Edge Current Density Research Articles

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.

Characterization of peeling modes in a low aspect ratio tokamak

Peeling modes are observed at the plasma edge in the Pegasus Toroidal Experiment under conditions of high edge current density (Jedge ∼ 0.1 MA m−2) and low magnetic field (B ∼ 0.1 T) present at near-unity aspect ratio. Their macroscopic properties are measured using external Mirnov coil arrays, Langmuir probes and high-speed visible imaging. The modest edge parameters and short pulse lengths of Pegasus discharges permit direct measurement of the internal magnetic field structure with an insertable array of Hall-effect sensors, providing the current profile and its temporal evolution. Peeling modes generate coherent, edge-localized electromagnetic activity with low toroidal mode numbers n ⩽ 3 and high poloidal mode numbers, in agreement with theoretical expectations of a low-n external kink structure. Coherent MHD fluctuation amplitudes are found to be strongly dependent on the experimentally measured Jedge/B peeling instability drive, consistent with theory. Peeling modes nonlinearly generate ELM-like, field-aligned filamentary structures that detach from the edge and propagate radially outward. The KFIT equilibrium code is extended with an Akima spline profile parameterization and an improved model for induced toroidal wall current estimation to obtain a reconstruction during peeling activity with its current profile constrained by internal Hall measurements. It is used to test the analytic peeling stability criterion and numerically evaluate ideal MHD stability. Both approaches predict instability, in agreement with experiment, with the latter identifying an unstable external kink.

Linear calculations of edge current driven kink modes with BOUT++ code

This work extends previous BOUT++ work to systematically study the impact of edge current density on edge localized modes, and to benchmark with the GATO and ELITE codes. Using the CORSICA code, a set of equilibria was generated with different edge current densities by keeping total current and pressure profile fixed. Based on these equilibria, the effects of the edge current density on the MHD instabilities were studied with the 3-field BOUT++ code. For the linear calculations, with increasing edge current density, the dominant modes are changed from intermediate-n and high-n ballooning modes to low-n kink modes, and the linear growth rate becomes smaller. The edge current provides stabilizing effects on ballooning modes due to the increase of local shear at the outer mid-plane with the edge current. For edge kink modes, however, the edge current does not always provide a destabilizing effect; with increasing edge current, the linear growth rate first increases, and then decreases. In benchmark calculations for BOUT++ against the linear results with the GATO and ELITE codes, the vacuum model has important effects on the edge kink mode calculations. By setting a realistic density profile and Spitzer resistivity profile in the vacuum region, the resistivity was found to have a destabilizing effect on both the kink mode and on the ballooning mode. With diamagnetic effects included, the intermediate-n and high-n ballooning modes can be totally stabilized for finite edge current density.

Toroidicity and shape dependence of peeling mode growth rates in axisymmetric toroidal plasmas

The growth rate of the peeling mode instability with large toroidal mode number is calculated for general axisymmetric toroidal plasmas, including tokamaks and the spherical torus (ST) equilibia by using formalism presented by Connor et al. Analytic equilibia with non-zero edge current density and quasi-uniform current profiles are assumed. It is found that in sharp D-shape tokamak plasma, the derivative of the safety factor with respect to the poloidal flux becomes very large, making the perturbed poloidal motion very large, in turn making a significant reduction of the growth rate of the peeling mode, similar to the X-point effect in diverted plasma. The large aspect ratio effect is also studied, which reduces the growth rate further.

Impact of plasma response on plasma displacements in DIII-D during application of external 3D perturbations

The effects of applied 3D resonant magnetic perturbations are modelled with and without self-consistent plasma response. The plasma response is calculated using a linear two-fluid model. A synthetic diagnostic is used to simulate soft x-ray (SXR) emission within the steep gradient region of the pedestal, 0.98 > ψ > 0.94. Two methods for simulating the SXR emission given the perturbed fields are considered. In the first method, the emission is assumed to be constant on magnetic field lines, with the emission on each line determined by the penetration depth into the plasma. In the second method, the emission is taken to be a function of the perturbed electron temperature and density calculated by the two-fluid model. It is shown that the latter method is more accurate within the plasma, but is inadequate in the scrape-off layer due to the breakdown of the linearized temperature equation in the two-fluid model. The resulting synthetic emission is compared to measured SXR data, which show helical m = 11 ± 1 displacements around the 11/3 rational surface of sizes up to 5 cm, depending on the poloidal angle. The helical displacements around the 11/3 surface are identified to be directly related to the kink response, caused by amplification of non-resonant components of the magnetic field due to plasma response. The role of different plasma parameters is investigated, but it appears that the electron rotation plays a key role in the formation of screening and resonant amplification, while the kinking appears to be sensitive to the edge current density. It is also hypothesized that the plasma response affects the edge-localized-mode (ELM) stability, i.e. the discharge's operational point relative to the peeling–ballooning stability boundary.

Influence of plasma diagnostics and constraints on the quality of equilibrium reconstructions on Joint European Torus

One of the main approaches to thermonuclear fusion relies on confining high temperature plasmas with properly shaped magnetic fields. The determination of the magnetic topology is, therefore, essential for controlling the experiments and for achieving the required performance. In Tokamaks, the reconstruction of the fields is typically formulated as a free boundary equilibrium problem, described by the Grad-Shafranov equation in toroidal geometry and axisymmetric configurations. Unfortunately, this results in mathematically very ill posed problems and, therefore, the quality of the equilibrium reconstructions depends sensitively on the measurements used as inputs and on the imposed constraints. In this paper, it is shown how the different diagnostics (Magnetics Measurements, Polarimetry and Motional Stark Effect), together with the edge current density and plasma pressure constraints, can have a significant impact on the quality of the equilibrium on JET. Results show that both the Polarimetry and Motional Stark Effect internal diagnostics are crucial in order to obtain reasonable safety factor profiles. The impact of the edge current density constraint is significant when the plasma is in the H-mode of confinement. In this plasma scenario the strike point positions and the plasma last closed flux surface can change even by centimetres, depending on the edge constraints, with a significant impact on the remapping of the equilibrium-dependent diagnostics and of pedestal physics studies. On the other hand and quite counter intuitively, the pressure constraint can severely affect the quality of the magnetic reconstructions in the core. These trends have been verified with several JET discharges and consistent results have been found. An interpretation of these results, as interplay between degrees of freedom and available measurements, is provided. The systematic analysis described in the paper emphasizes the importance of having sufficient diagnostic inputs and of properly validating the results of the codes with independent measurements.

MHD stability of the pedestal in ITER scenarios

The linear ideal magnetohydrodynamic (MHD) limits of the pedestal in ITER scenarios associated with the preparation and realization of the nominal fusion gain Q = 10 (inductive scenario at 15 MA/5.3 T, half-field/half-current and intermediate H-mode scenario at 10 MA/3.5 T), as well as the hybrid scenario at 12 MA/5.3 T, are investigated in this work. The accessible part of the MHD stability diagram is determined by computing the bootstrap current and self-consistently evaluating the corresponding pedestal current. This procedure shows that only a small part of peeling–ballooning diagrams is physically accessible. Uncertainties about the foreseen plasma profiles motivate studies evaluating the impact of various parameters on the pedestal limits. We have addressed issues such as the pedestal width, the global performance, pressure peaking, edge current density, internal inductance and plasma shaping. A scaling law for the maximum pedestal pressure in the ITER scenarios is proposed, highlighting that the main dependences are on the plasma current, the edge safety factor, the pedestal width and the internal inductance.

Fabrication of microprism mould by electroforming with high electrolyte flowrate

Electroforming is applied to fabricate microprism moulds, however only low working current density is employed because the higher current density at the edge limits the usable value of the working current density. Reduction of current density at the edge is a key in the enhancement of the working current density. In this paper, a secondary cathode was introduced to lower the edge current density. By this technique, the edge current density of the primary cathode surface is not only weakened obviously but can be even lower than that of the others. In addition, a high electrolyte flow rate has been introduced to improve working current density. Experimental results show that both the microhardness and tensile strength of the electroformed layer increase with electrolyte flowrate. By using both secondary cathode and high speed electrolyte flow, the electroforming time could be reduced significantly and mechanical properties of the electroformed layer are not adversely affected in electroforming of microprism moulds.

Measurement of neoclassically predicted edge current density at ASDEX Upgrade

Experimental confirmation of neoclassically predicted edge current density in an ELMy H-mode plasma is presented. Current density analysis using the CLISTE equilibrium code is outlined and the rationale for accuracy of the reconstructions is explained. Sample profiles and time traces from analysis of data at ASDEX Upgrade are presented. A high time resolution is possible due to the use of an ELM-synchronization technique. Additionally, the flux-surface-averaged current density is calculated using a neoclassical approach. Results from these two separate methods are then compared and are found to validate the theoretical formula. Finally, several discharges are compared as part of a fuelling study, showing that the size and width of the edge current density peak at the low-field side can be explained by the electron density and temperature drives and their respective collisionality modifications.

Modelling of edge localized modes with a current relaxation model on JET and TEXTOR

The mitigation of edge localized modes (ELMs) has been investigated using external resonant magnetic perturbations (RMPs) on JET. An interesting observation encountered is the formation of resonant structures in the dependence of ELM frequency on the edge safety factor. Using a theory based on an extended Taylor relaxation process, initialized by an external peeling mode, this behaviour is modelled and analysed leading to a prediction of a condition that a low edge current density is required for the resonant nature to be observed. This model is outlined and the results compared with recent experimental observations from JET.The TEXTOR tokamak already has a low edge current density due to its limiter configuration and so is predicted to show the resonant behaviour even without the RMP fields being applied. Similar experiments investigating the effect of the edge safety factor on the ELM frequency are conducted on TEXTOR to validate this prediction. It was found from the model that a case with a low normalized edge current density of 0.01 shows good agreement with observations. For such a case the multi-resonance effect is less well defined than observed on JET due to the appearance of highly detailed structure in the model predictions.

Stabilizing effects of edge current density on pedestal instabilities

Resistive MHD computations using the NIMROD code have found strong dependence of the low-n edge localized instabilities on edge current density distribution. The computations confirm that the low-n edge localized modes can be driven unstable by increasing the edge current density. When the edge peaked current density is sufficiently large, the q profile develops a region where the magnetic shear becomes negative. In these cases, the low-n edge instabilities are partially or fully stabilized. The stabilizing effects of edge current density in regions with reversed magnetic shear appear to be consistent with analytical predictions on a necessary condition for the stability of peeling modes. Nonlinear simulations indicate that the stabilizing effects of edge current density on the low-n edge instabilities through reverse shear can persist throughout the nonlinear exponential growth phase. Near the end of this nonlinear phase, the filament size in radial direction can exceed the pedestal width, and disconnected blob-like substructures start to develop within the filaments. Relative pedestal energy loss from these radially extending filaments can reach above the average experimental level of 10%.

Measurements of the edge current evolution and comparison with neoclassical calculations during MAST H-modes using motional Stark effect

Edge localized modes (ELMs), that are present in most tokamak H- (high confinement) modes, can cause significant damage to plasma facing components in fusion reactors. Controlling ELMs is considered necessary and hence it is vital to understand the underlying physics. The stability of ELMs is typically expressed in terms of the pressure gradient ∇p in the edge and the edge current density jϕ. Both ∇p and jϕ are usually derived from profiles fitted to the measured edge density and temperature profiles, where for the calculation of jϕ neoclassical theory is used.This paper presents direct measurements of the magnetic pitch angle γm evolution in the edge and the derived jϕ. These provide a method to validate the jϕ as derived with neoclassical theory and they open up the possibility to find a complete, self-consistent set of edge profiles, that fit density, temperature and γm measurements, hence allowing for a more accurate stability analysis.

Overview of physics results from MAST

Major developments on the Mega Amp Spherical Tokamak (MAST) have enabled important advances in support of ITER and the physics basis of a spherical tokamak (ST) based component test facility (CTF), as well as providing new insight into underlying tokamak physics. For example, L–H transition studies benefit from high spatial and temporal resolution measurements of pedestal profile evolution (temperature, density and radial electric field) and in support of pedestal stability studies the edge current density profile has been inferred from motional Stark effect measurements. The influence of the q-profile and E × B flow shear on transport has been studied in MAST and equilibrium flow shear has been included in gyro-kinetic codes, improving comparisons with the experimental data. H-modes exhibit a weaker q and stronger collisionality dependence of heat diffusivity than implied by IPB98(y,2) scaling, which may have important implications for the design of an ST-based CTF. ELM mitigation, an important issue for ITER, has been demonstrated by applying resonant magnetic perturbations (RMPs) using both internal and external coils, but full stabilization of type-I ELMs has not been observed. Modelling shows the importance of including the plasma response to the RMP fields. MAST plasmas with q > 1 and weak central magnetic shear regularly exhibit a long-lived saturated ideal internal mode. Measured plasma braking in the presence of this mode compares well with neo-classical toroidal viscosity theory. In support of basic physics understanding, high resolution Thomson scattering measurements are providing new insight into sawtooth crash dynamics and neo-classical tearing mode critical island widths. Retarding field analyser measurements show elevated ion temperatures in the scrape-off layer of L-mode plasmas and, in the presence of type-I ELMs, ions with energy greater than 500 eV are detected 20 cm outside the separatrix. Disruption mitigation by massive gas injection has reduced divertor heat loads by up to 70%.

Measurement of Peeling Mode Edge Current Profile Dynamics

Peeling modes, an instability mechanism underlying deleterious edge localized mode (ELM) activity in fusion-grade plasmas, are observed at the edge of limited plasmas in a low aspect ratio tokamak under conditions of high edge current density (J(edge) ∼ 0.1 MA/m2) and low magnetic field (B ∼ 0.1 T). They generate edge-localized, electromagnetic activity with low toroidal mode numbers n≤3 and amplitudes that scale strongly with measured J(edge)/B instability drive, consistent with theory. ELM-like field-aligned, current-carrying filaments form from an initial current-hole J(edge) perturbation that detach and propagate outward.

Observations of multi-resonance effect in ELM control with magnetic perturbation fields on the JET tokamak

Multiple resonances of the edge-localized mode (ELM) frequency caused by the application of low n (=1 or 2) magnetic perturbations for ELM control have been observed on JET. With a low n field applied, a strong increase in ELM frequency, fELM, by a factor of ∼4.5 was found in many separated narrow windows of q95 (resonant q95), while the fELM increased only by a factor of ∼2 for non-resonant q95 values. The fractions of increase in fELM with different resonant q95 values are not the same. An analysis of ideal external peeling modes shows that both the dominant unstable peeling mode number and fELM depend on the amplitude of the normalized edge current density as well as the edge safety factor, qa.

Dependence of pedestal performance on the characteristics of the H-mode pedestal**http://iopscience.iop.org/0029-5515/50/6

Given the small level of residual transport within the edge pedestal of H-mode tokamak plasmas, even low levels of additional transport within this region (e.g. due to ripple losses of thermal ions or edge ergodization) can have a significant effect on pedestal performance. Such additional transport will affect the shape of the plasma profiles within the pedestal. In this paper, the dependence of the sustainable level of pedestal pressure gradient and toroidal edge current density on the pedestal plasma profile shapes is systematically studied by means of ideal linear magnetohydrodynamic stability analysis. It is concluded that the further inside the separatrix the maximum pressure gradient is reached, the larger the level of pressure gradient that the plasma can sustain is. It is also found that the further inside the separatrix the pressure gradient maximum is located, the wider the eigenfunctions of the unstable modes are and the smaller the toroidal mode number of the most unstable mode is.

Zeeman polarimetry measurement for edge current density determination using Li-beam probe on JT-60U

Zeeman polarimetry system using Li-beam probe has been developed for the edge current density measurement in the JT-60U tokamak, which measures the polarization angle alpha (related to the pitch angle of the magnetic field) by means of photoelastic modulators, etalons, and phase sensitive detection using digital lock-in amplifiers with the accuracy in the alpha of Delta alpha approximately 0.1 degrees. The diagnostic has 20-channel viewing chords covering the plasma peripheral region of normalized minor radius r/a approximately 0.8-1 with a spatial resolution of up to approximately 1 cm. Li-beam injection with beam current of up to approximately 5 mA has been achieved. A new tuning method of the wavelength for the etalon has been demonstrated, scanning the beam acceleration voltage and keeping a beam current constant during a single shot. The peak wavelength of the etalon is adjusted in the direction to both blue- and redshifts by changing the angle of incidence and increasing the temperature, respectively. Time evolution of the edge current density profile has been determined for the current ramp experiment in the Ohmically heated discharges. In addition, the edge current density profile with the local peak of j(ped) approximately 0.15-0.25 MA/m(2) at r/a approximately 0.9 has been identified in the H-mode plasma, which is correlated with large pressure gradient in the pedestal region.

The role of edge current-driven modes in ELM activity

We propose a model for edge localized mode (ELM) evolution which goes beyond linear stability arguments by hypothesizing that peeling modes initiate a Taylor relaxation (a constrained minimization of the magnetic energy) of an outer annular plasma region. The relaxation has two effects on peeling mode stability: (a) As the relaxation process proceeds radially inwards it leaves in its wake a Taylor state, which for conventional tokamak ordering is simply a flattened equilibrium toroidal current density. This effect acting in isolation would provide a destabilizing effect (for conventional current profiles the edge current density would increase); (b) The formation of a (negative for conventional current profiles) skin current at the plasma–vacuum interface which has a counteracting stabilizing effect on peeling modes. For a finite relaxed annulus, these two opposing effects can balance and give a configuration that is stable to all possible peeling instabilities. The radial extent of the relaxed region required for stability can be calculated using this balance. This then leads to model predictions for ELM characteristics such as the widths and mode numbers, the magnitude of the attendant energy losses and the natural (deterministic) scatter in these quantities. We compare these model predictions with a number of experimentally observed ELM properties. Further, expanding the governing equations gives analytic expressions for ELM widths in terms of localized edge parameters. Peeling modes can occur even when the critical pressure gradient for the onset of ballooning modes has not been reached. For this reason ‘type III’ ELMs, which typically occur just above the threshold for L–H transitions, may be best described by this model.

The effect of plasma collisionality on pedestal current density formation in DIII-D

The evolution and performance limits for the pedestal in H-mode are dependent on the two main drive terms for instability: namely the edge pressure gradient and the edge current density. These terms are naturally coupled though neoclassical (Pfirsch–Schluter and bootstrap) effects. On DIII-D, local measurements of the edge current density are made using an injected lithium beam in conjunction with Zeeman polarimetry and compared with pressure profile measurements made with other diagnostics. These measurements have confirmed the close spatial and temporal correlation that exists between the measured current density and the edge pressure in H- and QH-mode pedestals, where substantial pressure gradients exist. In the present work we examine the changes in the measured edge current for DIII-D pedestals which have a range of values for the ion and electron collisionalities {} due to fuelling effects. Such changes in the collisionality in the edge are expected to significantly alter the level of the bootstrap current from the value predicted from the collisionless limit and therefore should correspondingly alter the pedestal stability limits. We find a clear decrease in measured current as ν increases, even for discharges having similar edge pressure gradients.

Current Profile Measurement on the DIII-D Tokamak

The measurement of the plasma current profile is crucial to many operating regimes and investigations on the DIII-D tokamak. The measurement is required to obtain accurate equilibria and to accurately calculate stability and transport characteristics of the plasma. The measurement of the profile is also required to obtain the different components of the current to guide efforts on the control of the current profile and experiments toward obtaining steady-state operating regimes. The edge current profile measurement is necessary to understand the formation of edge pedestal and edge-localized modes. The DIII-D tokamak has a three-array, 45-channel motional Stark effect (MSE) diagnostic to measure the plasma current density and radial electric field. A 32-channel lithium-beam (Li-beam) diagnostic has recently been installed on the DIII-D tokamak for the measurement of edge current density. Both diagnostics measure the current profile from the measurement of the pitch angle of the magnetic field that, in turn, is derived from the orientation angle of polarization of the appropriate neutral beam spectral line. The MSE and the Li-beam diagnostics are described, and some examples of measurements are shown.