Table of contents

The physical mechanisms that cause tokamak plasmas to rotate toroidally without external momentum input are of considerable interest to the plasma physics community. This paper documents a substantial change in both the magnitude of the core-rotation frequency, −1 < ω(r/a = 0) < +10 kHz, and the sign of rotation shear at mid-radius, u' = −R² dω/dr/v_th,i, which varies in the range −0.6 < u' < +0.8 in response to very small changes in the electron density. In 0.8 MA, 5.4 T Alcator C-Mod L-mode plasmas using 1.2 MW of on-axis ion-cyclotron resonance heating, plasmas with line-averaged densities in the range $1.0<\bar{n}_{\rm e} <1.2\times 10^{20}\,{\rm m}^{-3}$ exhibit a transition from a peaked intrinsic rotation profile to one that is hollow. Gradient scale lengths of the temperature and density profiles, the drive for plasma turbulence thought to play a role in intrinsic rotation, are indistinguishable within experimental uncertainties between the plasmas, and linear stability analysis using GYRO shows the plasmas to be in the ion temperature gradient-dominated turbulence regime. The impact of changes in the rotation profile in response to minor changes under target plasma conditions is discussed in relation to established analysis techniques and cross-machine rotation scaling studies, with comparisons made with existing ASDEX-Upgrade work on intrinsic rotation shear.

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The dynamics of fluctuating electric field structures in the edge of the TJ-II stellarator, which display zonal-flow-like traits, is studied. These structures have been shown to be global and affect particle transport dynamically (Alonso J et al 2012 Nucl. Fusion52 063010). In this paper we discuss the possible drive (Reynolds stress) and damping (neoclassical viscosity, geodesic transfer) mechanisms for the associated E × B velocity. We show that (a) while the observed turbulence-driven forces can provide the necessary perpendicular acceleration, a causal relation could not be firmly established, possibly because of the locality of the Reynolds stress measurements, (b) the calculated neoclassical viscosity and damping times are comparable to the observed zonal-flow relaxation times and (c) although an accompanying density modulation is observed to be associated with the zonal flow, it is not consistent with the excitation of pressure sidebands, as those present in geodesic acoustic oscillations, caused by the compression of the E × B flow field.

Intrinsic flow velocities of up to ∼20 km s⁻¹ have been measured using charge exchange recombination spectroscopy (CHERS) in the quasi-helically symmetric HSX stellarator and are compared with the neoclassical values calculated using an updated version (Lore 2010 Measurement and Transport Modeling with Momentum Conservation of an Electron Internal Transport Barrier in HSX (Madison, WI: University of Wisconsin); Lore et al 2010 Phys. Plasmas17 056101) of the PENTA code (Spong 2005 Phys. Plasmas.12 056114). PENTA uses the monoenergetic transport coefficients calculated by the drift kinetic equation solver code (Hirshman et al 1986 Phys. Fluids29 2951; van Rij and Hirshman 1989 Phys. Fluids B 1 563), but corrects for momentum conservation. In the outer half of the plasma good agreement is seen between the measured parallel flow profile and the calculated neoclassical values when momentum correction is included. The flow velocity in HSX is underpredicted by an order of magnitude when this momentum correction is not applied. The parallel flow is calculated to be approximately equal for the majority hydrogen ions and the C⁶⁺ ions used for the CHERS measurements. The pressure gradient of the protons is the primary drive of the calculated parallel flow for a significant portion of the outer half of the plasma. The values of the radial electric field calculated with and without momentum correction were similar, but both were smaller than the measured values in the outer half of the plasma. Differences between the measured and predicted radial electric field are possibly a result of uncertainty in the composition of the ion population and sensitivity of the ion flux calculation to resonances in the radial electric field.

A new algorithm based on metaheuristics has been developed to perform stellarator optimization. This algorithm, which is inspired by the behaviour of bees and is called distributed asynchronous bees, has been used for the optimization under three criteria: minimization of B × grad(B) drift, Mercier and ballooning stability. This algorithm is tested by partially optimizing TJ-II and, afterwards, a three-period optimized configuration is found by performing a full optimization that starts from a three-period heliac.

Straight-field-line coordinates are very useful for representing magnetic fields in toroidally confined plasmas, but fundamental problems arise regarding their definition in 3D geometries because of the formation of islands and chaotic field regions, i.e. non-integrability. In Hamiltonian dynamical systems terminology these coordinates are similar to action-angle variables, but these are normally defined only for integrable systems. In order to describe 3D magnetic field systems, a generalization of this concept was proposed recently by the present authors that unified the concepts of ghost surfaces and quadratic-flux-minimizing (QFMin) surfaces. This was based on a simple canonical transformation generated by a change of variable θ = θ(Θ, ζ), where θ and ζ are poloidal and toroidal angles, respectively, with Θ a new poloidal angle chosen to give pseudo-orbits that are (a) straight when plotted in the ζ, Θ plane and (b) QFMin pseudo-orbits in the transformed coordinate. These two requirements ensure that the pseudo-orbits are also (c) ghost pseudo-orbits. In this paper, it is demonstrated that these requirements do not uniquely specify the transformation owing to a relabelling symmetry. A variational method of solution that removes this lack of uniqueness is proposed.

The primary goal of hybrid scenarios in tokamaks is to enable high performance operation with large plasma currents whilst avoiding MHD instabilities. However, if a local minimum in the safety factor is allowed to approach unity, the energy required to overcome stabilizing magnetic field line bending is very small, and as a consequence, large MHD structures can be created, with typically dominant m = n = 1 helical component. If there is no exact q = 1 rational surface the essential character of these modes can be modelled assuming ideal nested magnetic flux surfaces. The methods used to characterize these structures include linear and non-linear ideal MHD stability calculations which evaluate the departure from an axisymmetric plasma state, and also equilibrium calculations using a 3D equilibrium code. While these approaches agree favourably for simulations of ITER relevant hybrid regimes in this paper, the relevance of the ideal MHD model itself is tested through empirical examination of helical states in MAST and TCV. While long lived modes in MAST do not have island structures, some of the continuous mode oscillations exhibited in high elongation experiments in TCV indicate that resistivity may play a role in further weakening the ability of the tokamak core to remain axisymmetric. The simulations and experiments consistently highlight the need to control the safety factor in hybrid scenarios planned for future fusion grade tokamaks such as ITER.

The objective of Wendelstein 7-X is to demonstrate steady-state operation at β -values of up to 5%, at ion temperatures of several keV and plasma densities of up to 2 × 10²⁰ m⁻³. The second operational phase foresees a fully steady-state high heat flux (HHF) divertor. Preparations are underway to cope with residual bootstrap currents, either by electron cyclotron current drive or by HHF protection elements. The main steady-state heating system is an electron cyclotron resonance heating facility. Various technical improvements of the gyrotrons have been implemented recently. They enable a reliable operation at the 1 MW power level. Some of the technical issues preparing plasma diagnostics for steady-state operation are exemplified. This includes the protection against non-absorbed microwave radiation.

We quantify the impact of poloidal and toroidal rotation, anisotropy and energetic particle pressure produced by neutral beam injected energetic particles on the magnetic configuration and wave modes in tokamaks. Specifically, we focus on the class of spherical tokamaks, for which the impact of neutral beam heating is larger due to the relatively low toroidal field and large trapped particle fraction. Recently, (Hole et al 2011 Plasma Phys. Control. Fusion53 074021) we have used Bayesian inference techniques to compute rotating MAST equilibria, and thereby compute toroidal and poloidal Mach numbers and their uncertainties, as well as computed MAST anisotropic equilibria in the presence of neutral beam heating. Motivated by this work, we compute the impact of rotation and anisotropy on magnetohydrodynamic (MHD) waves of the plasma. Specifically, we determine how a change in q profile due to rotation and anisotropy could affect frequency scalings of the Alfvén continuum, Alfvén gap modes and compressional Alfvén eigenmodes. We also use Bayesian inference to infer energetic particle pressure, and compare the result with the inferred pressure from high-fidelity TRANSP simulations.

Based on particle-in-cell (PIC) simulation results of collisionless driven reconnection in a steady state, an effective resistivity model is developed for a magnetohydrodynamic (MHD) simulation in order to bridge the huge gap between macro- and microphysics of magnetic reconnection. The PIC simulation reveals that the reconnection electric field sustained by microscopic physics is found to evolve so as to balance the flux inflow rate, which is determined by global dynamics in a macroscopic system. This effective resistivity model is applied to MHD phenomena controlled by magnetic reconnection in the Earth's magnetosphere. Although this model does not include any adjustable parameters related to kinetic dissipation processes, some global phenomena such as the onset of magnetic substorm, dipolarization and propagation of flux rope, detailed processes of which are longstanding questions, are reproduced well in the MHD simulation and are consistent with the observations.

A partial collapse observed in magnetic axis swing experiments in the Large Helical Device (LHD) is analyzed with a nonlinear magnetohydrodynamic (MHD) simulation. Real time control of the background field in the operation is incorporated by means of a multi-scale numerical scheme in the simulation. The simulation result indicates that the changing background field accelerates the growth of an infernal-like mode and causes the partial collapse.

Microwave heating of overdense low-temperature plasmas, whose density exceeds the cutoff density of the injected microwave, is described for the stellarator TJ-K. Three different methods featuring each of their own characteristics are briefly presented. It is shown that TJ-K allows both fusion relevant scenarios such as heating by electron Bernstein waves and fundamental wave-plasma interactions like parametric decay instabilities to be investigated.

Dynamic transport study taking account of the slowing-down effect on the neutral beam injection heating is applied to a high ion temperature plasma with an ion internal transport barrier (ITB) obtained by carbon pellet injection, which records the highest ion temperature of around ∼7 keV in the Large Helical Device. The transient increase in ion heating is clarified during the density decay phase just after the carbon pellet injection by considering the slowing-down effect. The dynamic transport analysis also includes the change in heat flux due to the change in kinetic energy inside the plasma with the time scale of the global energy confinement time, which is required to investigate the heat and momentum transport during the transient phase more exactly. The characteristics of the ion heat and momentum transport improvement during the ion ITB formation phase are clarified by the dynamic transport study.

Inter-scale magnetic energy transfer associated with the Hall effects in homogeneous and isotropic magnetohydrodynamics (MHD) turbulence and the applicability of a Smagorinsky-type diffusive sub-grid-scale (SGS) model to Hall MHD turbulence are studied numerically. Low-pass filter analysis on magnetic energy transfer functions shows that their profiles change considerably when the cut-off wave number is comparable to the Taylor-scale wave number. It is shown that the Smagorinsky-type model is applicable to Hall MHD turbulence as a basic SGS model, while the Hall effects tend to overestimate the grid-scale magnetic energy transfer.

Nonlinear stability of magnetic islands in a helical plasma with resonant magnetic perturbation (RMP) is investigated using reduced magnetohydrodynamic equations including neoclassical viscosity. Coexistence of RMP-driven islands and the resistive interchange mode is numerically simulated. The self-healing of locked magnetic islands by neoclassical flows is observed. It is found that the curvature effect modifies the threshold of the self-healing, where the unfavorable curvature drives not only the interchange mode but also the curvature-driven tearing mode. An analytical model based on a Rutherford equation with a momentum equation is also introduced to understand the simulation results. Criterion of the self-healing considering the curvature effect is newly obtained.

The effect of resonant magnetic perturbation (RMP) on MHD characteristics is investigated in high-beta plasmas of the Large Helical Device. The ramp-up and static m/n = 1/1 RMP field are applied in medium- (∼2%) and high- (∼4%) beta plasmas in order to find beta dependences of mode penetration, MHD activities and confinement. The results show that the threshold of mode penetration linearly increases with the beta value and/or plasma collisionality. The threshold of mode penetration in the RMP ramp-up experiments is roughly consistent with the static RMP case. The beta value gradually decreases with the RMP field strength before mode penetration, which is caused by a reduction in the pressure inside the ι/2π = 1 resonance. The width of the magnetic island after the penetration becomes larger than the given RMP field, and it is further enhanced by the increment of the beta value.

The results of global linear gyrokinetic simulations of residual flows carried out with the code EUTERPE in the TJ-II three-dimensional geometry are reported. The linear response of the plasma to potential perturbations homogeneous in a magnetic surface shows several oscillation frequencies: a Geodesic-acoustic-mode-like frequency, in qualitative agreement with the formula given by Sugama and Watanabe (2006 Plasma Phys.72 825), and a much lower frequency oscillation in agreement with the predictions of Mishchenko et al (2008 Phys. Plasmas15 072309) and Helander et al (2011 Plasma Phys. Control. Fusion53 054006) for stellarators. The dependence of both oscillations on ion and electron temperatures and the magnetic configuration is studied. The low-frequency oscillations are in the frequency range supporting the long-range correlations between potential signals experimentally observed in TJ-II.

We have newly developed a large-scale equilibrium database for real-time magnetic coordinate mapping system in the Large Helical Device. Thousands of free-boundary equilibria for each vacuum configuration have been calculated under wide ranges of central beta, pressure peaking factor, toroidal current and current peaking factor. We have also prepared a line of sight database which tabulates pre-calculated mapping results for all equilibria along several selected lines of sight to accelerate the mapping procedure. A user library has been developed to retrieve results of the inverse mapping as well as additional equilibrium parameters from the databases. A mapping program iteratively searches for the best-fitted equilibrium so as to minimize the discrepancy between inboard and outboard side of an electron temperature profile measured by the Thomson scattering diagnostic. Real-time mapping of all the time slices of the Thomson data enables us to provide time evolutions of equilibrium parameters and electron temperature/density profiles as functions of effective minor radius, which can be applied specifically for subsequent analyses of transport phenomena based on experiments.

Gyrokinetic simulations of the ion temperature gradient (ITG) turbulence in non-axisymmetric configurations modeled on the Large Helical Device (LHD) are performed with the entropy transfer analysis (Nakata et al 2012 Phys. Plasmas19 022303). It is clarified that a fluctuation spectrum elongated in the radial wavenumber direction is formed in a neoclassically optimized field configuration with the inward-shifted magnetic axis position, where the zonal flows are more effectively generated than in the standard case. The strong interaction between zonal flows and turbulence causes the successive entropy transfer from low to high radial wavenumber space and the spectral broadening of ITG turbulence.

Inhomogeneous magnetic field gives rise to interesting properties of plasmas which are degenerate in homogeneous (or zero) magnetic fields. Magnetospheric plasmas, as observed commonly in the Universe, are the most simple, natural realization of strongly inhomogeneous structures created spontaneously in the vicinity of magnetic dipoles. The RT-1 device produces a 'laboratory magnetosphere' by which stable confinement (particle and energy confinement times ∼0.5 s) of high-β (local electron β ∼ 0.7; electron temperature ≳10 keV) plasma is achieved. By producing a pure-electron plasma, we obtain clear-cut evidence of inward (or up-hill) diffusion of particles. A statistical mechanical model reveals the 'distortion' of phase space, induced by the inhomogeneity of the ambient magnetic field, on which the plasma relaxes into an equilibrium with inhomogeneous density while it maximizes the entropy.

A description and transport analysis (energy and particles) of neutral beam heated plasmas is shown for two almost identical magnetic configurations except for a ≈1% difference in their rotational transform, . Due to the low magnetic shear of TJ-II magnetic fields, such difference takes the low order rational to the plasma edge in one of them, while in the other the 8/5 value is near the edge but inside the plasma. A transport transition happens at lower density and plasma energy for the configuration that includes the , which exhibits better particle confinement already before the transition.

The magnetic field structure associated with edge localized ideal ballooning mode bursts is analysed by nonlinear gyrofluid computation. The linear growth phase is characterized by the formation of small-scale magnetic islands. Ergodic magnetic field regions develop near the end of the linear phase when the instability starts to perturb the equilibrium profiles. The nonlinear blow-out gives rise to an ergodization of the entire edge region. The time-dependent level of ergodicity is determined in terms of the mean radial displacement of a magnetic field line. The ergodicity decreases again during the nonlinear turbulent phase of the blow-out in dependence on the degrading plasma beta in the collapsing plasma pedestal profile.

The three-dimensional structure of drift-wave turbulence and turbulent transport is investigated in plasmas of the stellarator experiment TJ-K. By means of two poloidal Langmuir probe arrays placed at different toroidal positions, density and potential fluctuations are recorded simultaneously at 128 positions on a single flux surface. From these data, the spatial drift-wave turbulence pattern including perpendicular and parallel structure sizes are obtained using a cross-correlation technique. A comparison with the magnetic field structure indicates an initially perfect alignment of turbulent structures with magnetic field lines. Passing over regions with different field-line pitches according to the local variation of the rotational transform, however, results in a measured displacement of turbulent structures with respect to the field lines during their radial propagation. A reduction in the perpendicular correlation lengths in regions of high absolute values of local magnetic shear is found. Prominent and poloidally narrow turbulent transport maxima are measured at different toroidal positions. They are connected by the magnetic field lines and located in regions of negative normal curvature. The poloidal propagation pattern of turbulent structures and the exact position of the transport maximum depend on the magnetic field direction.

Recent ion cyclotron range of frequency (ICRF) experiments combined with lower hybrid wave (LHW) on EAST show that LHW coupling can be strongly modified when the LHW launcher is connected magnetically to a powered ICRF antenna. Using Langmuir probes, investigation of radio frequency (RF)-enhanced potential and local plasma parameters under an applied ICRF pulse is carried out on EAST. When the ICRF antenna connected to the probe is powered, localized high positive peaks appear on the floating potential. The dependence of floating potential modifications on various parameters is investigated. These initial results are shown to be consistent with RF sheath physics. A new four-strap antenna is modelled with the high frequency structural simulator (HFSS) code for evaluation of the parallel electrical fields (E_∥) and sheath potentials. It is found that the E_∥ fields with the (0, 0, π, π) phase are much higher than those with other phases. Only the (0, π, π, 0) phasing has a significant reduction potential compared with the original two-strap antenna at the dipole phase.

Self-generation and sustainment of toroidal flux via a dynamo is one of the unique characteristics of the reversed-field pinch (RFP) configuration. In a small aspect ratio RFP machine RELAX, it has been observed that a sudden dynamo usually occurs at a localized toroidal location. This localized dynamo evolves in time, causing a toroidally asymmetric flux distribution. The degree of asymmetry depends on the location and propagation of the localized dynamo. It has been observed that the position where the localized dynamo occurs coincides with the position where the phases of the internally resonant tearing modes align. The phase alignment plays an important role in triggering a localized dynamo activity and in the formation of asymmetric toroidal flux distribution especially in deep-reversal plasmas in RELAX.

The application of resonant magnetic perturbations (RMPs) with a toroidal mode number of n = 4 or n = 6 to lower single null plasmas in the MAST tokamak produces up to a factor of 5 increase in edge-localized mode (ELM) frequency and reduction in plasma energy loss associated with type-I ELMs. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. Despite a large scan of parameters, complete ELM suppression has not been achieved. The results have been compared with modelling performed using either the vacuum approximation or including the plasma response. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. The size of these lobes is correlated with the increase in ELM frequency observed. The characteristics of the mitigated ELMs are similar to those of the natural ELMs suggesting that they are type-I ELMs which are triggered at a lower pressure gradient. The application of the RMPs in the n = 4 and n = 6 configurations before the L–H transition has little effect on the power required to achieve H-mode while still allowing the first ELM to be mitigated.

The modification of particle distributions by magnetohydrodynamic modes is an important topic for magnetically confined plasmas. Low amplitude modes are known to be capable of producing significant modification of injected neutral beam profiles. Flattening of a distribution due to phase mixing in an island or due to portions of phase space becoming stochastic is a process extremely rapid on the time scale of equilibrium parameter changes in an experiment. In this paper, we examine the effect of toroidal Alfvén eigenmodes (TAE) and reversed shear Alfvén eigenmodes (RSAE) in ITER on alpha particle and injected beam distributions using theoretically predicted mode amplitudes using perturbative linear theory. It is found that for the equilibrium of a hybrid scenario even at ten times the predicted saturation level the modes have negligible effect on these distributions. A strongly reversed shear (or advanced) scenario, having a spectrum of modes that are much more global, is somewhat more susceptible to induced loss due to mode resonance, with alpha particle losses of over 1% with predicted amplitudes and somewhat larger with the assistance of toroidal field ripple. The elevated q profile contributes to stronger TAE (RSAE) drive and more unstable modes. An analysis of the existing mode-particle resonances is carried out to determine which modes are responsible for the profile modification and induced loss. We find that losses are entirely due to resonance with the counter-moving and trapped particle populations, with co-moving passing particles participating in resonances only deep within the plasma core and not leading to loss.

When analysing data from fast ion measurements it is normally assumed that the gyro-phase distribution of the ions is isotropic within the field of view of the measuring instrument. This assumption is not valid if the Larmor radii of the fast ions are comparable to—or larger than—the gradient scale length in the spatial distribution of the ions, and if this scale length is comparable to—or smaller than—the width of the field of view of the measuring instrument. In this paper the effect of such an anisotropy is demonstrated by analysing neutron emission spectrometry data from a JET experiment with deuterium neutral beams together with radiofrequency heating at the third harmonic of the deuterium cyclotron frequency. In the experiment, the neutron time-of-flight spectrometer TOFOR was used to measure the neutrons from the d(d,n)³He-reaction. Comparison of the experimental data with Monte Carlo calculations shows that the finite Larmor radii of the fast ions need to be included in the modelling to get a good description of the data. Similar effects are likely to be important for other fast ion diagnostics, such as γ-ray spectroscopy and neutral particle analysis, as well.

The exact electromagnetic gauge invariance of the nonlinear gyrokinetic theory is discussed. It is shown that the guiding-center distribution function is an electromagnetic gauge invariant with all the $O(\epsilon_\delta^2)$ terms in the nonlinear gyrokinetic equations retained. _δ is the amplitude ordering parameter of the perturbations. All the $O(\epsilon_\delta^2)$ terms have to be retained in the nonlinear gyrokinetic simulation to guarantee the electromagnetic gauge invariance.

In the all-tungsten ASDEX Upgrade tokamak nitrogen seeding is a reliable method for radiative cooling at the plasma edge, regularly applied in high power scenarios. Interestingly, in the presence of nitrogen seeding the energy confinement is observed to improve significantly, compared with similar unseeded discharges, with an increase by 10–25% in plasma stored energy and H_IPB98(y,2). In this paper, we document the improvement and we analyse the transport properties in the core plasma, by comparing similar discharges with and without nitrogen seeding. The increase in the suprathermal energy content is assessed as well. The impurity nitrogen is shown not to penetrate significantly into the core plasma. Non-linear gyro-kinetic simulations predict that the improvement observed in the pedestal confinement is transferred to the core via profile stiffness, in agreement with the experimental evidence, whereas the direct contribution from core confinement is small.