved up to 1.2 MA plasma current.The compatibility of high performance improved H-modes with unboronized W wall was demonstrated, achieving H98 = 1.1 and βN up to 2.6 at modest triangularities δ ⩽ 0.3 as required for advanced scenarios in ITER. With boronization the light impurities and the radiated power fraction especially in the divertor were reduced and the divertor plasma was actively cooled by N2 seeding. N2 seeding does not only protect the divertor tiles but also considerably improves the performance of improved H-mode discharges. The energy confinement increased to H98-factors of 1.25 (βN ∼ 2.7) and thereby exceeded the best values in a carbon-dominated AUG machine under similar conditions. Recent investigations show that this improvement is due to higher temperatures rather than to peaking of the electron density profile.Further ITER discharge scenario tests include the demonstration of ECRF assisted low voltage plasma start-up and current rise to q95 = 3 at toroidal electric fields below 0.3 V m−1, to achieve a ITER compatible range of plasma internal inductance of 0.71–0.97. The results reported here strongly support tungsten as a first wall material solution.

RETRACTED ARTICLE: Determination of the Plasma Internal Inductance and Evaluation of its Effects on Plasma Horizontal Displacement in IR-T1 Tokamak

In this paper we presented comparison between two techniques in order to investigate the effects of the plasma internal inductance on plasma horizontal displacement in IR-T1 tokamak. For this purpose, a diamagnetic loop with its compensation coil, and also an array of magnetic probes were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber, and then the poloidal beta and poloidal and radial magnetic fields measured. Moreover, a few approximate values of the internal inductance for different possible profiles of the plasma current density are also calculated. Then, the Shafranov parameter and also the plasma horizontal displacement were determined. Experimental results compared. Comparing of the results on IR-T1, show that (1) by increasing the internal inductance from one, plasma column shifted inward, and also (2) IR-T1 plasma current density profile relate to the power of υ = 3.