The external kink mode in diverted tokamaks

Local helicity injection (LHI) is a non-inductive startup and current drive method via Taylor relaxation for the spherical torus. In achieving Taylor relaxation, it has been suggested that kink instability in 3D helical flux ropes plays an important role. However, the role and occurrence of kink instability during LHI have yet to be validated. Experimentally, determining the kink mode in a flux rope relies on measuring internal information using a probe. However, for LHI, the 3D geometry complicates this measurement process. Here, we propose a new approach for determining the kink modes of 3D helical flux ropes without any internal probe measurements. It is confirmed by this approach that flux ropes exhibit two different kink modes. With increasing plasma current in the flux ropes, a transition from the coherent internal kink mode to the external kink mode is observed. Kink mode properties such as rotating frequency calculated from the kink theory agree well with the magnetic signature driven by the kink mode. During the LHI experiment in the versatile experiment spherical torus, three distinguishable phases are confirmed by the approach, consistent with NIMROD simulation. Before driving the toroidal plasma current, the external kink mode is observed for 3D helical flux ropes. As the toroidal plasma current increases, the external kink mode disappears while generating broadband internal modes instead of coherent internal kink of flux ropes. Decoupling between the toroidal plasma and flux rope results in both decay of toroidal plasma current and re-appearance of the external kink mode in the flux ropes.

A detailed analysis of the ideal kink instability in line-tied cylindrically symmetric coronal loops is presented. Using a rapidly converging Fourier series expansion technique, the growth rate, as well as the eigenfunction, of ideal m = 1 kink modes is calculated for two topologically distinct models of force-free static MHD equilibria: one in which all the magnetic field lines are connected to the photosphere and one presenting a polarity inversion surface. The growth rates depend crucially on the loop length. Loops of the former type are found to be more unstable, and possess higher growth rates, than loops of the latter type, which are unstable to sausage-tearing modes and may also be unstable to m = 1 resistive kink modes. Applications of these results to the structure of coronal loops are presented. 14 refs.

Runaway currents have been detected during unintended disruptions in the circular plasma with the limiter configuration in the Experimental Advanced Superconducting Tokamak (EAST). The runaway electron (RE) plateau can carry up to 80% of the pre-disruption plasma current. The highest runaway currents correspond to the lowest loop voltage, which is contrary to the observations made in most tokamaks. This anomalous behavior is attributed to the acceleration of the pre-existing wave resonant suprathermal electrons by lower hybrid waves during the disruption decay phase. Two distinct types of RE-related relaxation phenomena, distinguished on the basis of the amplitude of the magnetic fluctuations, have been found during the disruptions. Large-amplitude magnetohydrodynamic activity with indications of RE loss is observed during the RE plateau when the edge safety factor decreases to less than 3, and the external kink mode is discussed to resolve this anomaly. Burst-like relaxations with small-amplitude magnetic fluctuations and ∼0.6 kHz frequency are confirmed from the spikes in the hard x-ray array signals under a negative loop voltage. Measurement of the RE energy distribution suggests that the instability is driven by medium-energy REs.

Thermonuclear controlled fusion research is a highly active branch of plasma physics. The main goal is the production of energy from the fusion reaction of hydrogen isotope nuclei, the same reaction that powers stars. The most promising present approach are Tokamaks, toroidal devices where high temperature plasmas are confined by means of magnetic fields. This thesis is devoted to a detailed and systematic study of plasma rotation nthe Tokamak à Configuration Variable (TCV), at the Centre de Recherches en Physique des Plasmas (CRPP) in Lausanne Switzerland. In a tokamak, confinement is limited by particle and energy transport from the hot core to the cold edge and by macroscopic perturbations of magnetic equilibrium. Recently, plasma rotation has been demonstrated to beneficially affect both confinement and stability, explaining the great recent interest in plasma rotation studies Relatively little is understood about plasma rotation physics and, in particular, the so called "intrinsic" rotation that will constitute the main component of plasma rotation in next generation machines. That is why a great theoretical and experimental effort is being deployed in studying intrinsic rotation and this work is part of this context. In TCV, plasma rotation is measured by the Charge eXchange Recombination Spectroscopy diagnostic (CXRS). The spectroscopic signal comes from the perpendicular observation of a low power Diagnostic Neutral Beam Injector (DNBI), which applies a negligible torque to the plasma. Hence, the DNBI/CXRS pair is an effective tool for the experimental study of intrinsic tokamak plasma rotation. During this work, the pre existing toroidal observation view was complemented with two new systems, permitting the measurement of toroidal rotation, on inboard plasma radius, and poloidal rotation in the plasma periphery. The implementation of an automated wavelength calibration procedure, based on reference Neon spectra, permitted the first viable (toroidal and poloidal) rotation measurements of TCV, with uncertainties down to 1km/s. Using upgraded light collection optics and fiber optic transmission lines, simultaneous measurement of core and edge plasma was achieved, with a doubling of of the radial resolution of the toroidal rotation measurements. The measurable range of plasma parameters was also extended to higher densities by the installation of back illuminated CCD detectors. In the present configuration (CXRS09), the diagnostic is capable of routinely measuring toroidal and poloidal plasma rotations with a radial resolution of ≲ 1 cm and a sample frequency of 10 ÷ 20 Hz, for plasma densities of 0.8 ≲ ne,av ≲ 8 × 1019 m-3. The basic scenario of Ohmically heated discharges in limiter L-mode configuration was initially addressed. A large core toroidal rotation up to uφ ≈ 50 km/s in the counter current direction is measured, reversing nearly exactly upon reversal of plasma current Ip. The toroidal rotation profile may be schematically divided into a core, a peripheral and an intermediate region. For qe ≈ 3 (magnetic safety factor at the plasma edge) the core region velocity is relatively flat or slightly "bulged" in the co current direction inside the sawtooth inversion radius. In the peripheral region, the toroidal rotation is small with a monotonic intermediate region. The central rotation appears to be limited to approximately its value at the sawtooth inversion radius. Poloidal rotation uθ ≲ 3 km/s, measured in Ohmic discharges, is only weakly dependent on plasma parameters but reverses with reversed magnetic field, with values and direction coherent with neoclassical predictions. Combining uφ and uθ measurements, the profile of the radial electric field Er was estimated through the radial force balance equation. Er down to 8 kVm (inward directed) is found in the plasma bulk, and close to zero at the plasma edge. A spontaneous reversal of the toroidal rotation profile is observed when the average density exceeds ne,av ≈ 4 × 1019 m-3 at low qe ≈ 3, with the plasma now rotating in the co current direction. The transition between the co and counter rotation regimes is studied dynamically using ne and Ip ramps and with the application of Electro Cyclotron Heating (ECH). The rotation reversal is weakly sensitive to impurity concentration and positive plasma triangularity appears to be a key ingredient. Whilst a physical explanation has not been identified yet, dynamic uφ reversal observations indicate that it results from a changed balance of radial non-diffusive fluxes of toroidal momentum. The study was extended to the divertor magnetic configuration in which the plasma column rotates in the co current direction at low ne, and uφ reverses at high ne opposite from the limited configuration. The rotation profile may again be divided into three regions, although the rotation at the plasma periphery does not always remain close to zero but evolves with the plasma parameters. In particular, independently on the core rotation regime, peripheral uφ decreases with ne and Ip and is strongly sensitive to the ion B→ × ∇B direction, suggesting a link with parallel fluxes in the Scrape-Off Layer (SOL). Combined measurements of of CXRS and Mach probe indicate that in the plasma edge toroidal rotation matches the toroidal component of SOL flows. From the analysis of toroidal rotation in stationary and transient phases, a characterization of the momentum transport is presented. The resulting radial momentum diffusivity, of the order of Χφ ∼ 0.1 – 0.3 m2/s, exceeds by 2 orders of magnitude the neoclassical estimation. A remarkable result is the existence of a "residual stress" component, which sustains a substantial stationary rotation gradient for null background rotation. Conversely, the analysis suggests a minor role for the convective (pinch) component, that is preliminarily confirmed by gyro-kinetic simulations including turbulent Coriolis convective pinch. Neoclassical predictions are in quantitative and qualitative disagreement with the experimental observations. The effect of the sawtooth instability on the core rotation was addressed in a specific experimental scenario where the inter crash evolution of the core uφ could be measured. The measurement required the development of a fast CXRS acquisition scheme based on a trigger constructed in real time from a Soft X-ray measurement. At the sawtooth crash the plasma core undergoes a strong acceleration in the co current direction (∆uφ ≈ 9 km/s in the experimental scenario), possibly related to a strong transient toroidal electric field. The systematic and varied observations reported in this work extend the experimental knowledge of bulk plasma rotation in low confinement regimes. In particular, the rotation reversal phenomena constitute an important test for momentum transport models of tokamak plasmas.

Magnetohydrodynamic (MHD) stability studies of low-mode-number free-boundary kink modes in a finite-β Large Helical Device (LHD) [A. Ilyoshi, et al. Fusion Technology 17, 169 (1990)] equilibrium series with self-consistent bootstrap current find some serious free-boundary modes. They indicate that care must be taken in the design of high-β experiments. Since the LHD configuration is flexible, with the possibility of introducing or modifying dipole and quadrapole fields, unbalancing the currents in the helical coils, operating with a high-temperature divertor, and changing the collisionality regime by working with different values of temperature and density, paths to high-β operation should exist. Comparison of the experimental results with these theoretical predictions for the studied equilibrium sequence will provide understanding of the MHD stability properties of LHD.

In recent years, Bayesian probability theory has been used in a number of experiments to fold uncertainties and interdependences in the diagnostic data and forward models, and together with prior knowledge of the state of the plasma, thus increase accuracy of inferred physics variables. Key developments include the application to current and flux surface tomography, effective charge, the electron energy distribution function, neutron spectrometry and density. Virtual observations have also been introduced to better constrain inferred quantities in current tomography. In this work we present Bayesian inference results of toroidal and poloidal current and flux surface tomography. Whilst the uncertainty in these profiles, as well as the uncertainty in inferred parameters such as the safety factor profile is small (<5%), the inference can change substantially depending on the physics model used. We also present Bayesian inference results for Thomson scattering and charge-exchange recombination spectroscopy. In separate work we have computed radial force balance components on the midplane in the Mega Ampére Spherical tokamak. Our aim is to establish a validation framework for different equilibrium physics models. We find that in the overlapping region of the core (normalized poloidal flux less than 0.4) and motional Stark effect (MSE) chords, the plasma is consistent with static Grad–Shafranov force balance to within two standard deviations. In the outboard edge region, where MSE data are also available, the pressure gradient exceeds the Lorentz force. Most likely, this is because the poloidal current is not constrained to zero at the plasma edge. To lowest order, the results suggest computing components of force balance are useful to assess data-consistency, independent of any equilibrium solution. To first order, we have integrated the residue to force balance to infer an energetic particle pressure.

Particle balance in a TFTR supershot

Recent studies suggest significant time delay between the Shattered Pellet Injection (SPI) fragment arrival and the temperature radiative collapse could exist in ITER, depending on the impurity assimilation and the plasma thermal reservoir. Hence in some cases the fragments could reach the core even before the edge radiative collapse occurs and triggers strong stochastic transport. This could be beneficial for heat load mitigation and hot-tail runaway electron suppression. To investigate the expected assimilation and radiation, thus the magneto-hydrodynamic (MHD) response after SPIs in 3D, we carry out simulations of collisional–radiative impurity mixed SPIs into ITER L-mode equilibrium. Localized cooling around the fragments is found to cause current perturbations which destabilize MHD modes. Meanwhile, slower injections are found to result in stronger and more complete radiative collapse, thus stronger MHD amplitude. Due to the q = 1 surface enclosing a significant volume, the resistive kink mode is shown to couple with outer modes to bring global stochasticity and convective core density mixing, although a transport barrier outside of the q = 1 surface prevents immediate temperature relaxation over the whole plasma. The impact of various physical assumptions and numerical treatments, such as the use of the flux-averaged ambient plasma parameters for ablation calculation, the exclusion of the magnetic constraining effect in ablation, the localization of the density source and the use of constant parallel thermal conduction instead of the Braginskii one and different injection velocities are also investigated. In general, stronger and more localized ablation results in stronger radiation, faster radiative collapse and a more violent MHD response, while the assimilation changes little due to a self-regulation effect.

Optimized current profiles are shown to be capable of providing simultaneous stability against all resistive kink modes in the tokamak.

The toroidal Alfvén eigenmode (TAE), excited by trapped energetic particles (EPs), is numerically investigated in a tokamak plasma, using the non-perturbative magnetohydrodynamic-kinetic hybrid formulation based MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503). Compared with the fixed boundary condition at the plasma edge, a free boundary enhances the critical value of the EPs kinetic contribution for driving the TAE. Free boundary also induces finite perturbations at the plasma edge as expected. An anisotropic distribution of EPs, in the particle pitch angle space, strongly enhances the instability and results in a more global mode structure, compared with the isotropic case. The plasma resistivity is also found to play a role in the EPs-destabilized TAE. In particular, the mode stability domain is mapped out, in the 2D parameter space of the plasma resistivity and a quantity defining the width of the particle distribution in pitch angle (for anisotropic distribution). A resonance layer in the poloidal mode structure, with the layer width increasing with the plasma resistivity, appears at the large width of the particle distribution in pitch angle space. A mode conversion, from the modified ideal kink by the EPs kinetic effect to the TAE, is also observed while increasing the birth energy of EPs. Computational results suggest that the TAE mode structure can be modified by certain key plasma parameters, such as the EPs kinetic contribution, the equilibrium pressure, the plasma resistivity, the distribution of EPs, as well as the birth energy of EPs. Such modification of the eigenmode structure can only be obtained following the non-perturbative hybrid approach (Wang et al 2013 Phys. Rev. Lett. 111 145003, Wang et al 2015 Phys. Plasmas 22 022509), as adopted in this study. More importantly, numerical results show that near the marginal stability point, the dominant poloidal harmonics of the TAE overlap with each other, and are localized at the tip positions of the Alfvén continua. This kind of TAE structure in high beta plasma with unstable ideal kink is substantially different from that of the conventional TAE.

EVOLUTION OF NEUTRAL-BEAM-DRIVEN CURRENT IN TOKAMAK PLASMAS

The roles of a magnetic separatrix and of a steep-edge pressure gradient on finite beta external kink and tearing modes in tokamaks are examined by using a newly developed initial value code. For fixed profiles of current density and pressure, the separatrix is found to have a weak effect on the linear characteristics of the global mode. The presence of a steep pressure gradient at the plasma edge reduces the overall growth rate in a similar fashion for both cases with and without the separatrix.

The carbon concentration in the plasma of the stellarator experiment Wendelstein 7-AS is measured in the framework of the first island divertor campaign to examine divertor impurity control. Dedicated plasma density and electron cyclotron resonance heating power scans are performed and the influence of both the magnetic configuration and boronization of the vessel are investigated. A new diagnostic system is employed to measure C6+ densities via charge-exchange collisions with the neutral high-energy Li beam in the plasma edge and the core region. Carbon concentrations with respect to electron density are derived by using the density evaluation of the Li(2p) light profile. The results obtained during a period of approximately 2500 shots demonstrate that boronization reduces the carbon core concentration by a factor of three to a base level of 0.5–1%, which is not affected by further boronizations. The carbon concentration in island divertor configurations is found to be far below those obtained in a limiter configuration, which is attributed to a more than a factor two better impurity screening. The analysis of the carbon influx by spectroscopic measurements of C1+ radiation suggests that the carbon core concentration in discharges of different densities and heating power is adequately described using the electron density at the last closed flux surface normalized to the line-averaged electron density as a scaling parameter. This simple global approach underlines the important role of the balance of impurity sources and impurity dilution. The effect of changes in impurity confinement on the measured carbon concentrations is also discussed.

A combined model for current profile control and MHD stabilityanalysis has been used to identify stable operating modes near theideal stability limit (βN ≃ 3) in the AlcatorC-Mod tokamak. These discharges are characterized by relatively highfractions of bootstrap current (fBS = 0.70) andnon-monotonic profiles of the safety factor with qmin > 2. Inthe absence of a conducting shell, stability was determined bythe onset of the low (n = 1) external kink mode. In these studies,current profile control in the plasma periphery (r/a ≳ 0.5)was provided by 2.5-3.0 MW of LHCDpower. Internal and edge transport barriers were introduced into the model calculations in the form of density transitions. Excellent waveaccessibility and absorption were still found in the presence of anH-mode-like edge density barrier. However, the presence of thesebarriers resulted in about a 10% decrease in the stability limit, fromβN ≃ 3 to βN ≃ 2.7.

The L-H transition power threshold (PLH) is found to have a significant dependence on q95, at ne ∼ 3.2 × 1019 m−3 on DIII-D. Comprehensive 2D turbulence and flow measurements in the plasma edge reveal the co-existence of two frequency bands of broadband modes across the L-H transition with higher flow shear at higher q95, which can help explain the linear decrease in PLH as q95 is increased from 3.5 to 4.9. Density fluctuation measurements by beam emission spectroscopy at higher q95 show that the lower frequency band (&amp;lt;20 kHz) of the broadband modes propagates in the ion diamagnetic direction in the lab frame (identified as an ion mode), whereas the higher frequency band (&amp;gt;20 kHz) propagates in the electron diamagnetic direction (identified as an electron mode). The turbulence amplitude at the plasma edge is higher at higher q95, implying a higher drive for a Reynolds stress driven zonal flow. At lower density, ne ∼ 1.5 × 1019 m−3, there is little dependence of PLH on q95. Linear CGYRO kinetic simulation has shown a switch from one mode to two modes at higher q95 at ne ∼ 3.2 × 1019 m−3 compared to lower q95. The ion temperature profile has been shown to strongly impact the dual mode characteristics with the increasing growth rate of the ion mode at a higher edge Ti gradient. The observations suggest that it may be possible to reduce the required input power to trigger the L-H transition for ITER if both the ion and electron modes are similarly driven in the plasma edge.