Low-order Rational Surfaces Research Articles

Suppression of equilibrium magnetic islands by density profile effect in quasi-axisymmetric stellarator plasmas

In a quasi-axisymmetric stellarator, a significant bootstrap current will result in the generation of low-order rational surfaces and three-dimensional (3D) magnetic islands. In this paper, the influence of plasma density profiles on the equilibrium magnetic islands for the Chinese first quasi-axisymmetric stellarator (CFQS) is investigated using the HINT code. It is found that the flattening of the core plasma density profile leads to a significant suppression of magnetic islands. When the peaking factor of plasma density is 1.19, complete suppression of magnetic islands occurs while maintaining excellent integrity of the magnetic surface even with the volume-averaged plasma beta <β> increase up to 2%. On the other hand, during the transition of a plasma density profile from flat to hollow, there is a reversal in the core bootstrap current, resulting in reduction of rotational transform values to pass through the rational surface. Hence, formation of magnetic islands in the core region. Therefore, effective inhibition of CFQS’s magnetic islands can be achieved by appropriately controlling density profiles through methods like gas injection.

Experimental study of core MHD behavior and a novel algorithm for rational surface detection based on profile reflectometry in EAST

Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER, so understanding the influence of plasma perturbations on the reflect signal is important. The characteristics of the reflect signal from profile reflectometry, the time-of-flight (TOF) signal associated with the MHD instabilities, are investigated in EAST. Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain (FDTD) method, it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude. Experimental TOF signals under different types of MHD instabilities (sawtooth, sawtooth precursors and tearing mode) are studied in detail and show agreement with the simulation. Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface, the cross-correlation and gradient threshold (CGT) method and the 2D convolutional neural network approach (CNN) are presented for the first time. It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control, which will be beneficial for the advanced tokamak operation.

The effect of pellet injection on turbulent transport in TJ-II

An improvement in confinement associated with the injection of pellets has been observed in TJ-II and other devices. By means of a simple model, we study here the modification of turbulent transport by the injection of pellets in TJ-II and how this modification affects the particle confinement time. The analysis of the results shows the relationship of the confinement improvement with the evolution of the shear flow due to turbulence, especially near low order rational surfaces. This work is based on pellet injections into the neutral beam injection heated phase of TJ-II plasmas. For this, single, double, or triple hydrogen pellet injection are considered and the post-injection evolution of selected plasma parameters are analyzed and compared.

Rational surfaces, flows and radial structure in the TJ-II stellarator

In this work, we report on the results obtained by measuring several turbulent quantities well inside the plasma edge by means of a Langmuir probe during dynamical rotational transform scans in the TJ-II stellarator, while applying a radial electric field to the edge plasma using a biasing probe. By calculating the intermittence parameter from floating potential measurements, we are able to identify a major low order rational surface and hence relate the probe measurements to the local value of the rotational transform. Based on the former, we are able to show that the poloidal plasma velocity (and hence radial electric field) has a significant radial structure that is clearly related to the rotational transform profile and in particular the lowest order rational surfaces in the range studied. The poloidal velocity is also affected by the edge biasing. The particle flux Γ was also found to exhibit a radial pattern, as did the flow shear suppression term , but the relation of the former to the low-order rational surfaces was less clear. We surmise that this lack of direct correspondence is due to an unknown term in the turbulence evolution equation: the instability growth rate, γ. We make use of a reduced Magnetohydrodynamic turbulence model to interpret the results. Overall, a picture is obtained in which the plasma self-organizes towards a state with a clear radial pattern of the radial electric field, in line with expectations from some numerical studies describing the spontaneous formation of an ‘E × B staircase’, consisting of alternating layers with fast and slow radial transport. In this state, the radial profiles of various quantities (density, temperature, pressure) will not be smooth.

Role of secondary long wavelength fluctuation in nonlinear saturation of the kinetic ballooning mode in tokamak plasmas

Nonlinear saturation dynamics of electromagnetic turbulence and associated transport are investigated using a global simulation based on the Landau-fluid model in the finite β tokamak plasmas. The focus is on the kinetic ballooning mode (KBM), while a comparison to the β stabilized ion temperature gradient mode is carried out. Results show that the KBM turbulence creates relatively weaker zonal flows in finite β plasmas. Zonal current could be formed around the low order rational surfaces, but is too narrow and localized to affect the global transport level. It is found that the KBM turbulence is nonlinearly saturated in two sequential stages. The linear KBM instability is first saturated transiently at a low fluctuation level by weak zonal flows. Afterward, robust, linearly stable long wavelength fluctuations are nonlinearly excited and then interact feedback with primary unstable KBM components through the modulation process. As a result, the KBM is finally saturated with a down-shifted wavenumber spectrum. The suppression of turbulent transport by long wavelength fluctuations is identified as mainly resulting from the reduction of KBM turbulence intensity.

The impact of radial electric fields and plasma rotation on intermittence in TJ-II

This work explores the impact of an imposed radial electric field on the intermittence parameter in magnetically confined plasmas. The intermittence is sensitive to both the magnetic configuration (dominant helical modes or low order rational surfaces) and to poloidal flows or radial electric fields. This behaviour was verified both in numerical turbulence calculations using a resistive magnetohydrodynamic model, and using Langmuir probe data obtained in experiments at the TJ-II stellarator. It is shown that the intermittence parameter can be used to detect when the local plasma rotation velocity, with respect to the laboratory frame of reference, is minimum.

Topology of 2D turbulent structures based on intermittence in the TJ-II stellarator

This work estimates the degree of turbulent intermittence of the plasma potential measured by a heavy ion beam probe in the core plasma region of the TJ-II stellarator. It is shown that the intermittence varies in a significant way with the plasma state (ion or electron root). In addition, radial minima of the intermittence are found to be associated with the location of topological structures of the flow associated with some important low-order rational surfaces. The local pressure gradient was also estimated, and a clear correlation was found between the steepening of the pressure gradient and the deepening of the minima of the intermittence, suggesting that the minima are associated with pressure gradient driven modes. By estimating the rotation velocity of the plasma from the measured plasma potential, it was possible to make a rough reconstruction of the two-dimensional radial–poloidal map of intermittence, thus clarifying the topological structure of the intermittence. The experimental results were put into context by comparing with simulations performed using a resistive magneto-hydrodynamic turbulence model.

Islands and current singularities in quasisymmetric toroidal plasmas

The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch–Schlüter singularities, to leading order, to a single magnetic surface resonant with the helicity of the symmetry. The effects of pressure driven currents are analyzed, indicating that exclusion of this surface from the plasma volume reduces the potential opening of islands but does not generally eliminate them completely due to higher order asymmetric geometric effects. These three-dimensional effects are contained in quasisymmetry and indicate the complexity of finding consistent solutions and their potential sensitivity. The δ-function current singularities show a distinct quasisymmetric behavior only when the higher-order Fourier content of B is relevant for the resistive stability parameter DR (not included in leading-order near-axis expansions). In such scenarios, quasisymmetry proves advantageous, both in simplicity and avoidance of amplification by low-order rational surfaces.

The interpretation of magnetic activity associated with pellet injections into plasmas created in the stellarator TJ-II

Pellet injection into magnetic confinement plasma is widely employed for plasma fuelling and impurity transport studies. While post-injection effects include changes in density and temperature, several short-lived effects have been identified during and immediately after pellet ablation, e.g. pre-cooling of the plasma core or a strong reduction in fluctuations. Here, transitory effects observed in magnetic signals during and immediately after the injection of fuel and tracer encapsulated solid pellets into microwave and neutral beam heated plasma in the stellarator TJ-II are reported. One effect is the excitation of a clear, short-lived, magnetic instability during the ablation phase of a cryogenic pellet. Another effect is a brief reduction in broadband magnetic fluctuations immediately after an injection while a third effect is frequency jumps of already excited Alfvén eigenmodes (AE) when neutral beam heating is employed. The interpretation of these effects is facilitated by signals from 2 recently installed toroidal arrays of magnetic coils that follow the helicity of this device along one of its quadrants. It is concluded that interactions between outward drifting pellet particles and a low-order rational surface lead to the magnetic instability, that pellet-induced plasma cooling induces a transitory reduction in broadband magnetic fluctuations and that plasma mass density changes dominate jumps in AE frequencies.

Radiation asymmetry and MHD destabilization during the thermal quench after impurity shattered pellet injection

The radiation response and the MHD destabilization during the thermal quench after a mixed species shattered pellet injection with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the n = 0 global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The thermal quench (TQ) is triggered as the fragments arrive on the q = 1 or q = 2 surface depending on the exact q profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than 1 ms. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases.

How eigenmode self-interaction affects zonal flows and convergence of tokamak core turbulence with toroidal system size

Self-interaction is the process by which a microinstability eigenmode that is extended along the direction parallel to the magnetic field interacts non-linearly with itself. This effect is particularly significant in gyrokinetic simulations accounting for kinetic passing electron dynamics and is known to generate stationary $E\times B$ zonal flow shear layers at radial locations near low-order mode rational surfaces (Weikl et al. Phys. Plasmas, vol. 25, 2018, 072305). We find that self-interaction, in fact, plays a very significant role in also generating fluctuating zonal flows, which is critical to regulating turbulent transport throughout the radial extent. Unlike the usual picture of zonal flow drive in which microinstability eigenmodes coherently amplify the flow via modulational instabilities, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. It is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds to an increase in the toroidal system size, leading to a finite system size effect that is distinct from the well-known profile shearing effect.

The localization of low order rational surfaces based on the intermittence parameter in the TJ-II stellarator

This work intends to show that the multifractal concept of intermittence can be fruitfully applied to the identification of the radial location of low order rational surfaces inside a magnetically confined plasma. To do so, we make use of Langmuir probe data from a set of experiments in which the rotational transform was scanned dynamically in the TJ-II stellarator. It is shown that up to five rational surfaces can be identified from the data, which is a first in plasma physics, to the best of our knowledge. The effect of the radial electric field on intermittence was also studied using a specific subset of experiments in which the electron density was raised on a shot by shot basis. The observations are contrasted with results from numerical calculations using a resistive magneto-hydrodynamic model to facilitate interpretation.

MHD equilibria with magnetic islands in the TJ-II heliac

ABSTRACTMagnetic islands normally form at the low-order magnetic rational surfaces in toroidal confinement systems when a symmetry-breaking perturbation arises. In stellarators, the equilibrium state for the plasma once the perturbation has created the islands is not easy to describe due to its complexity. Numerical computation of equilibria can be done following a variational principle that minimizes the energy under given boundary constraints when no islands are allowed, as the VMEC code does. Islands can be included by adding helical perturbations and allowing magnetic field line slipping, which was incorporated in the SIESTA code. Here we use these two codes for the TJ-II heliac in order to compute the MHD equilibrium state that provides the environment for the occurrence of all other plasma processes. The computation was done in two parts, first, obtain an equilibrium with VMEC for the whole toroidal cycle and second, superimpose the magnetic islands to obtain a final equilibrium with SIESTA by adjusting the appropriate parameters.

Turbulence evolution and transport behavior during current ramp-up in ITER-like plasmas on DIII-D

Low-wavenumber density fluctuations exhibit unique characteristics during the current ramp-up phase of ITER-like discharges that can partially explain the challenges of correctly modeling transport behavior and predicting global plasma parameters during this period. A strong interaction takes place between the evolving transport, safety factor (q) and kinetic profiles as well as the appearance and evolution of low-order rational surfaces. Density fluctuations from 0.75 < ρ < 0.9 are transiently reduced to exceptionally low levels during early times and from 0.8 < ρ < 0.9 at late times in the ramp-up in a manner that is different from behavior observed during steady-state plasma conditions with similar values of q95. Turbulence is suppressed as low-order-rational q-surfaces enter the plasma; the local electron temperature likewise exhibits transient increases during these periods of reduced fluctuations indicating changes in transport that impact temperature and consequently the evolution of current density and plasma inductance. These observations can explain discrepancies between CORSICA modelling and the higher electron temperature found previously over the outer half radius. Comparison of turbulence properties with time-varying linear growth rates with GYRO and GENE demonstrate qualitative consistency with measured fluctuation levels, but calculations don’t exhibit reduced growth rates near low-order rational surfaces, which is inconsistent with experimental observations. This indicates a mechanism that can contribute to reconciling observed turbulence behavior with transport models, allowing for the development of more accurate predictive tools.

An arbitrary wavelength solver for global gyrokinetic simulations. Application to the study of fine radial structures on microturbulence due to non-adiabatic passing electron dynamics

The influence of the fine layers of the non-adiabatic passing electron response on electrostatic turbulent transport, previously studied systematically in flux tube geometry [Dominski et al., Phys. Plasmas 22, 062303 (2015)], is pursued in global geometry in conditions relevant for the TCV tokamak with a deuterium plasma (mi/me = 3672). The spectral organization of the passing electron turbulent flux and its dependence on the radial profile of the safety factor are revealed. A radially dependent toroidal spectral analysis of the turbulent fluxes led to the key result that the particle and heat diffusivities of passing-electrons are proportional to the local density of low-order mode rational surfaces. To permit this study of the short radial scales associated with the passing electron dynamics, a new field solver valid at an arbitrary wavelength is implemented in ORB5, for the gyrokinetic quasi-neutrality equation. A benchmark is conducted against the global version of the gyrokinetic code GENE, showing very good agreement.

Causal impact of magnetic fluctuations in slow and fast L–H transitions at TJ-II

This work focuses on the relationship between L–H (or L–I) transitions and MHD activity in the low magnetic shear TJ-II stellarator. It is shown that the presence of a low order rational surface in the plasma edge (gradient) region lowers the threshold density for H-mode access. MHD activity is systematically suppressed near the confinement transition. We apply a causality detection technique (based on the Transfer Entropy) to study the relation between magnetic oscillations and locally measured plasma rotation velocity (related to Zonal Flows). For this purpose, we study a large number of discharges in two magnetic configurations, corresponding to “fast” and “slow” transitions. With the “slow” transitions, the developing Zonal Flow prior to the transition is associated with the gradual reduction of magnetic oscillations. The transition itself is marked by a strong spike of “information transfer” from magnetic to velocity oscillations, suggesting that the magnetic drive may play a role in setting up the final sheared flow responsible for the H-mode transport barrier. Similar observations were made for the “fast” transitions. Thus, it is shown that magnetic oscillations associated with rational surfaces play an important and active role in confinement transitions, so that electromagnetic effects should be included in any complete transition model.

Plasma flow, turbulence and magnetic islands in TJ-II

The effect of magnetic islands on plasma flow and turbulence has been experimentally investigated in ohmically induced magnetic configuration scans at the stellarator TJ-II. This operational mode allows sweeping the radial position of a low order rational surface from the plasma core towards the edge in a controlled way, what reveals effects that are difficult to notice in scans performed on a shot to shot basis. The main diagnostic used in the present work is a two-channel Doppler reflectometer that allows the measurement of the perpendicular rotation velocity of the turbulence and density fluctuations with good spatial and temporal resolution. A characteristic signature of the n/m = 3/2 magnetic island as it crosses the measurement position is clearly detected: the perpendicular flow reverses at the center of the magnetic island and a flow shear develops at the island boundaries. Fluctuations of the perpendicular flow and density have been also measured along the 3/2 magnetic island. An increase in the low frequency flow oscillations is measured at the magnetic island boundaries together with a reduction in the density fluctuation level; the later being more pronounced at the inner island boundary. These observations could explain the link between magnetic islands and transport barriers observed in a number of fusion devices.

The role of magnetic islands in modifying long range temporal correlations of density fluctuations and local heat transport

This work explores the relation between magnetic islands, long range temporal correlations and heat transport. A low order rational surface () was purposely scanned outward through an electron cyclotron resonance heated (ECRH) plasma in the TJ-II stellarator. Density turbulence and the poloidal flow velocity were characterized using a two channel Doppler reflectometer. Simultaneously, the ECRH power was modulated to characterize heat transport, using measurements from a 12 channel electron cyclotron emission diagnostic. A systematic variation of the poloidal velocity was found to be associated with the rational surface. Near the rational surface, the Hurst exponent, quantifying the nature of long-range correlations, was reduced below 0.5 (indicating subdiffusion), while at radii smaller than that of the rational surface, it was found to be significantly enhanced (superdiffusion). In the latter region, heat transport was enhanced as well, thus establishing a link between density fluctuations and anomalous heat transport. The observed variation of the Hurst exponent was consistent with a magnetohydrodynamic turbulence simulation.

Mechanisms of plasma disruption and runaway electron losses in the TEXTOR tokamak

Based on the analysis of data from the numerous dedicated experiments on plasma disruptions in the TEXTOR tokamak the mechanisms of the formation of runaway electron (RE) beams and their losses are proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode-number magneto-hydro-dynamics (MHD) modes. It is hypothesized that the RE beam is formed in the central plasma region confined by an intact magnetic surface due to the acceleration of electrons by the inductive toroidal electric field. In the case of plasmas with the safety factor $q(0)&lt;1$ the most stable RE beams are formed by the outermost intact magnetic surface located between the magnetic surface $q=1$ and the closest low-order rational surface $q=m/n&gt;1~(q=5/4,q=4/3,\dots )$. The thermal quench (TQ) time caused by the fast electron transport in a stochastic magnetic field is calculated using the collisional transport model. The current quench (CQ) stage is due to the particle transport in a stochastic magnetic field. The RE beam current is modelled as a sum of a toroidally symmetric part and a small-amplitude helical current with a predominant $m/n=1/1$ component. The REs are lost due to two effects: (i) by outward drift of electrons in a toroidal electric field until they touch the wall and (ii) by the formation of a stochastic layer of REs at the beam edge. Such a stochastic layer for high-energy REs is formed in the presence of the $m/n=1/1$ MHD mode. It has a mixed topological structure with a stochastic region open to the wall. The effect of external resonant magnetic perturbations on RE loss is discussed. A possible cause of the sudden MHD signals accompanied by RE bursts is explained by the redistribution of runaway current during the resonant interaction of high-energetic electron orbits with the $m/n=1/1$ MHD mode.

Tokamak plasma high field side response to an n = 3 magnetic perturbation: a comparison of 3D equilibrium solutions from seven different codes

In comparing equilibrium solutions for a DIII-D shot that is amenable to analysis by both stellarator and tokamak three-dimensional (3D) equilibrium codes, a significant disagreement has been seen between solutions of the VMEC stellarator equilibrium code and solutions of tokamak perturbative 3D equilibrium codes. The source of that disagreement has been investigated, and that investigation has led to new insights into the domain of validity of the different equilibrium calculations, and to a finding that the manner in which localized screening currents at low order rational surfaces are handled can affect global properties of the equilibrium solution. The perturbative treatment has been found to break down at surprisingly small perturbation amplitudes due to overlap of the calculated perturbed flux surfaces, and that treatment is not valid in the pedestal region of the DIII-D shot studied. The perturbative treatment is valid, however, further into the interior of the plasma, and flux surface overlap does not account for the disagreement investigated here. Calculated equilibrium solutions for simple model cases and comparison of the 3D equilibrium solutions with those of other codes indicate that the disagreement arises from a difference in handling of localized currents at low order rational surfaces, with such currents being absent in VMEC and present in the perturbative codes. The significant differences in the global equilibrium solutions associated with the presence or absence of very localized screening currents at rational surfaces suggests that it may be possible to extract information about localized currents from appropriate measurements of global equilibrium plasma properties. That would require improved diagnostic capability on the high field side of the tokamak plasma, a region difficult to access with diagnostics.