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A particle-in-cell simulation of symmetric reconnection with zero guide field is carried out to understand the dynamics of ions along the separatrices. Through the investigation of ion velocity distributions at different moments and locations along the separatrices, a typical distribution is found: two counter-streaming populations in the perpendicular direction, with another two populations accelerated into distinct energy levels in the parallel direction. Backward tracing of ions reveals that the counter-streaming cores are mostly composed of ions initially located at the same side of the separatrix, while the other two accelerated populations in the parallel direction are composed of ions crossing through the neutral sheet. Through analysis of energy conversion of these populations, it is found that the ion energization along the separatrix is attributable primarily to the Hall electric field, while that in the region between the two separatrices is caused primarily by the induced reconnection electric field. For the counter-streaming population, the low-energy ions that cross the separatrix twice are affected by both Hall and reconnection electric fields, while the high-energy ions that directly enter the separatrix from the unperturbed plasma are energized mainly by the Hall electric field. For the two energized populations in the parallel direction, the ions with lower-energy are accelerated mainly by the in-plane electric field and the Hall electric field on the opposite side of the separatrix, whereas the ions with higher-energy not only experience the same energization process but also are constantly accelerated by the reconnection electric field.

At the present time, Magnetic Confinement Fusion (MCF) is considered as a way to produce energy. In this work, one of the Magnetohydrodynamic (MHD) limitations has been discussed. As closed magnetic surfaces, the Magnetic Islands (MIs) which are generated due to pressure effects, need to be surrounded by a separatrix which separate them from the other parts. External Magnetic Fields (EMFs), the safety factor (q) and the pressure profiles would be used to take the MIs under control. This could be achieved through an exterior medium, exclusively the Electron Cyclotron Heating (ECH) as well as the Current Drive (ECCD). Study of the magnetic flux surfaces and the effect of magnetic perturbation on tokamak plasmas, inform us about the formation of the MIs and their locations. In this work, together with the comprehensive review of the MIs and their importance, the conventional methods for improving the magnetic confinement has been introduced and discussed. In this regards, the Hot Limiter Biasing (HLB) method and the Resonant Helical Field (RHF) which is produced by external Helical Coils (HCs) were introduced and used. Then, the plasma current (), the Loop voltage, and the MO were obtained for different states. Finally, the Magnetic Islands Width (W) and their Growth Rate (GR) were calculated and compared with the experimental results.

A strong ~11-min-long surge of the lobe reconnection was observed during a substorm on the tailward side of the near-Earth neutral line. In the southern lobe near the reconnection separatrix the MM ...

This paper presents necessary and sufficient conditions for the existence of bright/dark solitary solutions in the Hodgkin–Huxley model. The second-order analytic solitary solutions are derived using the generalized differential operator technique. It is shown that the heteroclinic bifurcation in the Hodgkin–Huxley model yields a symmetry breaking effect. Trajectories of solitary solutions before the bifurcation lie on manifolds of one of the saddle points and the separatrix between periodic and non-periodic solutions. A new separatrix emerges after the heteroclinic bifurcation—but solitary solutions do not lie on this trajectory. This symmetry breaking effect is demonstrated using analytic and computational experiments.

The reversibility of the transfer of energy from the magnetic field to the surrounding plasma during magnetic reconnection is examined. Trajectories of test particles in an analytic field model demonstrate that irreversibility is associated with separatrix crossings and passages through regions of weaker magnetic field. Inclusion of a guide field enhances the magnetization of particles and the extent to which forward and reverse trajectories overlap. Full kinetic simulations with a particle-in-cell code support these results and demonstrate that while time-reversed simulations at first “un-reconnect,” they eventually evolve into a reconnecting state.

We report Magnetospheric Multiscale observations of large amplitude, parallel, electrostatic, proton plasma frequency waves on the magnetospheric side of the reconnecting magnetopause. The waves ar...

We investigate whistler-mode waves and broadband electrostatic waves (EWs) within an ion diffusion region (IDR) at the magnetopause. The quasi-parallel whistlers are observed in the separatrix regi...

The tokamak scrape-off layer (SOL) model is discussed on the assumption of drift mechanisms of electron heat transport and dominant role of recycling outside the separatrix comparing to the ion outflow from the core. The SOL width estimate is given. It is shown that drift mechanisms give minimal SOL width corresponding to present day scalings which is close by the order of magnitude to the experimental values.

Accurate tokamak plasma equilibrium solution in flux coordinates is crucial for many stability and transport studies. Different approaches for dealing with singularities in solving the nonlinear Grad–Shafranov (GS) equation in flux coordinates or also known as straight field line coordinates are proposed in this paper. The GS equation is solved by iterating the position of grids directly in flux coordinates, and hence, no additional errors are introduced due to mapping process for a convergent solution. The singularity at magnetic axis in flux coordinates is removed by using a novel coordinate transform technique. Different from other techniques previously developed, no assumption in boundary condition at magnetic axis is used. This is consistent with the fact that there is no physical boundary at the magnetic axis. A flux coordinate system with poloidal coordinate chosen as the geometric poloidal angle is proposed. It conquers the difficulty in no definition of poloidal coordinate in flux coordinates at separatrix because of the singularity at x-point(s) in a divertor configuration. It also simplifies the process for computing poloidal flux coordinate during the iteration for solving the nonlinear GS equation. Non-uniform grids can be applied in both radial and poloidal coordinates, which allows it to increase the spacial resolution near x-point(s) in a divertor configuration. Based on the model proposed in this paper, a new Flux coordinates based EQuilibrium solver (FEQ) in tokamaks is developed. The numerical solutions from this code agree well with both the analytic Solov’ev solution and the numerical one from the EFIT code for a divertor configuration in the EAST tokamak. This code can be applied for simulating different equilibria with prescribed shape, pressure and current profiles, i.e. including both limiter and divertor configurations, positive triangularity and negative triangularity, different β, arbitrary magnetic shear profile etc. It provides a powerful and convenient fixed-boundary inverse equilibrium solver including both magnetic axis and separatrix in the solution for tokamak researches.

The JT-60SA superconducting tokamak is proposed to be equipped with a Lithium Beam Emission Spectroscopy (LiBES) and Deuterium Beam Emission Spectroscopy (DBES) diagnostic systems. The purpose of the LiBES system is scrape-off layer (SOL) and plasma edge density profile measurements and density fluctuation measurements in the SOL and outer edge regions, whereas the DBES system on a heating beam would have the capacity of density fluctuation measurements in the edge and the core regions, as well. Considerations for an optimal LiBES system require sufficient plasma penetration beyond the separatrix and a reasonable amount of emission collected by the optical system, while an optimal DBES system mostly requires adequate spatial resolution and a sufficient Doppler shift to enable discrimination of beam emission from emission of the background plasma. Various concepts and geometries of the LiBES system for JT-60SA are analysed in detail, and a potential DBES observation geometry is characterized.

Whistler waves are believed to play an important role during magnetic reconnection. Here we report the near-simultaneous occurrence of two types of the whistler-mode waves in the magnetotail Hall r ...

We present Magnetospheric Multiscale (MMS) mission measurements during a full magnetopause crossing associated with an enhanced southward ion flow. A quasi-steady magnetospheric whistler mode wave ...

At Earth's dayside magnetopause asymmetric magnetic reconnection occurs between the cold dense magnetosheath plasma and the hot tenuous magnetospheric plasma, which differs significantly from symme ...

A magnetic field configuration of an island divertor for a quasi-axisymmetric stellarator (CFQS) is proposed. The configuration incorporates large islands surrounding the core confinement region. The interface between the core region and the peripheral region of the island divertor is a clear magnetic separatrix similar to a tokamak divertor. The structure of divertor magnetic field lines is very regular without stochasticity and the connection length is sufficiently long for good divertor performance. Such a divertor configuration is produced in the magnetic field configuration for the CFQS device, which is now under construction in China.

By keeping nonlinear Boltzmann factor in electron density dependence on electrostatic potential it is demonstrated that large plasma density blobs, often seen in experiment inside separatrix, can exist within the framework of drift wave dynamics. The estimates show that plasma density in a blob can be ∼3 times higher that average plasma density, but hardly exceeds this limit, which in a ball park is in agreement with experimental observations.

With two-dimensional (2-D) particle-in-cell (PIC) simulations we investigate the evolution of the double layer (DL) driven by magnetic reconnection. Our results show that an electron beam can be generated in the separatrix region as magnetic reconnection proceeds. This electron beam could trigger the ion-acoustic instability; as a result, a DL accompanied with electron holes (EHs) can be found during the nonlinear evolution stage of this instability. The spatial size of the DL is about 10 Debye lengths. This DL propagates along the magnetic field at a velocity of about the ion-acoustic speed, which is consistent with the observation results.

A study of the role of microinstabilities at the reconnection separatrix can play in heating the electrons during the transition from inflow to outflow is being presented. We find that very strong flow shears at the separatrix layer lead to counterstreaming electron distributions in the region around the separatrix, which become unstable to a beam-type instability. Similar to what has been seen in earlier research, the ensuing instability leads to the formation of propagating electrostatic solitons. We show here that this region of strong electrostatic turbulence is the predominant electron heating site when transiting from inflow to outflow. The heating is the result of heating generated by electrostatic turbulence driven by overlapping beams, and its macroscopic effect is a quasi-viscous contribution to the overall electron energy balance. We suggest that instabilities at the separatrix can play a key role in the overall electron energy balance in magnetic reconnection.

The conventional approach to Vlasov algorithms is to discretize the Vlasov partial differential equation and advect in time. However, the Vlasov equation advects along phase space characteristics — therefore an explicit method that relies on time-advancing characteristics may prove useful for some applications. We present such a method, based on local basis functions for the phase space density, that can adapt any single-particle integration scheme for use with a Vlasov code. To demonstrate this, we show two results: separatrix dynamics in the pendulum equation, and simulating a free-electron laser to saturation.

"Tears of the heart" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields. In [arXiv:1506.06797], it was discovered that generically, the bifurcation of a vector field with "tears of the heart" is structurally unstable. The authors proved that the classification of such bifurcations has a numerical invariant. In this article, we study the bifurcations of "tears of the heart" in more detail, and find out that the classification of such bifurcation may have arbitrarily many numerical invariants.

Intrinsic Scrape Off Layer (SOL) instabilities are studied using flute approximation and incorporating the appropriate sheath boundary conditions at the target. The linear growth rate and the structure of the modes are obtained. The associated diffusion is estimated using a γ / k ⊥ 2 approach for the fastest growing modes. The model used includes curvature and sheath drives, finite Larmor radius effects and partial line tying at the target. The magnetic geometry is obtained using current carrying wires, representing the plasma current and the divertor coils, and naturally generates X-point geometry and magnetic shear effects. The calculation is performed for ITER relevant parameters and scans in SOL width and distance from the separatrix are presented. In addition to a standard Lower Single Null, Super-X and Snowflake configurations are examined in order to assess the importance of the geometry on the stability of the boundary plasma.

In the previous analytical description of the neoclassical polarization current effect on the neoclassical tearing modes (NTMs), it is usually assumed that the magnetic island is much larger than the finite-ion-banana-width (FBW). This assumption is questionable when the experimentally observed seed island width of the NTMs is comparable to the FBW. We introduce a simple and direct theoretical method to investigate the FBW effect on the neoclassical polarization contribution to the NTM evolution in collisional plasmas. The results show that, the FBW effect can strongly modify the neoclassical polarization current profile near the island separatrix, and thus weaken its probably stabilizing effect on the NTMs.

This paper describes a new filamentary probe recently introduced on the COMPASS tokamak. It allows the measurement of electrostatic and magnetic properties of the filaments and their changes in dependence on distance from the separatrix in the region between a divertor and midplane. The probe head is mounted on a manipulator moving the probe radially on a shot-to-shot basis. This configuration is suitable for the long term statistical measurement of the plasma filaments and the measurement of their evolution during their propagation from the separatrix to the wall. The basics of the filamentary probe construction, the evolution of the plasma parameters, and first conditional averages of the plasma filaments in the scrape-off layer of the COMPASS tokamak during the L-mode regime are presented.

The concept of a new form of solitary waves-super solitary waves-is proposed, specific for embracing one or several interior separatrices on their wave phase portraits. The super solitary waves of an ion-acoustic type exist, for example, in nonmagnetized plasma containing five species of charged particles. For such plasma, electrostatic potential for ion-acoustic super solitary waves is calculated. The super solitary waves can be easily identified among usual solitons, e.g., in differential circuits installed into the measuring channel.

The convective radial transport effects of SOL turbulence have been estimated using recent turbulence data from the gas puff imaging (GPI) camera diagnostic on Alcator C-Mod. The average radial turbulence speed within the region 1-2 cm outside the separatrix near the outer was calculated by a 2-0 cross-correlation technique to be V-t similar to 0.2-0.3 km/s. Assuming this to be the local convective plasma velocity, the density SOL width lambda(n) was evaluated using a simple convective model to be lambda(n) similar to 4-7 cm, which is similar to 2-3 times higher than that measured using a Langmuir probe. This convective velocity was also similar to 2-3 times lower than the velocities estimated from analytic blob models, but showed a similar scaling with plasma current at constant q(95). The measured blob speeds were lower than both the convective speeds and the analytic blob model speeds.

The development of a new parallel framework for integrated modeling of tokamak plasmas is a primary objective of the SciDAC Framework Architecture for Core-Edge Transport Simulations (FACETS) project. The FACETS code will be used to predict the performance of tokamak discharges and to optimize tokamak discharge scenarios. Novel parallel numerical algorithms and solvers have been developed in the FACETS project in order to simulate the multi-scale dynamics of tokamak plasmas. The status of development of modules for anomalous transport in the FACETS code is described in this paper. Mechanisms that are used for coupling 1D anomalous transport in the plasma core together with 2D transport in the plasma edge (in near separatrix and scrape-off-layer regions) are considered. Results of the first verification studies based on predictive modeling of several analytical and experimental equilibria are presented.

Variations in magnetic or electrostatic confinement fields give rise to trapping separatrices, and standard neoclassical transport theory analyzes effects from collision-induced separatrix crossing...

Axial variations in magnetic or electrostatic confinement fields create local trapping separatrices, and traditional neo-classical theory analyzes the effects from collision-induced separatrix cros...

When weakly collisional plasmas have locally trapped particle populations, perturbations to the plasma equilibrium (such as waves or static field-errors) can induce phase-space discontinuities in the particle distribution function that strongly enhance entropy production, plasma loss, and wave damping via superbanana transport. This paper presents a simple version of this superbanana transport process, wherein a plasma is heated as it is slowly forced back and forth across a squeeze potential (at a frequency ω that is small compared with the particle bounce frequency). The squeeze potential traps low-energy particles on either side of the squeeze, but particles with higher energy can pass through it. Trapped and passing particles have different responses to the forcing, causing a collisionless discontinuity in the distribution function at the separatrix between the trapped and passing particles. Expressions for both the adiabatic and non-adiabatic distribution functions are presented, and the heating rate...

Magnetic reconnection plays a key role in the energy release and transformation in geospace. Though Electrostatic Solitary Wave (ESW) is widely observed in space, direct observations in the vicinity of reconnection site are rare, which makes it ambiguous of the characteristics of ESW associated with reconnection. Here we present a reconnection event for which ESW is ample in the separatrix of the reconnection diffusion region. Characteristics of the ESW associated with reconnection are studied and the effect of ESW to reconnection is discussed. The result shows that the ESW observed in the separatrix of reconnection which takes place during a substorm is more solitary and more nonlinear than that in other regions. The ESW observed associated with reconnection can propel the reconnection process via presenting a parallel electric field and accelerate electron.

A generalized pinch-diffusion transport relation previously derived from momentum conservation is combined with the continuity equation to derive a “generalized diffusion theory” for ion particle transport in the tokamak plasma edge inside the separatrix. The resulting generalized diffusion coefficients are evaluated for a representative experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Collapse events at theq= 2 surface occurring during the mode locking process of anm/n= 2/1 tearing mode have been observed on TEXTOR. The plasma confinement within theq= 2 surface collapses without much influence on the width of the island (O-point). With an external rotating resonant magnetic perturbation (RMP) field induced by the dynamic ergodic divertor, secondary structures moving near the separatrix of the primary large 2/1 island with the same frequency as the RMP have been observed after the collapse events. The plasma confinement recovers when the secondary structures vanish.

International audience; The 3D global edge turbulence code TOKAM3X is used to study the properties of edge particle turbulent transport in circular limited plasmas, including both closed and open flux surfaces. Turbulence is driven by an incoming particle flux from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed. Simulations show the existence of a complex self-organization of turbulence transport coupling scales ranging from a few Larmor radii up to the machine scale. Particle transport is largely dominated by small scale turbulence with fluctuations forming quasi field-aligned filaments. Radial particle transport is intermittent and associated with the propagation of coherent structures on long distances via avalanches. Long range correlations are also found in the poloidal and toroidal direction. The statistical properties of fluctuations vary with the radial and poloidal directions, with larger fluctuation levels and intermittency found in the outboard scrape-off layer (SOL). Radial turbulent transport is strongly ballooned, with 90% of the flux at the separatrix flowing through the low-field side. One of the main consequences is the existence of quasi-sonic asymmetric parallel flows driving a net rotation of the plasma. Simulations also show the spontaneous onset of an intermittent E × B rotation characterized by a larger shear at the separatrix. Strong correlation is found between the turbulent particle flux and the E × B flow shear in a phenomenology reminiscent of H-mode physics. The poloidal position of the limiter is a key player in the observed dynamics.

The formation of plasma blobs is studied by analyzing their trajectories in a gyrofluid simulation in the vicinity of the separatrix. Most blobs arise at the maximum radial electric field outside the separatrix. In general, blob generation is not bound to one particular radial position or instability. A simple model of turbulence spreading for the scrape-off layer is derived. The simulations show that the blob dynamics can be represented by turbulence spreading, which constitutes a substantial energy drive for far scrape-off layer turbulence and is a more suitable quantity to study blob generation compared to the skewness.

The effects of the drifts have been studied on the high parallel Mach flows near the X-point associated with the divertor plasma detachment. Numerical calculations using a 2D edge plasma simulation code (the SOLPS 5.0 code) have been applied to the analysis of the JT-60U W-shaped divertor plasmas. The following three cases are compared for the detached plasma: without the drifts, with only the diamagnetic drift, with both of the diamagnetic drift and the E × B drift. The parallel Mach number near the separatrix with both drifts becomes slightly larger than the results obtained without drifts or with only the diamagnetic drift. This increase in the parallel Mach number near the separatrix is mainly due to the radial E × B drift. However, the main features and the basic mechanism of the high Mach flows near the X-point associated with the divertor plasma detachment still remain unchanged even under the presence of the effects of drifts.

The electrostatic and density fluctuation are measured simultaneously with a heavy ion beam probe. The electrostatic fluctuation with the geodesic acoustic mode (GAM) frequency is observed in L-mode plasmas and not in H-mode plasmas. The poloidal and radial structure is consistent with the GAM. So the fluctuation is concluded to be the GAM.The amplitude of the GAM changes in the radial direction; it is small near the separatrix, has a maximum at 3 cm inside the separatrix and decreases again to 5 cm inside the separatrix.The GAM and the temporal behaviour of the ambient density fluctuation show a significant coherence, and the phase of modulation of the ambient density fluctuation tends to delay the potential oscillation of the GAM. It is clearly verified that the GAM affects ambient fluctuation and also the local particle transport through modulation of the amplitude of the ambient fluctuation.

Effects of drifts have been studied on high Mach flows near the X -point associated with the divertor plasma detachment. Numerical calculations using a 2D edge plasma simulation code (the B2.5-EIRENE code) have been made for the JT-60U W-shaped divertor geometry. In this article, we mainly focus our attention to the effect of E × B drift. The cases with and without E × B drift in the partial detached state are compared. Due to the strong decrease of electron temperature near the separatrix and the resultant radial electric field, poloidal E × B drift flows are observed in the simulation. But the radial profiles of basic plasma parameters are not so much affected. In addition, simple model has been applied to discuss the numerical results. Although the drifts possibly act as a parallel momentum source/sink, the effect on the parallel flows is shown to be relatively small.

Divertor stabilization is considered as an alternative MHD stability concept for mirror-based plasma confinement systems. The discussed concept is based on thermodynamics and self-organization of magnetized plasmas, contrary to the conventional MHD stabilization, based on the presence of averaged "magnetic well". We show that self-organized plasma maintenance near a relaxed marginally-stable state with decreasing pressure profile can be realized in essentially non-parazial longitudinally linked mirror cells restricted by a joint divertor-like magnetic separatrix with one or several magnetic field nulls at the plasma edge. Brief history, basic principles, and main advantages of the divertor stabilization concept are discussed.

An instability driven by electron temperature gradient in combination with sheath boundary condition at the divertor plate is considered. A mode localized between the divertor plate and the X point is found. The further propagation of the mode is terminated by a strong shear near the X point. Heuristic boundary condition at the control surface situated somewhat below the X point is suggested. The mode manifests a strong dependence on the radial tilt of the divertor plate, thereby providing some degree of control over the plasma transport in the divertor leg. Estimates of the diffusion coefficient show that it may reach the Bohm value.

The 2D multifluid code TECXY is used to study the evolution of so-called Marfes, thermal instabilities which arise locally in the front of the bumper limiter of the TEXTOR tokamak. The physical model is based on Braginskij-like equations and incorporates drift motions and currents in a fully self-consistent way. The radial electric field in the transition layer inside the separatrix is derived from the global ambipolarity condition. We model the bumper region by assuming high additional recombination losses inside this region and a suitably chosen profile for the recycled neutrals penetrating from the bumper surface into the adjacent plasma. A parameter study has been carried out to investigate the influence of impurities and of localized gas-puffing on the Marfe evolution. Results of numerical simulations are compared with experimental measurements.

A possible mechanism for the generation and motion of so-called blobs—peculiar perturbations that are observed in a tokamak edge plasma—is proposed. It is suggested that blobs are self-contracting plasma filaments generated either by the thermal-radiative instability of a plasma with impurities or by the nonradiative resonant charge-exchange instability resulting from the presence of neutral hydrogen atoms near the tokamak wall. Instability occurs in a narrow temperature range in which pressure is a decreasing function of density. Under these conditions, the most typical perturbations are the local ones that originate spontaneously in the form of separate growing hills and wells in the density. The temperature at the centers of the hills is lower than that in the surrounding plasma, but they are denser and, consequently, brighter than the background. The (denser) hills should move (“sink”) toward the separatrix, while the (less dense) wells should “rise” in the opposite direction, as is observed in experiments. It may even be said that they behave in accordance with a peculiar Archimedes' principle.

The equilibria of non-neutral plasmas confined in Penning–Malmberg traps with axial varying (mirror) magnetic fields exhibit numerous unusual features, including potential differences along field lines, plasma density variations, trapped particles in both the high and low field regions, and unusual separatrices between trapped and untrapped particles. Mirror fields play prominent roles in a number of recent experiments, and overly simplistic models of the equilibria can lead to errors in the interpretation of experimental results.

Recent measurements of the neutral densities both inside and outside the separatrix near the X-point of the DIII-D tokamak, in both L- and H-mode plasmas, are analysed with the two-dimensional transmission/escape probability neutral transport code GTNEUT and with the two-dimensional Monte Carlo code DEGAS. The predictions of the two codes are in good agreement with each other and agree with the experiment to within the experimental error bars in most cases.

Mechanisms of the impurity transfer inside a tokamak separatrix have been studied. It is shown that poloidal rotation significantly influences the poloidal distribution of impurities. An analysis of the neoclassical component of the radial impurity flux showed that this fraction is described by an expression that is more complicated than the standard neoclassical variant.

It is shown that plasma rotation near the tokamak the wall can result in a shift of the isobaric separatrix with respect to the magnetic one. This shift is calculated analytically, and this effect is exemplified by simple plasma equilibrium states. The plasma rotation that causes the shift of the separatrices can be driven either by a nonzero radial electric field at the plasma edge or by the Hall effect, which may take place even in the absence of the electric field.

L-mode to H-mode (LH) transitions are observed in a large variety of plasma conditions in TCV Ohmic plasmas. The power flowing through the separatrix at the LH transition differs by up to a factor of two from the predicted H-mode threshold power. Variations in this deviation are due to the large operational domain covered by the transitions as well as from the different scenarios identified to access the H-mode regime. LH transitions obtained during the plasma current ramp at low plasma current, elongation and triangularity have a threshold power below the standard expression while transitions at high current and triangularity or during the stationary phase of the discharge have a threshold power above the standard expression.

A simple two-point representation of the tokamak scrape-off layer (SOL) in the conduction limited regime, based on the parallel and perpendicular energy balance equations in combination with the heat flux width predicted by a heuristic drift-based model, was used to derive a scaling for the cross-field thermal diffusivity ${\chi }_{\perp }.$ For fixed plasma shape and neglecting weak power dependence indexes 1/8, the scaling ${\chi }_{\perp }\propto {P}_{{\rm{S}}{\rm{O}}{\rm{L}}}/(n{B}_{\theta }{R}^{2})$ is derived.

A model of neoclassical tearing modes (NTMs) allowing for a finite width of the transition layer near the island separatrix, where perturbed plasma parameters vary significantly, is proposed. In contrast to traditional models of NTMs, this model includes the parameter ρi/w properly, where ρi is the ion Larmor radius, and w is the magnetic island width. It is shown that both the polarization current and bootstrap current effects on these modes prove to be weakened compared with those predicted by traditional theories of NTMs. The competition of these effects results in a critical beta for NTM onset which is lower than that usually used for interpretation of experimental observations and predictions for reactor-grade tokamaks.

Effects induced by the finite number $N$ of particles on the evolution of a monochromatic electrostatic perturbation in a collisionless plasma are investigated. For growth as well as damping of a single wave, discrete particle numerical simulations show a $N$-dependent long time behavior which differs from the numerical errors incurred by vlasovian approaches and follows from the pulsating separatrix crossing dynamics of individual particles., LaTeX, 4 figures

The linear behavior of resistive ballooning modes in the edge and scrape-off layer of diverted tokamaks is explored in the context of a collisional fluid model. It is shown that the large magnetic shear and small poloidal field in the X-point region act to increase the wave number, and hence the importance of resistivity, near the X point. The resulting “disconnection” of the eigenmodes across the X point profoundly influences the unstable spectrum. A new class of modes called resistive X-point (RX) modes exploits this synergism between resistivity and the X-point geometry, giving rise to robust growth rates at moderate-to-low mode numbers. Relative to an equivalent limited plasma, the diverted plasma is shown to be more unstable in the edge (inside the separatrix), and more stable in the scrape-off layer.

A computationally efficient modelling procedure for the calculation of neutral atom densities in the plasma edge is described and applied to calculate the recently measured neutral densities in DIII-D. The agreement of the calculated and measured neutral densities in the plasma edge inside the separatrix is quite good. The implications of these results for neutral transport in the plasma edge are discussed.