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The Mega Ampère Spherical Tokamak (MAST) programme is strongly focused on addressing key physics issues in preparation for operation of ITER as well as providing solutions for DEMO design choices. In this regard, MAST has provided key results in understanding and optimizing H-mode confinement, operating with smaller edge localized modes (ELMs), predicting and handling plasma exhaust and tailoring auxiliary current drive. In all cases, the high-resolution diagnostic capability on MAST is complemented by sophisticated numerical modelling to facilitate a deeper understanding. Mitigation of ELMs with resonant magnetic perturbations (RMPs) with toroidal mode number n RMP = 2, 3, 4, 6 has been demonstrated: at high and low collisionality; for the first ELM following the transition to high confinement operation; during the current ramp-up; and with rotating n RMP = 3 RMPs. n RMP = 4, 6 fields cause less rotation braking whilst the power to access H-mode is less with n RMP = 4 than n RMP = 3, 6. Refuelling with gas or pellets gives plasmas with mitigated ELMs and reduced peak heat flux at the same time as achieving good confinement. A synergy exists between pellet fuelling and RMPs, since mitigated ELMs remove fewer particles. Inter-ELM instabilities observed with Doppler backscattering are consistent with gyrokinetic simulations of micro-tearing modes in the pedestal. Meanwhile, ELM precursors have been strikingly observed with beam emission spectroscopy (BES) measurements. A scan in beta at the L–H transition shows that pedestal height scales strongly with core pressure. Gyro-Bohm normalized turbulent ion heat flux (as estimated from the BES data) is observed to decrease with increasing tilt of the turbulent eddies. Fast ion redistribution by energetic particle modes depends on density, and access to a quiescent domain with ‘classical’ fast ion transport is found above a critical density. Highly efficient electron Bernstein wave current drive (1 A W−1) has been achieved in solenoid-free start-up. A new proton detector has characterized escaping fusion products. Langmuir probes and a high-speed camera suggest filaments play a role in particle transport in the private flux region whilst coherence imaging has measured scrape-off layer (SOL) flows. BOUT++ simulations show that fluxes due to filaments are strongly dependent on resistivity and magnetic geometry of the SOL, with higher radial fluxes at higher resistivity. Finally, MAST Upgrade is due to begin operation in 2016 to support ITER preparation and importantly to operate with a Super-X divertor to test extended leg concepts for particle and power exhaust.

The interaction of L-mode and inter-ELM Scrape-Off Layer (SOL) filaments is investigated by simulating the dynamics of two seeded density perturbations with different initial separation. A numerical campaign of 2D and 3D simulations is presented to explore the effect that different filaments’ perpendicular size and relative distance have on their reciprocal action. It is shown that the interaction is weak unless the filaments are in close proximity, i.e. with a separation of the order of the filaments’ diameter in the drift plane. The interaction occurs when the dipolar electrostatic fields associated with the filaments merge or cancel each other and it leads to changes in the radial velocity in the centre of mass of the system that are modest (≤ 50%) and quickly decaying with separation. These results show that filaments travelling in the SOL can be considered to a good approximation as independent entities.

Using high speed imaging of the divertor volume, the region close to the X-point in MAST is shown to be quiescent. This is confirmed by three different analysis techniques and the quiescent X-point region (QXR) spans from the separatrix to the ψ N = 1 . 02 flux surface. Local reductions to the atomic density and effects associated with the camera viewing geometry are ruled out as causes of the QXR, leaving quiescence in the local plasma conditions as being the most likely cause. The QXR is found to be ubiquitous across a significant operational space in MAST including L-mode and H-mode discharges across maximal ranges of 9 . 8 × 10 19 m − 2 in line integrated density, 0 . 36MA in plasma current, 0 . 11T in toroidal magnetic field and 3 . 2MW in NBI power. When mapped to the divertor target the QXR occupies approximately an e-folding length of the heat-flux profile, containing ∼ 60% of the total heat flux to the target, and also shows a tendency towards higher frequency shorter lived fluctuations in the ion-saturation current. This is consistent with short- lived divertor localised filamentary structures observed further down the outer divertor leg in the camera images, and suggests a complex multi-region picture of filamentary transport in the divertor.

The linear stability parameter delta is commonly used as a figure of merit for the nonlinear dynamics of the tearing mode. It is shown, through state of the art numerical simulations, that factors other than delta can play a very important role in determining the evolution of nonlinear magnetic islands. In particular, two different equilibria are analysed and it is shown that, once perturbed, they have a qualitatively and quantitatively different response despite the fact that they are characterised by the same delta. The different behaviour can still be associated with linear properties of the equilibrium. It is also studied how the nonlinear and saturation phase are affected by an increasing delta in the two equilibria. As the instability drive is increased, the systems move from a dynamics characterised by a "universal" generalised Rutherford equation to a Y-point configuration and then to a plasmoid unstable Y-point. Finally, for even larger delta the second harmonic overcomes the fundamental,leading to an interesting double island structure., 5 pages, 4 figures. This article has been submitted to Physical Review Letters. After it is published, it will be found at http://journals.aps.org/prl/

We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, . The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered , where is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with . By using these new coordinates as variables in the limit , we obtain a generalised ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.

Statistical analysis of the ion flux to the JET outer-wall is conducted in outer-wall limiter mounted Langmuir probe (OLP) time-series across a wide range of plasma current and line-averaged density during Ohmically heated horizontal target L-mode plasmas. The mean, μ, and the standard deviation, σ, of the ion-saturation current measured by the OLP show systematic variation with plasma current and density. Both increase as either plasma current decreases and/or density increases. Upon renormalization, achieved by subtraction of μ and rescaling by σ, the probability distribution functions (PDFs) of each signal collapse approximately onto a single curve. The shape of the curve deviates from a distribution in the tail of the PDF and is better described by a log-normal distribution. The invariance in the shape of the PDF, which occurs over approximately four decades of the ordinate, is shown to be the result of a balance between the duration time of the average burst wave-form, and the waiting time between bursts, . This implies that the intermittency parameter, , can be considered constant at the JET outer wall during horizontal target Ohmic L-mode operation. This result may be important both for model validation and prediction.

Numerical simulations of L-mode plasma turbulence in the Scrape Off Layer of MAST are presented. Relevant features of the boundary plasma, such as the thickness of the density layer or the statistics of the fluctuations are related to the edge density and temperature, plasma current and parallel connection length. It is found that the density profile is weakly affected by the edge density, it broadens when the current or the temperature are decreased while the connection length has the opposite effect. The statistics of the turbulence is relatively insensitive to variations of all the edge parameters and show a certain degree of universality. Effective transport coefficients are calculated for several plasma conditions and display a strong nonlinear dependence on the parameters and on the radial variable. Finally, it is shown how the perpendicular particle fluxes in the Scrape Off Layer are related to the edge parameters., Comment: 21 pages, 6 figures

A theoretical framework is developed to clarify the relation between the profiles of density and temperature in the Scrape Off Layer (SOL) with the fluctuations (filaments) that generate them. The framework is based on the dynamics of independent filaments and on their statistical behaviour and can be used to rigorously understand the mechanisms that lead to the non-exponential nature of the radial SOL profiles as well as the increase of the relative fluctuation amplitude in the far SOL. Several models for the dynamics of the filaments, which can be applied to the framework, are derived and discussed for the purpose of identifying how different assumptions lead to the emergence of features in the profiles. It is found that multiple alternative models can explain the observations, thus motivating more stringent and focused experimental analysis. In particular, radially accelerating filaments, less efficient parallel exhaust and also a statistical distribution of the velocity of the filaments can all contribute to induce flatter profiles in the far SOL. A quite general result is the resiliency of the non-exponential nature of the profiles. At the same time, several of the models discussed can also capture the increase of the relative fluctuation amplitude observed in the far SOL. It is also shown that several scenarios are compatible with the broadening of the SOL, which could be caused by charge exchange interactions with neutral particles or by a significant radial acceleration of the filaments., Comment: 28 pages, 5 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. arXiv admin note: text overlap with arXiv:1604.08790

Simulations have been carried out to establish how electron thermal physics, introduced in the form of a dynamic electron temperature, affects isolated filament motion and dynamics in 3D. It is found that thermal effects impact filament motion in two major ways when the filament has a significant temperature perturbation compared to its density perturbation: They lead to a strong increase in filament propagation in the bi-normal direction and a significant decrease in net radial propagation. Both effects arise from the temperature dependence of the sheath current which leads to a non-uniform floating potential, with the latter effect supplemented by faster pressure loss. The reduction in radial velocity can only occur when the filament cross-section loses angular symmetry. The behaviour is observed across different filament sizes and suggests that filaments with much larger temperature perturbations than density perturbations are more strongly confined to the near SOL region., Comment: 24 pages, 15 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The linear stability of the tearing mode (TM) in a plasma column is investigated in the presence of viscosity and finite equilibrium current density gradients (i.e., asymmetries). It is shown that for low beta, both effects are essential in order to properly describe the mode behaviour close to marginality. In particular, the theory introduces a critical threshold for the destabilization, such that the perturbation grows only if Delta'>Delta'(cr). The value of Delta'(cr) depends on the equilibrium configuration and on the plasma parameters. Most importantly, Delta'(cr) can take negative values, thus allowing unstable tearing modes for Delta' < 0 (even in the absence of bootstrap current). [doi:10.1063/1.3660410]

The nonlinear saturation of the tearing mode is revisited in slab geometry by taking into account higher-order harmonics in the outer solution. The general formalism for tackling this problem in the case of a vanishing current gradient at the resonant surface is derived. It is shown that, although the higher-order harmonics lead to corrections in the final saturation equation, they are of higher order in the perturbation parameter, which provides a formal proof that the standard one-harmonic approach is asymptotically correct., Comment: Accepted to Plasma Physics and Controlled Fusion

New, rigorous results for the tearing island saturation problem are presented. These results are valid for the realistic case where the magnetic island structure is non-symmetric about the reconnection surface and the electron temperature, on which the electrical resistivity depends, is evolved self-consistently with the island growth.

It is shown that local features of the equilibrium current density profile, i.e., its gradient and curvature evaluated at the resonant magnetic surface, can modify considerably the linear behavior of tearing modes. These features can become particularly important in cylindrical geometry, at moderate values of the electrical resistivity and of the tearing stability parameter, Δ′. A new analytic dispersion relation is derived, which takes into account in a consistent way these new terms and which agrees very well with numerically computed growth rates.

Recent theoretical work on magnetic reconnection in hot plasma confinement devices is reviewed. The presentation highlights the common aspects of reconnection phenomena, and current research trends are emphasized. Progress in understanding the dynamics of slowly evolving modes of the tearing family, based on advanced analytic techniques and numerical simulation, as well as of faster modes that lead to internal disruptions, is reported.

Unstable electrostatic resistive modes, driven by density gradients, are identified in a bounded sheared slab. The boundary conditions play a crucial role and are shown to change the nature of the problem, which is related to so called "universal" mode. The dispersion relation and the structure of the eigenmodes of the instability are derived and are shown to depend on a limited set of dimensionless parameters. The occurrence and possible impact of these modes on numerical simulations and actual plasmas are discussed., Comment: 27 pages, 10 figures. The following article has been submitted to Physics of Plasmas. After it is published it will be found at http://pop.aip.org/pop

New diagnostic, modelling and plant capability on the Mega Ampère Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved Ti measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L-H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. Te inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfvén eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows. © 2013 IAEA, Vienna.

The impact of lithium impurities on the microstability and turbulent transport characteristics in the core of a typical FTU Liquid Lithium Limiter (LLL)(Mazzitelli et al., Nucl. Fusion, 2011) discharge during the density ramp-up phase is studied. A non-linear gyrokinetic analysis performed with GKW (Peeters et al.,Comp. Phys. Comm., 2009) accompanied by a quasi-linear fluid analysis is presented. We show that a centrally peaked, high concentration lithium profile contributes to the electron peaking by reducing the outward electron flux, and that it leads to inward turbulent deuterium transport through ion flux separation., Comment: 23 pages, 12 figures

A new model of the L–H transition in tokamaks is proposed, based on the criterion that the transition occurs when plasma turbulence and shear Alfvén waves compete in the vicinity of the last-closed flux surface. The model is used to predict the scaling of the H-mode access power, P L–H, with magnetic and plasma variables. The predictions are in good agreement with the experimental scaling of P L–H with plasma size, density, magnetic field and edge safety factor (plasma current). They are also qualitatively consistent with the dependence of P L–H on ion mass and charge, limiter versus divertor plasmas, single versus double null configurations, the divertor leg length and H–L versus L–H hysteresis. Most notably, the model explains the appearance of the minimum in P L–H with plasma density (in terms of the transition between sheath limited and conduction limited scrape-off layer (SOL) transport) and correctly predicts the scaling of the density minimum with magnetic field and Greenwald number. Finally, the effect of toroidal field reversal is included by making the normalized correlation length of the eddy and maximum safety factor in the edge-SOL layer functions of B × ∇B direction.

Inter-ELM and ELM divertor power loads were measured on JET in dedicated deuterium, hydrogen and helium discharges. Matched triplets (D, H, He) were obtained for different values of magnetic field, B, plasma current, I p, line average plasma density, n, and heating power, P. In this paper, the above experiments are described and the results are presented in terms of empirical scalings of inter-ELM and ELM wetted areas (power widths) versus engineering parameters. The inter-ELM wetted area on the outer target is found to scale roughly as , where A and Z and the fuel ion mass and charge numbers, and q cyl is the cylindrical safety factor, and the ELM wetted area as . The obtained inter-ELM scalings are then compared with those previously reported in the literature and with a wide range of 0D theoretical predictions. For this purpose a family of scrape-off layer power width models was constructed based on a permutation of different assumptions for parallel and perpendicular transport. It is found that a combination of parallel electron conduction and drift-ordered radial convection offers the best overall match to the empirical data, closely followed by models based on marginal stability to interchange/ballooning modes and ion convection with transport ordered radial velocity. Finally, implications for ITER are tentatively drawn, and a revised estimate for the power width in ITER is proposed. Extrapolating to ITER based on the empirical JET scaling and the optimum size scaling of R 0.7±0.6, obtained based on comparison with simple models, yields a median outer target inter-ELM power width of ∼5.5 ± 2 mm (mapped to the outer mid-plane), in close agreement with previous estimates and the ITER design value. The most pessimistic forecasts (little or no size scaling and inverse linear B dependence, i.e. pure inverse current scaling) yield values as small as 2 mm. The resolution of the size scaling issue calls for additional inter-machine comparisons.

The behaviour of the turbulence in magnetic fusion plasmas is discussed in the framework of dimensional analysis. Three main dimensionless parameters are identified, which directly affect the adiabatic response of the plasma and hence control the electron response. They were originally introduced by Scott (1997 Plasma Phys. Control. Fusion 39 1635) and Rogers and Drake (1997 Phys. Rev. Lett. 79 229), and represent the effect of the electromagnetic induction, collisions and electron inertia. The dimensionless parameters are then evaluated at different radial positions in four existing divertor machines (ALCATOR C-MOD, ASDEX-Upgrade, JET and MAST) and in three future experiments (MAST-Upgrade, ITER and DEMO). Clear multi-machine trends, suggesting a quasi-universal behaviour of the plasma, are identified and discussed. Exploiting this quasi-universality, useful insight into the physics of the machines is obtained without complex calculations or expensive numerical simulations. In particular, the trends show a clear separation of the plasma in four distinct regions: core, edge, scrape-off layer and divertor, each of them characterized by a different set of parameters which, in turn, lead to significant variation of the dominant physical mechanisms across the machine.

It is shown that drift wave plasma turbulence in the electromagnetic regime can significantly affect the zonal flow dynamics and drive zonal fields. A new interpretation of the effect of the zonal fields on the zonal flow stability is given as previous analytic predictions are shown to be inadequate for accurately describing the numerical results. The zonal flow/field excitation mechanism in the electromagnetic regime can provide a possible explanation for the observed correlation between transport barrier formation and low shear rational surfaces in the plasma.

The penetration of the magnetic field in a rotating inhomogeneous plasma is investigated with direct numerical simulations. The main focus of this work is to test the linear, singular-layer models when diamagnetic and finite Larmor radius effects are included. Our results confirm the existing analytical prediction when the plasma velocity at the resonant surface is outside the drift band, which is the band bounded by the electric drift velocity and the electron diamagnetic velocity. In the drift band, however, a revision of the theory is required. In this regime of velocity, the magnetic island radiates drift waves which can affect the dynamics of the system. Our results show that the penetration of the magnetic field occurs more easily than predicted by the theoretical models, which commonly neglect drift wave radiation effects.

A numerical analysis of the interaction of resistive drift wave and interchange turbulence with a magnetic island in a two-dimensional slab is presented. The time-scale for the evolution of the island is assumed to be much longer than that for the turbulence, allowing the use of an electrostatic model. The effects of the turbulence are isolated by choosing the parameters such that only even modes are unstable. This makes it possible to compare turbulent states with quiescent states in which turbulence is suppressed by enforcing odd parity. The turbulence is found to reduce the propagation velocity of the island. Its effect is destabilizing for thin islands but becomes stabilizing for islands greater than a few times the Larmor radius. Analysis of the quiescent solutions reveals the possibility of oscillations of the island amplitude and frequency through hysteretic transitions between bistable states.

The interaction between turbulence and a nonlinear tearing mode is investigated numerically using a 2D electrostatic model. Turbulence is found to cause transitions between the different roots for the propagation velocity of the mode. The transitions take the mode towards roots with slower propagation that are characterized by a locally flattened density profile. For sufficiently large islands the transition reduces the drive for the tearing mode.

Magnetic reconnection may occur as bursts of nonlinear plasma dynamics on the electron collisionless skin length scale de=c∕ωpe, during which a large fraction of the magnetic energy is converted to plasma thermal energy and plasma flow energy. An example of such a bursty energy release event is given with a simple set of electron Hall equations. The energization mechanism is the cross-field compression of the electron gas between interacting magnetic islands. The electron energization appears to be consistent with the rapid electron energy flux changes measured by the Cluster spacecraft crossing thin current sheets at −17RE in the geotail. The analysis is relevant to planned spacecraft missions for measuring electron scale magnetic reconnection events in the geomagnetic tail.

The influence of the ion polarization current on the stability of a constant-ψ magnetic island in a tokamak plasma is investigated numerically using a reduced two-fluid model in two-dimensional slab geometry. The polarization current is found to be negligibly small when the island is either too narrow or too wide. However, under certain circumstances, there exists an intermediate regime in which the polarization current is appreciable, and has a stabilizing influence on the island. This effect may account for the metastable nature of neoclassical tearing modes in tokamak plasmas.

a quiescent runaway beam carrying the entire electrical current appears to develop in some cases. Developments in plasma control have benefited from progress in individual controller design and have evolved steadily towards controller integration, mostly within an environment supervised by a tokamak profile control simulator. TCV has demonstrated effective wall conditioning with ECRH in He in support of the preparations for JT-60SA operation. © 2017 Ecole Polytechnique Federale de Lausanne., in particular, the double decay length in L-mode limited plasmas was found to be replaced by a single length at high SOL resistivity. Experiments on disruption mitigation by massive gas injection and electron-cyclotron resonance heating (ECRH) have begun in earnest, in parallel with studies of runaway electron generation and control, in both stable and disruptive conditions, The TCV tokamak is augmenting its unique historical capabilities (strong shaping, strong electron heating) with ion heating, additional electron heating compatible with high densities, and variable divertor geometry, in a multifaceted upgrade program designed to broaden its operational range without sacrificing its fundamental flexibility. The TCV program is rooted in a three-pronged approach aimed at ITER support, explorations towards DEMO, and fundamental research. A 1 MW, tangential neutral beam injector (NBI) was recently installed and promptly extended the TCV parameter range, with record ion temperatures and toroidal rotation velocities and measurable neutral-beam current drive. ITER-relevant scenario development has received particular attention, with strategies aimed at maximizing performance through optimized discharge trajectories to avoid MHD instabilities, such as peeling-ballooning and neoclassical tearing modes. Experiments on exhaust physics have focused particularly on detachment, a necessary step to a DEMO reactor, in a comprehensive set of conventional and advanced divertor concepts. The specific theoretical prediction of an enhanced radiation region between the two X-points in the low-field-side snowflake-minus configuration was experimentally confirmed. Fundamental investigations of the power decay length in the scrape-off layer (SOL) are progressing rapidly, again in widely varying configurations and in both D and He plasmas

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $\alpha$ between the wall and the magnetic field $\vec{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $\alpha \ll 1$, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $\alpha / \sqrt{\tau+1} \gg \sqrt{m_{\text{e}}/m_{\text{i}}}$, where $m_{\text{e}}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $\tau = T_{\text{i}}/ZT_{\text{e}}$, $T_{\text{e}}$ is the electron temperature, $T_{\text{i}}$ is the ion temperature, and $Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $\rho_{\text{s}} = \sqrt{m_{\text{i}} \left(ZT_{\text{e}} + T_{\text{i}} \right) } / ZeB$, where $e$ is the proton charge and $B = |\vec{B}|$ is the magnitude of the magnetic field. We study the dependence on $\tau $ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $\tau$. The kinetic model is shown to be asymptotically equivalent to Chodura's fluid model at small ion temperature, $\tau \ll 1$, for $|\ln \alpha| > 3|\ln \tau | \gg 1$. In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $\tau \gg 1$, relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrt{\alpha}$ or $1/\sqrt{\tau}$, depending on which is largest., Comment: 44 pages, 8 figures

A simple formula for predicting the width of a saturated island, formed as a consequence of tearing perturbation of linear force-free fields in cylindrical geometry, is derived. The formula makes it possible to calculate the saturated island width in terms of the values of parameters characterizing the initial force-free equilibrium and can be applied to equilibria of interest for reversed field pinches. In particular it is applied, in this paper, to force-free equilibria with piecewise constant radial profile of the pinch parameter, which have been recently suggested to be relevant for the formation of quasi-single-helicity states. The main result is that the island width becomes larger as a parameter, that quantifies the departure from a relaxed Taylor state, increases.

Numerical simulations of L-mode turbulence in the scrape-off layer (SOL) are used to construct power scaling laws for the characteristic decay lengths of the temperature, density and heat flux at the outer mid-plane. Most of the results obtained are in qualitative agreement with the experimental observations despite the known limitation of the model. Quantitative agreement is also obtained for some exponents. In particular, an almost linear inverse dependence of the heat flux decay length with the plasma current is recovered. The relative simplicity of the theoretical model used allows one to gain insight into the mechanisms determining the width of the SOL.

A complete model of the dynamics of scrape-off layer filaments will be rather complex, including temperature evolution, three dimensional geometry and finite Larmor radius effects. However, the basic mechanism of $\boldsymbol{E}\times\boldsymbol{B}$ advection due to electrostatic potential driven by the diamagnetic current can be captured in a much simpler model; a complete understanding of the physics in the simpler model will then aid interpretation of more complex simulations, by allowing the new effects to be disentangled. Here we consider such a simple model, which assumes cold ions and isothermal electrons and is reduced to two dimensions. We derive the scaling with width and amplitude of the velocity of isolated scrape-off layer filaments, allowing for arbitrary elliptical cross-sections, where previously only circular cross-sections have been considered analytically. We also put the scaling with amplitude in a new and more satisfactory form. The analytical results are extensively validated with two dimensional simulations and also compared, with reasonable agreement, to three dimensional simulations having minimal variation parallel to the magnetic field., Comment: This is an author-created, un-copyedited version of an article accepted for publication/published in Plasma Physics and Controlled Fusion. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0741-3335/58/1/014030

This paper presents simulations of isolated 3D filaments in a slab geometry obtained using a 3D reduced fluid code. First, systematic scans were performed to investigate how the dynamics of a filament are affected by its amplitude, perpendicular size and parallel extent. The perpendicular size of the filament was found to have a strong influence on its motions, as it determined the relative importance of parallel currents to polarisation and viscous currents, whilst drift-wave instabilities were observed if the initial amplitude of the blob was increased sufficiently. Next, the 3D simulations were compared to 2D simulations using different parallel closures; namely, the sheath dissipation closure, which neglects parallel gradients, and the vorticity advection closure, which neglects the influence of parallel currents. The vorticity advection closure was found to not replicate the 3D perpendicular dynamics and overestimated the initial radial acceleration of all the filaments studied. In contrast, a more satisfactory comparison with the sheath dissipation closure was obtained, even in the presence of significant parallel gradients, where the closure is no longer valid. Specifically it captured the contrasting dynamics of filaments with different perpen- dicular sizes that were observed in the 3D simulations which the vorticity advection closure failed to replicate. However, neither closure successfully replicated the Boltzmann spinning effects and associated poloidal drift of the blob that was observed in the 3D simulations. Although the sheath dissipation closure was concluded to be more successful in replicating the 3D dynamics, it is emphasised that the vorticity closure may still be relevant for situations where the parallel current is inhibited from closing through the sheath due to effects such as increased resistivity near the targets.