Table of contents

Recent progress in 'turbulent optimization' of toroidal configurations is described, using a method recently developed for evolving such configurations to ones having reduced turbulent transport. The method uses the GENE gyrokinetic code to compute the radial heat flux Q_gk, and the STELLOPT optimization code with a theory-based 'proxy' figure of merit Q_pr to stand in for Q_gk for computational speed. Improved expressions for Q_pr have been developed, involving further geometric quantities beyond those in the original proxy, which can also be used as 'control knobs' to reduce Q_gk. Use of a global search algorithm has led to the discovery of turbulent-optimized configurations not found by the standard, local algorithm usually employed, as has use of a mapping capability which STELLOPT has been extended to provide, of figures of merit over the search space.

Time-dependent behavior that follows from a recent theory of the quasi-single-helicity (QSH) state of the reversed field pinch is considered. The theory (Kim and Terry 2012 Phys. Plasmas19 122304) treats QSH as a core fluctuation structure tied to a tearing mode of the same helicity, and shows that strong magnetic and velocity shears in the structure suppress the nonlinear interaction with other fluctuations. By summing the multiple helicity fluctuation energies over wavenumber, we reduce the theory to a predator–prey model. The suppression of the nonlinear interaction is governed by the single helicity energy, which, for fixed radial structure, controls the magnetic and velocity shearing rates. It is also controlled by plasma current which, in the theory, sets the shearing threshold for suppression. The model shows a limit cycle oscillation in which the system toggles between QSH and multiple helicity states, with the single helicity phase becoming increasingly long-lived relative to the multiple helicity phase as plasma current increases.

Plasma flow is damped in stellarators because they are not intrinsically ambipolar, unlike tokamaks, in which the flux-surface averaged radial electric current vanishes for any value of the radial electric field. Only quasisymmetric stellarators are intrinsically ambipolar, but exact quasisymmetry is impossible to achieve in non-axisymmetric toroidal configurations. By calculating the violation of intrinsic ambipolarity due to deviations from quasisymmetry, one can derive criteria to assess when a stellarator can be considered quasisymmetric in practice, i.e. when the flow damping is weak enough. Let us denote by α a small parameter that controls the size of a perturbation to an exactly quasisymmetric magnetic field. Recently, it has been shown that if the gradient of the perturbation is sufficiently small, the flux-surface averaged radial electric current scales as α² for any value of the collisionality. It was also argued that when the gradient of the perturbation is large, the quadratic scaling is replaced by a more unfavorable one. In this paper, perturbations with large gradients are rigorously treated. In particular, it is proven that for low collisionality a perturbation with large gradient yields, at best, an O(|α|) deviation from quasisymmetry. Heuristic estimations in the literature incorrectly predicted an O(|α|^3/2) deviation.

An approximate model for a single fluid three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium with pure isothermal toroidal flow with imposed nested magnetic flux surfaces is proposed. It recovers the rigorous toroidal rotation equilibrium description in the axisymmetric limit. The approximation is valid under conditions of nearly rigid or vanishing toroidal rotation in regions with significant 3D deformation of the equilibrium flux surfaces. Bifurcated helical core equilibrium simulations of long-lived modes in the MAST device demonstrate that the magnetic structure is only weakly affected by the flow but that the 3D pressure distortion is important. The pressure is displaced away from the major axis and therefore is not as noticeably helically deformed as the toroidal magnetic flux under the subsonic flow conditions measured in the experiment. The model invoked fails to predict any significant screening by toroidal plasma rotation of resonant magnetic perturbations in MAST free boundary computations.

Experiments to reveal energetic ion dynamics associated with magnetohydrodynamic activity are ongoing in the Large Helical Device (LHD). Interactions between beam-driven toroidal Alfvén eigenmodes (TAEs) and energetic ions have been investigated. Energetic ion losses induced by beam-driven burst TAEs have been observed using a scintillator-based lost fast-ion probe (SLIP) in neutral beam-heated high β plasmas. The loss flux of co-going beam ions increases as the TAE amplitude increases. In addition to this, the expulsion of beam ions associated with edge-localized modes (ELMs) has been also recognized in LHD. The SLIP has indicated that beam ions having co-going and barely co-going orbits are affected by ELMs. The relation between ELM amplitude and ELM-induced loss has a dispersed structure. To understand the energetic ion loss process, a numerical simulation based on an orbit-following model, DELTA5D, that incorporates magnetic fluctuations is performed. The calculation result shows that energetic ions confined in the interior region are lost due to TAE instability, with a diffusive process characterizing their loss. For the ELM, energetic ions existing near the confinement/loss boundary are lost through a convective process. We found that the ELM-induced loss flux measured by SLIP changes with the ELM phase. This relation between the ELM amplitude and measured ELM-induced loss results in a more dispersed loss structure.

Fast ions are well confined in the stochastic magnetic field of the multiple-helicity (MH) reversed-field pinch (RFP), with fast ion confinement times routinely a factor of 5 to 10 higher than thermal confinement time. Recent experiments have examined the behavior and confinement of beam-born fast ions in the three-dimensional (3D) helical RFP state. In lower current discharges, where the onset of the helical state is uncertain, high power neutral beam injection (NBI) tends to suppress the transition to the single helicity mode. In high current discharges (I_p ∼ 0.5 MA), where the onset of n = 5 single helicity is quite robust, a short blip of NBI is used to probe the confinement of fast ions with minimal perturbation to the 3D equilibrium. The fast ion confinement time is measured to be substantially lower than fast ions in comparable MH RFP states, and there is a strong dependence on the strength of the helical perturbation. The established helical equilibrium is stationary in the laboratory frame but the locking occurs over the entire range of possible phase with respect to the Madison Symmetric Torus vessel. This effectively scans both the location of the NBI with respect to the helical structure and the pitch of the NBI-born fast ions. Fast ion confinement is observed to be insensitive to this angle, and in fact counter-NB injection into quasi-single helicity discharges shows fast ion confinement times similar to co-injection cases, in contrast to the MH RFP, where counter-injected fast ion confinement time is substantially lower.

Edge impurity transport has been studied in the stochastic magnetic field layer called the ergodic layer of the Large Helical Device. Chord-integrated full vertical profiles of C IV (312.4 Å: 1s²3p–1s²2s) near edge X-points are observed at horizontally elongated plasma cross sections. Measured C IV profiles are almost flat at low density (⩽2 × 10¹³ cm⁻³), while two peaks called the 'X-point peak' newly begin to appear near edge separatrix X-points with increase in density in addition to ordinary edge peaks. The X-point peaks become very clear at high-density range (⩾6 × 10¹³ cm⁻³). The C³⁺ ions analyzed with three-dimensional edge plasma transport code, EMC3–EIRENE, move upstream at low density due to large thermal force. The widely expanded C³⁺ distribution makes the C IV profile flat. With increasing the density, the friction force becomes dominant and the impurity ions start to move downstream. The C³⁺ ions stay in the vicinity of the edge X-point where magnetic field lines are very short. The X-point peaks are then clearly formed with increase in the C³⁺ density. Two-dimensional C IV distribution is also observed for different plasma axis positions. It is found that the C IV emission becomes strong along the poloidal trajectory of X-points and the C IV poloidal trace moves from inboard to outboard X-point trajectories when the plasma axis is changed from 3.60 to 3.75 m. The three-dimensional simulation can well reproduce the enhancement of C IV trajectory along the X-point. However, a discrepancy with the experiment is still seen in the C IV intensity between inboard and outboard X-points.

The development of a stellarator–mirror fission–fusion hybrid concept is reviewed. The hybrid comprises of a fusion neutron source and a powerful sub-critical fast fission reactor core. The aim is the transmutation of spent nuclear fuel and safe fission energy production. In its fusion part, neutrons are generated in deuterium–tritium (D–T) plasma, confined magnetically in a stellarator-type system with an embedded magnetic mirror. Based on kinetic calculations, the energy balance for such a system is analyzed. Neutron calculations have been performed with the MCNPX code, and the principal design of the reactor part is developed. Neutron outflux at different outer parts of the reactor is calculated. Numerical simulations have been performed on the structure of a magnetic field in a model of the stellarator–mirror device, and that is achieved by switching off one or two coils of toroidal field in the Uragan-2M torsatron. The calculations predict the existence of closed magnetic surfaces under certain conditions. The confinement of fast particles in such a magnetic trap is analyzed.

The Keda Torus eXperiment (KTX) is a medium-sized reversed field pinch (RFP) device under construction at the University of Science and Technology of China. The KTX has a major radius of 1.4 m and a minor radius of 0.4 m with an Ohmic discharge current up to 1 MA. The expected electron density and temperature are, respectively, 2 × 10¹⁹ m⁻³ and 800 eV. A combination of a stainless steel vacuum chamber and a thin copper shell (with a penetration time of 20 ms) surrounding the plasma provides an opportunity for studying resistive wall mode instabilities. The unique double-C design of the KTX vacuum vessel allows access to the interior of the KTX for easy first-wall modifications and investigations of power and particle handling, a largely unexplored territory in RFP research leading to demonstration of the fusion potential of the RFP concept. An active feedback mode control system is designed and will be implemented in the second phase of the KTX program. The recent progress of this program will be presented, including the design of the vacuum vessel, magnet systems and power supplies.

One of the most interesting research fields in laser–matter interaction studies is the investigation of effects and mechanisms produced by nano- or micro-structured targets, mainly devoted to the enhancing of laser–target or laser–plasma coupling. In intense and ultra-intense laser interaction regimes, the observed enhancement of x-ray plasma emission and/or hot electron conversion efficiency is explained by a variety of mechanisms depending on the dimensions and shape of the structures irradiated. In the present work, the attention is mainly focused on the lowering of the plasma formation threshold which is induced by the larger absorptivity.

Flat and nanostructured silicon targets were here irradiated with an ultrashort laser pulse, in the range 1 × 10¹⁷–2 × 10¹⁸ W µm² cm⁻². The effects of structures on laser–plasma coupling were investigated at different laser pulse polarizations, by utilizing x-ray yield and 3/2ω harmonics emission. While the measured enhancement of x-ray emission is negligible at intensities larger than 10¹⁸ W µm² cm⁻², due to the destruction of the structures by the amplified spontaneous emission (ASE) pre-pulse, a dramatic enhancement, strongly dependent on pulse polarization, was observed at intensities lower than ∼3.5 × 10¹⁷ W µm² cm⁻². Relying on the three-halves harmonic emission and on the non-isotropic character of the x-ray yield, induced by the two-plasmon decay instability, the results are explained by the significant lowering of the plasma threshold produced by the nanostructures. In this view, the strong x-ray enhancement obtained by s-polarized pulses is produced by the interaction of the laser pulse with the preplasma, resulting from the interaction of the ASE pedestal with the nanostructures.

In a magnetized plasma, particles may simultaneously be in resonance with two waves with essentially different frequencies and wave vectors. Such a situation is studied by an example of parallel propagating whistler-mode wave and highly oblique lower hybrid resonance wave. Depending on the relations between wave amplitudes and the distance between resonances in velocity space, particle dynamics varies considerably, and has different statistical properties. For well separated resonant regions related to each wave, the two wave problem is almost decoupled. When the resonant regions overlap, the particle motion becomes stochastic inside a bounded region of the phase space. The most striking effect happens when the resonance velocities are very close, and a phase trapping, typical of one wave problem, occurs. In the case of two waves, however, this trapping is asymmetric and leads to a monotonic or quasi-monotonic variation of particle momenta on a time scale much larger than the nonlinear period. The statistical characteristics of particle dynamics in the last two cases and possible applications to space plasmas are discussed.

We use three-dimensional simulations to study injection and electron beam quality in laser wakefield acceleration (LWFA) using the density transition technique. We vary the density transition length scale, covering both the sharp and gradual density transition regimes. We find that the injected charge decreases monotonically as the density transition scale length increases, and as a consequence the energy-spread and emittance improve monotonically. Therefore, there is no optimal transition length that gives the best quality beam, contrary to earlier suggestions. However, the density transition technique does give high brightness electron beams with kA current, energy-spread of around 1% and normalized rms emittance of around 1π mm-mrad. We study the application of these LWFA beams as drivers for a short-wavelength free-electron laser (FEL), using analytic formulae as well as three-dimensional simulations. Because higher current favours a shorter transition length, while smaller energy-spread and emittance favour a longer transition length, there is now an optimal density transition scale length (for our parameters, 50 µm) that gives the best FEL performance: lasing at 270 nm, with a saturated power of around 360 MW, over an undulator length of only 6 m. Further improvements, like lower plasma density and laser guiding, could result in GeV-class beams of sufficient brightness to drive a soft x-ray FEL.

A high-power edge-localized mode (ELM) striking onto divertor components presents one of the strongest lifetime and performance challenges for plasma facing components in future fusion reactors. A high-repetition-rate ELM replication system has been constructed and was commissioned at the Magnum-PSI linear device to investigate the synergy between steady state plasma exposure and the large increase in heat and particle flux to the plasma facing surface during repeated ELM transients in conditions aiming to mimic as closely as possible those in the ITER divertor. This system is capable of increasing the electron density and temperature from ∼1 × 10²⁰ m⁻³ to ∼1 × 10²¹ m⁻³ and from 1 to 5 eV respectively, leading to a heat flux increase at the surface to ∼130 MW m⁻². By combining Thomson scattering measurements with heat fluxes determined using the THEODOR code, the sheath heat transmission factor during the pulses was determined to be ≈7.7, in agreement with sheath theory. The heat flux is found to be linearly dependent upon the strength of the magnetic field at the target position, and, by adapting the system to Pilot-PSI, tests at 1.6 T showed heat fluxes of more than 600 MW m⁻². This gives confidence that with the installation of a 2.5 T superconducting magnetic solenoid at Magnum-PSI the heat flux will reach the ITER-relevant gigawatt per square metre heat flux regime.

The physical models implemented in the recently developed dust dynamics code MIGRAINe are described. A major update of the treatment of secondary electron emission, stemming from models adapted to typical scrape-off layer temperatures, is reported. Sputtering and plasma species backscattering are introduced from fits of available experimental data and their relative importance to dust charging and heating is assessed in fusion-relevant scenarios. Moreover, the description of collisions between dust particles and plasma-facing components, based on the approximation of elastic-perfectly plastic adhesive spheres, has been upgraded to take into account the effects of particle size and temperature.

The ITER magnetic diagnostic response to applied n = 3 and n = 4 resonant magnetic perturbations (RMPs) has been calculated for the 15 MA scenario. The VMEC code was utilized to calculate free boundary 3D ideal magnetohydrodynamic equilibria, where the non-stellarator symmetric terms were included in the calculation (Hirshman and Whitson 1983 Phys. Fluids26 3553). This allows an assessment to be made of the possible boundary displacements due to RMP application in ITER. As the VMEC code assumes a continuous set of nested flux surface, the possibility of island and stochastic region formation is ignored. At the start of the current flat-top (L-mode) application of n = 4 RMPs indicates approximately 1 cm peak-to-peak displacements on the low field side of the plasma while later in the shot (H-mode) perturbations as large as 3 cm are present. Forward modeling of the ITER magnetic diagnostics indicates significant non-axisymmetric plasma response, exceeding 10% the axisymmetric signal in many of the flux loops. Magnetic field probes seem to indicate a greater robustness to 3D effects but still indicate large sensitivities to 3D effects in a number of sensors. Forward modeling of the diagnostics response to 3D equilibria allows assessment of diagnostics design and control scenarios.

A long-lasting (for hundreds of milliseconds) m/n = 1 energetic particle mode driven by trapped fast ions, other than conventional fishbone bursts, is studied theoretically and in comparison with HL-2A experimental results. The mode can be observed in weak shear tokamak plasmas during neutral beam injection with a mostly steady amplitude envelope of long-lasting magnetic perturbation signals. The dispersion relation and radial structure of the mode are calculated with a weak shear q-profile. Both the m/n = 1/1 component and its higher frequency m/n = 2/2 harmonics are found to be unstable, in good agreement with experimental observations on HL-2A. On the other hand, due to the feature of weak magnetic shear, the mode is also significantly different from bursty fishbones, especially the mode structure, temporal behavior, instability threshold and growth rate dependence on the fast ion gradient. The nonlinear evolution of the mode and the comparison with fishbone bursts are also further investigated.

This paper investigates hybrid kinetic-magnetohydrodynamic (MHD) models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern hybrid simulations. This latter scheme suffers from being non-Hamiltonian and is unable to exactly conserve total energy. Upon adopting the Vlasov description for the hot component, the non-Hamiltonian PCS and a Hamiltonian variant are compared. Special emphasis is given to the linear stability of Alfvén waves, for which it is shown that a spurious instability appears at high frequency in the non-Hamiltonian version. This instability is removed in the Hamiltonian version.

The synergetic effects of feedback and toroidal plasma rotation on the stability of the resistive wall mode are systematically investigated by a full toroidal magnetohydrodynamic stability code MARS-F (Liu Y Q et al 2000 Phys. Plasmas7 3681). This synergy is studied for both resistive and ideal plasma models. It is found that a magnetic feedback scheme, combined with the passive stabilization from the plasma flow, can open two stability windows as the resistive wall moves away from the plasma, as opposed to the single stability window opened by the plasma flow alone. The width of the new stability window increases with the feedback gain. The plasma rotation frequency affects both stability windows. The synergy is achieved when the feedback pushes the mode rotating in the same direction as the plasma flow. The plasma resistivity significantly enlarges the stable domain in this synergetic scheme, compared to that predicted by the ideal plasma model.

This paper describes a detailed examination of the effects of a relatively small pulsed deuterium gas puff on the edge plasma and edge turbulence in NSTX. This gas puff caused little or no change in the line-averaged plasma density or total stored energy, or in the edge density and electron temperature up to the time of the peak of the gas puff. The radial profile of the Dα light emission and the edge turbulence within this gas puff did not vary significantly over its rise and fall, implying that these gas puffs did not significantly perturb the local edge plasma or edge turbulence. These measurements are compared with modeling by DEGAS 2, UEDGE, and with simplified estimates for the expected effects of this gas puff.

Effects of carbon impurities on the thermal confinement properties were discussed for carbon-pellet-injected high-T_i discharges in the Large Helical Device (LHD). To clarify their role, the amounts of carbon impurities introduced into plasmas were scanned by varying the number of injections in a discharge or the size of the pellet, and the changes of thermal confinement properties with these variations were examined. In all cases, strong correlations between the densities of carbon impurities and the thermal diffusivities of plasmas were found. Thermal diffusivities were small when the carbon densities were greater than a certain value, e.g. ∼1.5 × 10¹⁷ m³ at r/a ≈ 0.72, and the thermal diffusivity degraded drastically below this density. This indicates the existence of a threshold density of carbon impurity for an improved confinement in plasmas. Combined with the formation of the impurity hole, the variation of confinement property with carbon density can explain the degradation of ion temperature in high-T_i discharges with carbon pellet injection in the LHD.

Time-series analysis of magnetics data in tokamaks is typically done using block-based fast Fourier transform methods. This work presents the development and deployment of a new set of algorithms for magnetic probe array analysis. The method is based on an estimation technique known as stochastic subspace identification (SSI). Compared with the standard coherence approach or the direct singular value decomposition approach, the new technique exhibits several beneficial properties. For example, the SSI method does not require that frequencies are orthogonal with respect to the timeframe used in the analysis. Frequencies are obtained directly as parameters of localized time-series models. The parameters are extracted by solving small-scale eigenvalue problems. Applications include maximum-likelihood regularized eigenmode pattern estimation, detection of neoclassical tearing modes, including locked mode precursors, and automatic clustering of modes, and magnetics-pattern characterization of sawtooth pre- and postcursors, edge harmonic oscillations and fishbones.

In this study, we theoretically explore properties of non-resonant fishbone (NRF) instabilities with a safety factor profile slightly above unity (q_min ≳ 1) in tokamak plasmas with reversed magnetic shear configuration. From the dispersion relation of the NRF mode, it is found that the growth rate of the mode in general reversed shear scenarios with q_min ≳ 1 depends on fast ion beta β_h in a power law of ${\sim} \beta_{h}^{2/3}$, different from that of ∼β_h in a conventional positive magnetic shear configuration. Meanwhile, due to the slow ion precession and small continuum damping in ITER-like tokamaks with reversed shear, the mode has a lower trigger threshold than those with monotonously positive magnetic shear. In addition, the ion diamagnetic drift has been found to destabilize the fast ion-driven NRF mode. Other effects such as the shape of the q-profile, characterized by values of q_min and q(0), neutral beam energy, magnetohydrodynamic potential energy and the fraction of fast ions on the instability threshold are also discussed. Nonlinear behavior of the mode is further analyzed using a modified model.

Recent work has demonstrated that breaking the up–down symmetry of tokamak flux surfaces removes a constraint that limits intrinsic momentum transport, and hence toroidal rotation, to be small. We show, through MHD analysis, that ellipticity is most effective at introducing up–down asymmetry throughout the plasma. We detail an extension to GS2, a local δf gyrokinetic code that self-consistently calculates momentum transport, to permit up–down asymmetric configurations. Tokamaks with tilted elliptical poloidal cross-sections were simulated to determine nonlinear momentum transport. The results, which are consistent with the experiment in magnitude, suggest that a toroidal velocity gradient, (∂u_ζi/∂ρ)/v_thi, of 5% of the temperature gradient, (∂T_i/∂ρ)/T_i, is sustainable. Here v_thi is the ion thermal speed, u_ζi is the ion toroidal mean flow, ρ is the minor radial coordinate normalized to the tokamak minor radius, and T_i is the ion temperature. Though other known core intrinsic momentum transport mechanisms scale poorly to larger machines, these results indicate that up–down asymmetry may be a feasible method to generate the current experimentally measured rotation levels in reactor-sized devices.

Microscopic turbulence properties in the edge of toroidally confined fusion plasmas are studied by comparative analysis of experimental data from seven devices, collected in an international edge turbulence database. The database contains Langmuir probe measurements of fluctuations in the floating potential and ion saturation current across the last closed flux surface. They are used to address statistical properties and particle transport. Universal features of plasma edge turbulence such as an increase in skewness across the scrape-off layer (SOL) as footprints of density blobs are recovered in all devices. Analysis of the correlation lengths and times reveals power law scaling relations with macroscopic drift-wave parameters, albeit weaker than would be expected for drift-wave turbulence. As a result, the turbulent diffusivity scales with the inverse of the magnetic field strength, which is closer to Bohm-like scaling than to gyro-Bohm scaling. Nearly identical scaling relations are determined in the confined plasma edge and the SOL, pointing to a strong connection between drift-wave turbulence in the edge and blobs in the SOL. The contributions of blobs and holes (negative density spikes) to the radial particle transport are analyzed qualitatively with a conditional averaging approach. Blobs are connected to outward transport in the SOL of all devices whereas holes exhibit no uniform propagation pattern.

Edge turbulence and blobs are studied in the three-dimensional magnetic topology of the RFX-mod reversed field pinch. The edge of the RFX-mod shows a three-dimensional structure dominated by a helical equilibrium with (1, −7) symmetry, which gives the same space-time modulation to all of the kinetic properties. The interaction between the edge turbulence and this magnetic topology is studied. It is shown that the edge blobs are current-carrying filaments aligned with the magnetic field, and in the perpendicular plane each blob is a positive peak of electron density and a valley of temperature. The inner nature of these blobs is not affected by the presence of the O and X points of the (1, −7) island; however, the statistical properties are sensitive to them, pointing to the influence of the magnetic topology on the edge fluctuations.

The design of an electron cyclotron emission imaging (ECEI) system for two-dimensional (2D) observation of the magnetohydrodynamical modes in high temperature ITER (from 'International Thermonuclear Experimental Reactor') H-mode-like plasmas (5.3 T and 25 keV) based on fundamental ordinary mode (O1-mode) and second-harmonic extraordinary mode (X2-mode) measurements is explored conceptually. For studying the spatial resolution in high temperature plasmas, the relativistic broadening and inward shift of the emission layer in the mid-plane are calculated. The radial spatial resolution is significantly degraded in the range R < 5.1 m for the O1-mode and in the range R < 6.9 m for the X2-mode. The region with R < 6.5 m is inaccessible for X2-mode study. The emission layer width is enlarged in a narrow region of the pedestal due to the magnetic field being modified by the large pressure gradient. The broadening and shift in the poloidal plane are also calculated, to investigate their effects on 2D measurements. The frequency range of electron cyclotron emission measurements is selected to protect the system from stray radiations of the 170 GHz electron cyclotron resonance heating source and to avoid harmonic overlap. The frequency ranges of 115–160 GHz for the O1-mode and 230–320 GHz for the X2-mode provide radial coverage of 5.9 < R < 8.2 m or −0.15 < r/a < 1.The ECEI system utilizes a dual-array detection technique which provides a simultaneous measurement at two radial positions, and each array has 8 by 16 (radial by vertical) channels. The radial image size with 8 channels is ∼41–76 cm for the O1-mode and ∼19–36 cm for the X2-mode, with sufficient resolution. The front-end optics, which focuses the electron cyclotron emission to the low loss corrugated transmission waveguides, is designed with two flat mirrors and two focusing mini-lens arrays. The vertical image size with 16 channels is ∼150 cm and the spot size of each channel is 8–15 cm in the plasma region, taking into account the sensitivity pattern of the waveguide. The refraction effect due to inhomogeneous plasma enlarges the vertical image size up to 20% and 5% for the O1-mode and X2-mode cases, respectively. The horizontal distortion due to the relativistic inwards shift is reduced by the increased toroidal field in the core region.

Observations of lower hybrid (LH) radio frequency heating effects on toroidal plasma rotation in L-mode Tore Supra plasmas are reported. A database of more than 50 plasma discharges has been analysed. Core rotation is found to increment in co- or counter-current direction depending on the plasma current (I_p). At low plasma current, the induced rotation is up to +15 km s⁻¹ in the co-current direction, the rotation profile being affected over the whole plasma minor radius. At higher plasma current, an opposite trend is observed, the core plasma rotation incrementing up to −15 km s⁻¹ in the counter-current direction, the profile being affected up to r/a < 0.6 only. At the zero crossing point, which is defined when the plasma rotation profile is not affected by LH power injection, I_p ∼ 0.95 MA. In both low and high I_p cases, rotation increments are found to increase with the injected power. Several mechanisms in competition which can induce co- or counter-current rotation in Tore Supra LHCD plasmas are investigated and typical order of magnitude are discussed. How those effects evolve with plasma parameters and how they compete are important issues addressed in this paper. Rotation increment increase with I_p at fixed LH power is consistent with a dominant standard momentum confinement mechanism related to I_p increase. The co-current change in rotation is consistent with a fast electron ripple loss mechanism, while thermal ripple induced neoclassical friction and absorbed LH wave momentum from resonant electrons are expected to influence the rotation in the counter-current direction. Finally, the numerical simulations show that the radial turbulent momentum transport does impact the rotation behaviour inducing increment in co- or counter-current directions, depending on the plasma current amplitude.

With the advent of applied 3D fields in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous slowing down, and pitch angle scattering are modeled with the ADAS atomic physics database. Elementary benchmark calculations are presented to verify the collisionless particle orbits, NBI model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.

Global particle simulations of the lower hybrid (LH) waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The LH wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a LH wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. This poloidal asymmetry arises from the non-conservation of the poloidal mode number due to the non-uniform magnetic field. In contrast, the poloidal mode number is conserved in the cylindrical geometry with the uniform magnetic field.

Equilibrium pressure profiles of plasmas confined in the field of a dipole magnet are reconstructed using magnetic and x-ray measurements on the levitated dipole experiment (LDX). LDX operates in two distinct modes: with the dipole mechanically supported and with the dipole magnetically levitated. When the dipole is mechanically supported, thermal particles are lost along the field to the supports, and the plasma pressure is highly peaked and consists of energetic, mirror-trapped electrons that are created by electron cyclotron resonance heating. By contrast, when the dipole is magnetically levitated losses to the supports are eliminated and particles are lost via slower cross-field transport that results in broader, but still peaked, plasma pressure profiles.

A large 3D data set has been assembled using the relaxation scaling experiment (RSX) device to study the dynamics of flux ropes. In a series of single flux rope experiments, we have measured induced eddy currents inside the plasma that complicate the evolution of a nominally simple current system. It is also likely that the nominal MHD force balance is violated on ion inertial length scales. These phenomena appear irreducibly three dimensional.

Measurements of the dynamical behavior associated with edge localized modes (ELMs) have been carried out in the Experimental Advanced Superconducting Tokamak (EAST) by direct probing near the separatrix and far scrape-off layer (SOL) using electrostatic as well as magnetic probes. Type-III ELMs and dithering cycles have been investigated near the threshold power for the transition from the low confinement mode (L-mode) to the high confinement mode (H-mode). A precursor is observed prior to type-III ELM events with chirping frequency (130–70 kHz). It is located inside the separatrix and does not lead to considerable particle transport into the SOL. Distinct from type-III ELMs, no precursor modes precede the dithering cycles. It is evident from our measurements that the absence of precursor activity is a good indicator to distinguish the dithering cycles from type-III ELMs. A number of distinct current filaments are identified slightly inside the separatrix, both during type-III ELM events and dithering cycles. The characteristic current topology in these filaments is still ambiguous in our investigations. Furthermore, small ELMs are observed in type-I ELMy-like H-mode discharge regimes on EAST, in which solitary monopolar current filaments are observed to propagate in the SOL.

The influence of the curvature of the imposed magnetic field on reversed field pinch dynamics is investigated by comparing the flow of a magnetofluid in a torus with aspect ratio 1.83, with the flow in a periodic cylinder. It is found that an axisymmetric toroidal mode is always present in the toroidal, but absent in the cylindrical configuration. In particular, in contrast to the cylinder, the toroidal case presents a double poloidal recirculation cell with a shear localized at the plasma edge. Quasi-single-helicity states are found to be more persistent in toroidal than in periodic cylinder geometry.

This paper is devoted to the oscillatory screening effect on the electron scattering spin-asymmetry and spin-channel preference in quantum plasmas. It is found that the oscillatory quantum screening effects enhance the spin-singlet electron-scattering channel, but suppress the spin-triplet electron-scattering channel for the forward and backward scattering directions with increasing wave number for small quantum wave numbers. It is also found that the preference of the spin-singlet scattering, including the influence of oscillatory quantum shielding, has been reduced with increasing quantum wave number. The variation of the angular averaged scattering spin-asymmetry phenomenon is also discussed.

It is crucial for magnetic fusion devices that particle confinement occurs for long periods in a magnetic flux tube, and radial loss from the flux tube by a collision-free radial drift needs to be eliminated. Longitudinal, as well as radial, confinement is required. Two standard constants of motion, the energy and the magnetic moment of the gyrating particle, provide longitudinal confinement. A third constant of motion, which implies bounded radial motion, would be sufficient for radial confinement, but it is often impossible to identify such an invariant. A closed form expression for a radial invariant is derived for magnetic mirrors with a stabilizing quadrupolar field. A weak radial electric field, controlled by electrically biased endplates, is a tool for making a collision-free motion radially bounded in open systems. Experimental results in such magnetic confinement schemes indicate a qualitative agreement with our predictions for the existence of a radial invariant. Voltage and power requirements for the biased endplates are vanishingly small if the magnetic drifts are minimized in the magnetic field design. The power requirements to sustain the biased potentials are expected to be vanishingly small for a gross stable plasma.

The modulational instability and envelope solitons of ion acoustic waves in an unmagnetized nonthermal electron–positron–ion (epi) plasma are investigated. The ions are taken to be dynamic and warm while electrons and positrons are assumed to be inertialess and hot which follow the kappa (or Generalized Lorentzian) distribution. The Krylov–Bogoliubov–Mitropolsky method is used to derive the nonlinear Schrödinger equation for nonlinear amplitude modulation of ion acoustic waves in nonthermal epi plasmas with warm ions. The dispersive and nonlinear coefficients are obtained for ion acoustic waves in nonthermal epi plasmas which depend on spectral indices of kappa distributed electrons and positrons, ion temperature and positron density. The modulationally stable and unstable regions are studied for a wide range of wave numbers and it is found that the finite ion temperature, positron density and spectral indices of kappa distributed electrons and positrons play a significant role in the formation of bright and dark envelope solitons in nonthermal epi plasmas with adiabatically heated ions. Our findings are applicable to explain some aspects of nonlinear propagation of envelope solitons in astrophysical plasma situations such as neutron stars or pulsars where nonthermal epi plasmas with warm ions can exist (Arons J 2009 Astrophys. Space Sci. Library357 373, Blasi P and Amato E 2011 Astrophys. Space Sci. Proc. pp 623–41, Asif and Saeed 2011 Plasma Phys. Control. Fusion53 095006).

Transport of hydrocarbon impurities in a high-density (>10²⁰ m⁻³), low-temperature (<2 eV) plasma beam was studied with the ERO code. The high ion density and low temperature cause strong Coulomb collisionality between plasma ions and impurity ions. The collisionality is so strong that ions typically do not complete their Larmor orbits. The high collisionality causes impurity entrainment: impurity ions quickly acquire a velocity close to the plasma flow velocity. This causes a relatively high surface impact energy: the calculated mean impact energy of CH_x was 8.1 eV in a plasma with T_e = 0.7 eV. Simulation results were compared to an a-C : H erosion experiment in the linear plasma generator Pilot-PSI. The large uncertainties in literature values for the sticking probability of hydrocarbon radicals are shown to cause a serious uncertainty in the calculated re-deposition pattern. In contrast, the radial electric field component perpendicular to the axial magnetic field lines did not have a major effect on the redeposition profile.

We model the dissociation of injected methane (¹³CH₄) and nitrogen (¹⁵N₂) molecules and the subsequent transport of tracer ions in ASDEX Upgrade (AUG) low confinement (L-mode) plasma conditions resembling a tracer injection experiment conducted in 2011. Based on simulations with the ERO code, the dissociation is predicted to occur relatively close to the injection port in the far-scrape-off layer (far-SOL) plasma with the dissociation location moving closer to the injection location with increasing plasma density and heating power. Simulations of global transport of the tracer ions resulting from the dissociation using the ASCOT code predict that the decreasing penetration depth of the molecules (dissociation in the far-SOL) increases the ratio between main chamber and divertor deposition.

Analysis of neutron and fast-ion D_α data from the DIII-D tokamak shows that Alfvén eigenmode activity degrades fast-ion confinement in many high β_N, high q_min, steady-state scenario discharges. (β_N is the normalized plasma pressure and q_min is the minimum value of the plasma safety factor.) Fast-ion diagnostics that are sensitive to the co-passing population exhibit the largest reduction relative to classical predictions. The increased fast-ion transport in discharges with strong AE activity accounts for the previously observed reduction in global confinement with increasing q_min; however, not all high q_min discharges show appreciable degradation. Two relatively simple empirical quantities provide convenient monitors of these effects: (1) an 'AE amplitude' signal based on interferometer measurements and (2) the ratio of the neutron rate to a zero-dimensional classical prediction.

This is a correction to a reference error in our paper 'Quasi-separatrix layer reconnection for nonlinear line-tied collisionless tearing modes', which appeared in the special issue 'Self-organization in Magnetic Flux Ropes Cluster' in Plasma Physics and Controlled Fusion earlier in 2014.