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In this paper, DEMO-like shaped plasma equilibria are defined for RFX-mod2 tokamak operations by using the Inverse Equilibrium Tool (IET code). IET allows for the computation of the coil currents needed to obtain a predetermined plasma shape with well defined plasma global parameters (i.e. total plasma current and total poloidal magnetic flux at the boundary) by solving a constrained minimization problem. The new shape conditions would allow achieving higher plasma current and plasma density values at the same toroidal magnetic field and safety factor limits of previous RFX-mod tokamak operations. The feasibility of these new equilibria is explored in terms of coil current requirements and vertical stability analysis. This study shows that RFX-mod2 is a flexible device, able to perform DEMO-like shaped tokamak operations with low requirements on both magnitude and distribution of active coil currents. [ABSTRACT FROM AUTHOR]

The paper presents the latest results and summarizes the study of ion heat transport in the Globus-M spherical tokamak in regimes with neutral beam injection. Ion heat transport was investigated in discharges with various toroidal magnetic fields and plasma currents. Measurements of the ion temperature were carried out using charge-exchange recombination spectroscopy and a neutral particle analyzer. Plasma simulations using transport code ASTRA have shown that ion heat transport in Globus-M is predominantly neoclassical even for low collisionality range. The local transport analysis indicates that plasma core is stable to ion scale instabilities. [ABSTRACT FROM AUTHOR]

In this paper we present a method to compute spatial and time evolution of electromagnetic forces in magnetic confinement fusion devices based on a combination of signal analysis of magnetic measurements with a simple electromagnetic modelling. The method allows analyzing the whole plasma discharge including fast transient phenomena such as fast terminations or disruptions. It has been tested and verified on RFX-mod, an experiment equipped with a non-continuous toroidal passive stabilizing shell, but it can be applied to cases with continuous wall such as tokamak devices, as well. An experimental plasma discharge, with a fast termination phenomenon at the end of the flat-top phase, has been analyzed and the related forces have been computed by using two different sets of data: synthetic magnetic field measurements provided by ANSYS simulation and real experimental ones. The results are in good agreement in all the phases of the plasma discharge. Moreover, because of the very low-computational requirements, it is shown that the presented method can be used as a tool for real-time monitoring of the electromagnetic forces on the shell to be integrated in the protection system of the future RFX-mod2 experiment. [ABSTRACT FROM AUTHOR]

Modeling the propagation and damping of electromagnetic waves in a hot magnetized plasma is difficult due to spatial dispersion. In such media, the dielectric response becomes non-local and the wave equation an integro-differential equation. In the application of RF heating and current drive in tokamak plasmas, the finite Larmor radius (FLR) causes spatial dispersion, which gives rise to physical phenomena such as higher harmonic ion cyclotron damping and mode conversion to electrostatic waves. In this paper, a new numerical method based on an iterative wavelet finite element scheme is presented, which is suitable for adding non-local effects to the wave equation by iterations. To verify the method, we apply it to a case of one-dimensional fast wave heating at the second harmonic ion cyclotron resonance, and study mode conversion to ion Bernstein waves (IBW) in a toroidal plasma. Comparison with a local (truncated FLR) model showed good agreement in general. The observed difference is in the damping of the IBW, where the proposed method predicts stronger damping on the IBW. [ABSTRACT FROM AUTHOR]

In the present paper we investigate induced scattering of the pump microwave during electron Bernstein wave heating in the regimes with the high poloidal beta. It occurs in the upper hybrid resonance vicinity and leads to the nonlinear excitation of electron Bernstein waves confined within a finite 3D region limited in the radial direction by a potential well at the LFS and in the poloidal and toroidal directions by the dimensions of the spot on the magnetic flux surface illuminated by the pump beam. [ABSTRACT FROM AUTHOR]

Within the ideal magnetohydrodynamic (MHD) model, the geodesic acoustic modes (GAMs) in tokamaks derived by Winsor et al (1968 Phys. Fluids11 2448) belong to the continuous spectrum, characterised by unbounded non-square integrable eigenfunctions (delta functions) at the singular surfaces (Goedbloed 1975 Phys. Fluids18 1258). The eigenfunctions of the MHD continua in cylindrical as well as toroidal plasmas include, in addition, components that exist outside the singular surfaces and have singularities of type or where is a flux function that labels the magnetic surfaces, and defines the singular surface (Pao 1975 Nucl. Fusion15 631). Using a large aspect ratio approximation of tokamak plasmas it is shown in this paper that the GAMs indeed include such singular components. Hence, in addition to the non-square integrable and components of the plasma flow and of the density and pressure perturbations at the GAM surface, the GAM continua also include accompanying and singular components varying as This gives the and components of each GAM in the continuum radially extended profiles and a global character also within ideal theory. To the same order in the expansion, effects of a finite aspect ratio and a non-circular plasma cross section on the GAM frequency are also calculated, and we recover the dependence on inverse aspect ratio and Shafranov shift of the real GAM frequency previously calculated within gyrokinetic theory by Gao (2010 Phys. Plasmas17 092503). Furthermore, while the dominating shaping effect on the GAM frequency comes from plasma elongation, as shown previously, it is shown in this paper that there is a higher-order triangularity effect that can also be significant. The calculated triangularity effect predicts a nearly linearly increasing GAM frequency with increasing triangularity, a phenomenon observed also in the TCV tokamak. [ABSTRACT FROM AUTHOR]

This paper is concerned with the structure of ion-ion hybrid (IIH) waves in multicomponent magnetospheric plasma in the dipole geomagnetic field model. Like Alfvén waves, in IIH waves the field line can oscillate in different directions: in the azimuthal direction (the toroidal modes) and in the radial direction (the poloidal modes). Contrary to Alfvén waves, in IIH waves only the equatorial part of the field line can oscillate, since due to the heavy ions admixture the IIH waves are trapped in the resonator in the vicinity of the geomagnetic equator. The equatorial localization of the waves allow the calculation of the parallel structure of the toroidal and poloidal IIH modes analytically. It was found that the toroidal and poloidal modes have slightly different structures and that their frequencies are also slightly different. The difference between toroidal and poloidal frequencies (the polarization splitting) is small with respect to the basic harmonics of each mode. It was found that IIH modes have a considerable compressional component of the wave's magnetic field. [ABSTRACT FROM AUTHOR]

The impact of hyper-resistivity on non-ideal ballooning modes (BMs) is studied in the presence of resonant magnetic perturbation (RMP) through considering the hyper-resistivity, resistivity and diamagnetic effect in the BM model with an equilibrium distorted by RMP, which is stable for ideal BMs. Similar to the resistivity, the hyper-resistivity is also destabilizing for the BMs, but RMPs make the mode spectrum of the BMs destabilized by the hyper-resistivity move towards the low toroidal mode number side on the flux surface with a safety factor slightly larger than the RMP resonance safety factor, where the growth rates of the BMs destabilized by the resistivity decrease due to RMP. When both the hyper-resistivity and the resistivity are considered, there is a sort of competitive relationship between them in determining the properties of BMs. If either of the hyper-resistivity term and the resistivity term is much larger than the other one, the instability of BMs is mainly determined by the larger one, and the effect of the smaller one is masked. The destabilizing mechanisms of the hyper-resistivity and the resistivity on BMs are similar, namely, the diffusion and dissipation of current and magnetic field weaken the stabilizing effect of magnetic field line bending. The research results may be important for understanding the enhancement of plasma transport and the mechanism of small edge localized mode (ELM) during ELM control with RMP. [ABSTRACT FROM AUTHOR]

The physical mechanisms that cause tokamak plasmas to rotate toroidally without external momentum input are of considerable interest to the plasma physics community. This paper documents a substantial change in both the magnitude of the core-rotation frequency, -1 < ω(r/a = 0) < +10 kHz, and the sign of rotation shear at mid-radius, u' = -R² dω/dr/νth,i, which varies in the range -0.6 < u' < +0.8 in response to very small changes in the electron density. In 0.8 MA, 5.4 T Alcator C-Mod L-mode plasmas using 1.2MW of on-axis ion-cyclotron resonance heating, plasmas with line-averaged densities in the range 1.0 < ne < 1.2 × 1020 m-3 exhibit a transition from a peaked intrinsic rotation profile to one that is hollow. Gradient scale lengths of the temperature and density profiles, the drive for plasma turbulence thought to play a role in intrinsic rotation, are indistinguishable within experimental uncertainties between the plasmas, and linear stability analysis using GYRO shows the plasmas to be in the ion temperature gradient-dominated turbulence regime. The impact of changes in the rotation profile in response to minor changes under target plasma conditions is discussed in relation to established analysis techniques and cross-machine rotation scaling studies, with comparisons made with existing ASDEX-Upgrade work on intrinsic rotation shear. [ABSTRACT FROM AUTHOR]

Sheared E × B flows are known to stabilize turbulence. This paper investigates how the linear stability of the ion-temperature-gradient (ITG) mode depends on k&bottom; in both circular and MHD geometry. We study the effects of both rotation profiles of constant shear and of purely toroidal flow taken from experiment, using the global gyrokinetic particle-in-cell code NEMORB. We find that in order to effectively stabilize the linear mode, the fastest growing mode requires a shearing rate (γE) around 1-2 times its linear growth rate without flow (γ0), while both longer and shorter wavelength modes need much larger flow shear compared with their static linear growth rates. Modes with k&thetas;ρi < 0.2 need γE as much as 10 times their γ0. This variation exists in both large-aspect ratio circular cross-section and small-aspect ratio MHD geometries, with both analytic constant shear and experimental flow profiles. There is an asymmetry in the suppression with respect to the sign of γE, due to competition between equilibrium profile variation and flow shear. The maximum growth rate for cases using the experimental profile in MAST equilibria occurs at shearing rates of 10% the experimental level. [ABSTRACT FROM AUTHOR]

Equilibrium equations for magnetically confined, axisymmetric plasmas are derived by means of the energy-Casimir variational principle in the context of Hall magnetohydrodynamics (MHD). This approach stems from the noncanonical Hamiltonian structure of Hall MHD, the simplest, quasineutral two-fluid model that incorporates contributions due to ion Hall drifts. The axisymmetric Casimir invariants are used, along with the Hamiltonian functional to apply the energy-Casimir variational principle for axisymmetric two-fluid plasmas with incompressible ion flows. This results in a system of equations of the Grad–Shafranov–Bernoulli (GSB) type with four free functions. Two families of analytic solutions to the GSB system are then calculated, based on specific choices for the free functions. These solutions are subsequently applied to Tokamak-relevant configurations using proper boundary shaping methods. The Hall MHD model predicts a departure of the ion velocity surfaces from the magnetic surfaces which are frozen in the electron fluid. This separation of the characteristic surfaces is corroborated by the analytic solutions calculated in this study. The equilibria constructed by these solutions exhibit favorable characteristics for plasma confinement, for example they possess closed and nested magnetic and flow surfaces with pressure profiles peaked at the plasma core. The relevance of these solutions to laboratory and astrophysical plasmas is finally discussed, with particular focus on systems that involve length scales on the order of the ion skin depth. [ABSTRACT FROM AUTHOR]

The geodesic acoustic mode is a coherently oscillating mode, related to the zonal flows that can regulate turbulence in magnetized toroidal plasmas. Modes possessing geodesic acoustic character have been widely observed in the TCV tokamak. A transition has been observed in the course of a single discharge from a continuum regime to a radially extended single-frequency regime. The mode has been also observed and characterized for the first time in the scrape-off layer, primarily by Langmuir probes, suggesting a particle flow to the edge modulated at the mode frequency. These experimental observations are consistent with nonlinear global gyrokinetic simulations, reported in a companion paper (Merlo et al 2017 Plasma Phys. Control. Fusion). These also suggest a possible coupling with radial avalanche phenomena. [ABSTRACT FROM AUTHOR]

Many implementations of a model-based approach for toroidal plasma have shown better control performance compared to the conventional type of feedback controller. One prerequisite of model-based control is the availability of a control oriented model. This model can be obtained empirically through a systematic procedure called system identification. Such a model is used in this work to design a model predictive controller to stabilize multiple resistive wall modes in EXTRAP T2R reversed-field pinch. Model predictive control is an advanced control method that can optimize the future behaviour of a system. Furthermore, this paper will discuss an additional use of the empirical model which is to estimate the error field in EXTRAP T2R. Two potential methods are discussed that can estimate the error field. The error field estimator is then combined with the model predictive control and yields better radial magnetic field suppression. [ABSTRACT FROM AUTHOR]

In this paper we show how changes in toroidal rotation, by controlling the injected torque, affect particle transport and confinement. The toroidal rotation is altered using the co- and counter neutral beam injection (NBI) in low collisionality H-mode plasmas on DIII-D (Luxon 2002 Nucl. Fusion42 614) with dominant electron cyclotron heating (ECH). We find that there is no correlation between the toroidal rotation shear and the inverse density gradient, which is observed on AUG when is varied using ECH (Angioni et al 2011 Phys. Rev. Lett. 107 215003). In DIII-D, we find that in a discharge with balanced torque injection, the shear is smaller than the linear gyrokinetic growth rate for small for –0.85. This results in lower particle confinement. In the co- and counter- injected discharges the shear is larger or close to the linear growth rate at the plasma edge and both configurations have higher particle confinement. In order to measure particle transport, we use a small periodic perturbative gas puff. This gas puff perturbs the density profiles and allows us to extract the perturbed diffusion and inward pinch coefficients. We observe a strong increase in the inward particle pinch in the counter-torque injected plasma. Finally, the calculated quasi-linear particle flux, nor the linear growth rates using TGLF (Staebler et al 2005 Phys. Plasmas12 102508) agree with experimental observations. [ABSTRACT FROM AUTHOR]

The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal magnetohydrodynamics theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the mirror-induced Alfvén eigenmode (MAE) gap and the helicity-induced Alfvén eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside toroidal Alfvén eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island's long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry—an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum damping of global TAEs residing in the gap. [ABSTRACT FROM AUTHOR]

The m = 2, n = 1 (where m and n are the poloidal and toroidal mode numbers, respectively) neoclassical tearing mode (NTM) has been proposed as a candidate to explain the larger than expected losses of high energy ions produced by neutral beam injection observed in several experiments. Although the numerical simulations performed so far to study the effect of NTMs on energetic ions have reproduced several features observed in experiments, the agreement is not completely satisfactory. In particular, it has been difficult to reproduce the total amount of losses, which are affected by the details of the perturbation in the edge region. In this work, we study the effect of NTMs on the confinement of energetic ions produced by NBI injection using FOCUS, a full orbit code that runs in graphical processing units. This allows us to follow the evolution of a large number of ions with modest resources. A reconstruction technique that includes the experimental information available is employed to calculate the perturbed magnetic field. The main result of this study is that when the frequency of the NTM matches the toroidal precession frequency ω tp of the trapped ions ( ω t p ∼ E , where E is the energy of the ion), the losses increase significantly. [ABSTRACT FROM AUTHOR]

In this paper, a conservation equation is derived for the radially dependent entropy in toroidal geometry using the local approximation of the gyro-kinetic equation. This naturally leads to an operative definition for the turbulence intensity. It is shown that the conservation equation can be split into two contributions, one describing the dynamics of the zonal modes and one for the non-zonal modes. In essence the paper provides an operative tool for both analytic as well as numeric studies of the radial propagation of turbulence in tokamak plasmas. [ABSTRACT FROM AUTHOR]

The excitation of toroidicity-induced Alfvén eigenmodes (TAEs) using prescribed external electromagnetic perturbations (hereafter ‘antenna’) acting on a confined toroidal plasma, as well as its nonlinear couplings to other modes in the system, is studied. The antenna is described by an electrostatic potential resembling the target TAE mode structure along with its corresponding parallel electromagnetic potential computed from Ohm’s law. Numerically stable long-time linear simulations are achieved by integrating the antenna within the framework of a mixed representation and pullback scheme (Mishchenko et al 2019 Comput. Phys. Commun. 238 194). By decomposing the plasma electromagnetic potential into symplectic and Hamiltonian parts and using Ohm’s law, the destabilizing contribution of the potential gradient parallel to the magnetic field is cancelled in the equations of motion. Besides evaluating the frequencies and the growth/damping rates of excited modes compared to referenced TAEs, we study the interaction of antenna-driven modes with fast particles and indicate their margins of instability. Furthermore, we show the first nonlinear simulations in the presence of a TAE-like antenna exciting other TAE modes, as well as global Alfvén eigenmodes with different toroidal wave numbers from that of the antenna. [ABSTRACT FROM AUTHOR]

A novel scheme for generating relativistic high-order harmonics by a relativistic radially polarized laser interacting with a plasma annular grating is proposed. The particle-in-cell results show that the radial laser field can drive the relativistic electron bunches to oscillate radially in all azimuth directions, resulting in the emission of strong harmonics. Firstly, the interference of the laser field on the plasma grating structure significantly enhances the radiated harmonics which match the phase conditions. Secondly, due to the common ring symmetry of the grating structure and laser polarization, the transverse distribution of harmonics presents a Bessel form, and there is a sharp bright spot in the center with relativistic intensity. Such high-intensity short-wave structured harmonics have broad applications in areas such as plasma diagnostics, high resolution imaging and detection. [ABSTRACT FROM AUTHOR]

Edge localized modes (ELMs) are magnetohydrodynamic (MHD) instabilities that cause fast periodic relaxations of the strong edge pressure gradient in tokamak fusion plasmas. Magnetic pick-up coils allow the extraction of toroidal mode numbers n during the ELM cycle including the nonlinear crash on ASDEX Upgrade, providing a good comparability to nonlinear 3D MHD codes. This paper investigates how the mode numbers before and during the ELM crash change with a variation of plasma parameters. It is found that the toroidal structure size during the crash is similar to the one existing slightly before and always has a low n = 1–7 range. Furthermore, in the nonlinear phase of the ELM n does not show a clear trend with most peeling-ballooning relevant parameters such as normalized pressure gradient, bootstrap current density or triangularity, whereas a strong decrease of n with edge safety factor q95 is observed in agreement with nonlinear modeling in the here investigated high collisionality region. A simple geometric model is presented, which is capable of explaining the q scaling by existence of ballooned structures that minimize n. [ABSTRACT FROM AUTHOR]

Axisymmetric (n = 0) density fluctuations measured in the TCV tokamak are observed to possess a frequency f0 which is either varying (radially dispersive oscillations) or a constant over a large fraction of the plasma minor radius (radially global oscillations) as reported in a companion paper (Z Huang et al, this issue). Given that f0 scales with the sound speed and given the poloidal structure of density fluctuations, these oscillations were interpreted as Geodesic Acoustic Modes, even though f0 is in fact smaller than the local linear GAM frequency . In this work we employ the Eulerian gyrokinetic code GENE to simulate TCV relevant conditions and investigate the nature and properties of these oscillations, in particular their relation to the safety factor profile. Local and global simulations are carried out and a good qualitative agreement is observed between experiments and simulations. By varying also the plasma temperature and density profiles, we conclude that a variation of the edge safety factor alone is not sufficient to induce a transition from global to radially inhomogeneous oscillations, as was initially suggested by experimental results. This transition appears instead to be the combined result of variations in the different plasma profiles, collisionality and finite machine size effects. Simulations also show that radially global GAM-like oscillations can be observed in all fluxes and fluctuation fields, suggesting that they are the result of a complex nonlinear process involving also finite toroidal mode numbers and not just linear global GAM eigenmodes. [ABSTRACT FROM AUTHOR]

In this work, using solutions from a local gyrokinetic flux-tube code combined with higher order ballooning theory, a new analytical approach is developed to reconstruct the global linear mode structure with associated global mode frequency. In addition to the isolated mode (IM), which usually peaks on the outboard mid-plane, the higher order ballooning theory has also captured other types of less unstable global modes: (a) the weakly asymmetric ballooning theory (WABT) predicts a mixed mode (MM) that undergoes a small poloidal shift away from the outboard mid-plane, (b) a relatively more stable general mode (GM) balloons on the top (or bottom) of the tokamak plasma. In this paper, an analytic approach is developed to combine these disconnected analytical limits into a single generalised ballooning theory. This is used to investigate how an IM behaves under the effect of sheared toroidal flow. For small values of flow an IM initially converts into a MM where the results of WABT are recaptured, and eventually, as the flow increases, the mode asymptotically becomes a GM on the top (or bottom) of the plasma. This may be an ingredient in models for understanding why in some experimental scenarios, instead of large edge localised modes (ELMs), small ELMs are observed. Finally, our theory can have other important consequences, especially for calculations involving Reynolds stress driven intrinsic rotation through the radial asymmetry in the global mode structures. Understanding the intrinsic rotation is significant because external torque in a plasma the size of ITER is expected to be relatively low. [ABSTRACT FROM AUTHOR]

A theory to describe the conversion of poloidal momentum into toroidal momentum by phase space structures in trapped ion resonance driven turbulence is presented. In trapped ion resonance driven turbulence, phase space structures are expected to form and can contribute to transport by exerting dynamical friction. Toroidal momentum flux by dynamical friction is calculated. It is shown that dynamical friction exerted on trapped ion granulations can mediate momentum transfer between poloidal and toroidal flows. The conversion coefficient is calculated as measurable, which can be validated in current devices. [ABSTRACT FROM AUTHOR]

We investigate how the neoclassical thermal diffusivity of an axisymmetric toroidal plasma is modified by the effect of resonant magnetic perturbations (RMPs), using a drift-kinetic simulation code for calculating the radial thermal diffusivity of ion in the perturbed region under an assumption of zero electric field. Here, the perturbed region is assumed to be generated on and near the resonance surfaces, and is wedged in between the regular closed magnetic surfaces. We find that the dependence of the radial thermal diffusivity on parameters of the toroidal plasma is represented as Χr = Χr(0) {1 + c0 (ωb/νeff∆b²) <∥δBr∥²>/|Bt0|²}, where Χr(0) is the neoclassical thermal diffusivity and c0 is a positive coefficient. Here, ωb is the bounce frequency, νeff is the effective collision frequency, ∆b is the banana width, <∥δBr∥²1/2 is the strength of the RMPs in the radial directions, and |Bt0| is the strength of the magnetic field on the magnetic axis. The value of c0 := c0/(qRax/ √∈t)² is significantly reduced to c0 ~ 10-4 in the simulations because of the drift motion affected by the Coulomb collision, as contrasted with c0 = π predicted by the so-called field-line diffusion theory, where q is the safety factor, Rax is the major radius of the magnetic axis, and ∈t is the inverse aspect ratio. [ABSTRACT FROM AUTHOR]

MHD activity in a tokamak, in the form of waves and instabilities, generally has a preferred direction for propagation in a two-fluid plasma. When the radial component of magnetic field associated with this activity interacts with a resistive wall, momentum or angular momentum will be given to the wall. The equal and opposite reaction will be on the plasma, in particular, for ideal and resistive modes, at the singular or resonant surfaces for the various modes. In this case the torque exerted is electromagnetic. This is in contrast to other mechanisms for intrinsic or spontaneous rotation which may arise at the plasma boundary. The resistive wall is considered generally, and the thin and thick wall limits found, the latter being relevant to ITER parameters. Remarkably small radial perturbing fields of order 0.1G could produce a torque comparable in effect to the apparent anomalous toroidal viscosity. [ABSTRACT FROM AUTHOR]

The analytical treatment of plasma kinetic linear instabilities in toroidal geometry is commonly tackled employing a power series expansion of the resonant part of the dispersion relation. This expansion is valid under the assumption that the modulus of the mode frequency is smaller than the magnitude of the frequencies characterising the system (the drift, bounce and transit frequencies for example). We will refer to this approximation as high frequency approximation (HFA). In this paper the linear plasma dispersion relation is derived in the framework of the gyro-kinetic model, for the electrostatic case, in the local limit, in the absence of collisions, for a non rotating plasma, considering adiabatic electrons, in toroidal circular geometry, neglecting the parallel dynamics effect. A systematic analysis of the meaning and limitations of the HFA is performed. As already known, the HFA is not valid for tokamak relevant parameters. A new way to approximate the resonant part of the dispersion relation, called here Improved high frequency approximation (IHFA), is therefore proposed. A quantitative analysis of the ion temperature gradient (ITG) instability is presented. The IHFA is shown to be applicable to the treatment of the ITG instability in tokamaks. [ABSTRACT FROM AUTHOR]

The effects of nitrogen injection on the heat load in the scape-off layer are systematically investigated in the EAST double-null divertor configuration using EMC3-EIRENE code. Nitrogen impurities injected near the separatrix line and away from the separatrix line give rise to a non-axisymmetric distribution of heat load on the target plate. With impurity injection near the separatrix line, the occurrence of the toroidal asymmetric heat load is observed only nearby the toroidal injection location, while with injection away from the separatrix line the regions of the asymmetric heat load extend and deviate from the toroidal injection position. The competition between the friction force and the ion temperature gradient force has been analyzed. It shows that when impurities are injected away from the separatrix line more impurities can be parallelly transported to a further toroidal location, which results in the extension and deviation of the non-symmetric electron temperature. When the input power is increased, the non-symmetric phenomenon of the heat load turns to be insignificant due to the reduction of the impurity density in the downstream regions, as illustrated by the field line tracing technique. Furthermore, by scanning various injection positions in the EAST tokamak, the optimum location of impurity injection has been discovered. [ABSTRACT FROM AUTHOR]

Infinite toroidal mode number (n = ∞) ballooning mode analysis of negative triangularity discharges on DIII–D shows that the access to 2nd stability becomes strongly restricted when the top triangularity decreases even modestly from −0.18 to −0.36. This is observed in experiment to coincide with the suppression of the L–H-transition. Further theoretical analysis with ballooning mode limited pedestals shows that the threshold for opening the 2nd stability access rises from a pedestal temperature of 0.3–1 keV when the top triangularity is decreased from −0.18 to −0.36 indicating that to access the 2nd stability with the more negative triangular shape would require unrealistically high pedestal temperature. The pedestal predicted by the EPED code agrees with the experimental H-mode profile for the negative triangularity case but in contrast to positive triangular shapes the prediction shows no increase in pedestal height with increasing core pressure when triangularity is negative. This work provides a first model to predict when negative triangularity plasmas can be expected to access the H-mode. [ABSTRACT FROM AUTHOR]

Runaway electrons have great significance in fusion plasmas as they are considered to be responsible for the excitation of instabilities and for damage to the first wall components. The threshold for the generation of the runaway electron population in tokamaks strongly depends on the toroidal magnetic field and bulk electron temperature. The presence of these runaway electrons with a critical density and magnetic field value are correlated with the magnetosonic whistler activity. The Rosenbluth condition applies to the destabilization of upper hybrid modes, that remains mostly stable in large-scale tokamaks like Joint European Tokamakand International Thermonuclear Experimental reactor. On the other hand, whistlers with a frequency in the lower hybrid range are more likely to be destabilized in a lower magnetic field and temperature, along with the whistlers' excitation threshold. The process of destabilization of whistlers by energetic electrons thus has a finite overlap between fusion and basic plasma devices, and the outcome from the latter can be scalable to fusion machines. We report that in the linear large volume plasma device, the destabilization of quasi-longitudinal whistlers, driven by the reflected particles from the mirror, takes place in the bulk plasma region i.e. away from the mirror in the energetic belt region, and follows the frequency ordering of. Our explanation involves an alternate limit of quasi-linear analysis, commonly employed for recovering the instability threshold of runaways scattering off whistlers in fusion plasmas, and the growth rate due to the reflected particle is proportional to the inverse square root of electron temperature, where the reflected particle fraction is (Sharma and Vlahos 1984 Astrophys. J. 280 405). The measurements required to obtain the energy scaling of runaway electrons with whistler instability are critical for large devices but remain scarce. We have emphasized the analytic correlation between the two regimes in these investigations. [ABSTRACT FROM AUTHOR]

The ELM wetted area is a key factor in the peak power load during an ELM, as it sets the region over which the ELM energy is deposited. The deposited heat flux at the target is seen to have striations in the profiles that are generated by the arrival of filaments ejected from the confined plasma. The effect of the filaments arriving at the target on the ELM wetted area, and the relation to the midplane mode number is investigated in this paper using infrared (IR) thermography and high speed visible imaging (>10 kHz). Type I ELMs are analysed, as these have the largest heat fluxes and are observed to have toroidal mode numbers of between 5 and 15. The IR profiles during the ELMs show clear filamentary structures that evolve during the ELM cycle. An increasing number of striations at the target is seen to correspond to an increase in the wetted area. Analysis shows that the ratio of the ELM wetted area to the inter-ELM wetted area, a key parameter for ITER, for the type I ELMs is between 3 and 6 for lower single null plasmas and varies with the ELM midplane mode number, as determined by visible measurements. Monte-Carlo modelling of the ELMs is used to understand the variation seen in the wetted area and the effect of an increased mode number; the modelling replicates the trends seen in the experimental data and supports the observation of increased toroidal mode number generating larger target ELM wetted areas. ITER is thought to be peeling unstable which would imply a lower ELM mode number compared to MAST which is peeling–ballooning unstable. The results of this analysis suggest that the lower n peeling unstable ELMs expected for ITER will have smaller wetted areas than peeling–ballooning unstable ELMs. A smaller wetted area will increase the level of ELM control required, therefore a key prediction required for ITER is the expected ELM mode number. [ABSTRACT FROM AUTHOR]

Magnetic feedback stabilization of the tearing mode (TM) is numerically investigated, utilizing the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) for toroidal tokamak equilibria. With control coil configurations assumed in this study, magnetic feedback partially or fully stabilizes the TM, with either vanishing or finite equilibrium pressure. The best control is achieved by the combination of internal active coils and internal poloidal sensors. The internal and external tearing indices are evaluated for the close-loop system, based on the MARS-F computed mode eigenvalue and eigenfunction, respectively. In the absence of the favorable curvature effect, these two indices are real-valued and quantitatively agree well with each other. For the equilibrium with finite pressure gradient at the mode rational surface, the favorable average curvature effect becomes important and the close-loop tearing index also becomes complex-valued, partly due to interaction of the feedback system with the dissipative wall eddy current response. Isolating the inner layer and outer region response to magnetic feedback, with either proportional or proportional-derivative actions, allows to establish that feedback stabilization of the TM occurs mainly due to modification of the behavior of the external ideal solution, further confirming the analytic result reported in He et al 2021 Phys. Plasmas 28 012504. [ABSTRACT FROM AUTHOR]

The non-linear dynamics of a chain of stationary, saturated magnetic islands is studied by solving a four-field system of equations that include non-ideal effects, lowest order finite Larmor radius corrections and neoclassical terms. The magnetic island rotation velocity is calculated self-consistently with the fields profiles. The solutions for the island rotation velocity and for the ion polarization current are determined as a function of the characteristic parameters of the system and the results are discussed. The results of the calculations show that island rotation velocity and the ion polarization current depend in a non-trivial way on the parameters characterizing the system, and some clear patterns emerge only in particular cases. An analysis of magnetic island rotation velocity is performed on experiments in COMPASS tokamak. Measured island rotation velocity is compared with the calculated ion and electron flow velocities, for different hypotheses on the toroidal rotation of the plasma. The comparison shows that the island rotation velocity is consistent with the ion flow velocity, under the hypothesis of slow toroidal rotation and low collisionality. Theoretical calculation of the island rotation velocity according to the model here developed suggests that the islands rotate weakly in the ion direction, in the hypothesis of slow toroidal rotation and high collisionality. The impossibility of directly measuring the plasma rotation velocity makes it difficult to distinguish between these different regimes. [ABSTRACT FROM AUTHOR]

Linear and nonlinear effects of the equilibrium radial electric field on the ion temperature gradient (ITG) instability in the scrape-off layer (SOL) of a field-reversed configuration have been studied using gyrokinetic particle simulations for a single toroidal mode. Linear simulations with adiabatic electrons find that the flow shear reduces the growth rate and causes a radial tilting of the mode structure on the toroidal plane. Nonlinear simulations find that the flow shear significantly decreases ITG saturation amplitude and ion heat transport in the SOL by reducing both turbulence intensity and eddy size. The turbulence intensity is determined by fluid eddy rotation, which is the dominant saturation mechanism for the SOL ITG instability with a single toroidal mode number. On the other hand, parallel wave-particle decorrelation is the dominant mechanism for the SOL ITG turbulent transport. A random walk model using the guiding center radial excursion as the characteristic length scale and the eddy turnover time as the characteristic time scale fits very well to the scaling of ion heat conductivity with the flow shear. [ABSTRACT FROM AUTHOR]

Significant noise suppression for magnetohydrodynamics (MHD) mode characterization in the spatial and spectral domain is achieved by processing two-dimensional (2D) electron cyclotron emission imaging (ECEI) data with a one-dimensional (1D) ECEI technique using a short time window (). The technique is applied to detect toroidal Alfven eigenmodes (TAEs) in the temporal spectrum and fit their radial envelope using the data from the DIII-D tokamak W-band 2D ECEI system. Using the data length (time window) of only 1 , the 1D ECEI can clearly detect the TAEs (∼100) on the spectrum, while similar spectrum quality requires ∼10 data length with the cross power spectrum between two midplane ECEI channels. The 1D ECEI technique also effectively avoids biased fitting when resolving the fine structure of the TAE's radial envelope. The radially spatial resolution of 1D ECEI is constrained by the finite ECE radiation volume of the ECEI receiver. With forward radiation modeling, we find the DIII-D ECEI system can sensitively measure the even parity MHD activities, for which the mode width is >15 mm, and tearing modes (odd parity MHD activities), for which the island full width is >30 mm. [ABSTRACT FROM AUTHOR]

A matrix inversion technique is derived to calculate local ion temperature from line-integrated measurements of an extended emission source in an axisymmetric plasma which exactly corrects for both toroidal velocity and radial velocity components. Local emissivity and toroidal velocity can be directly recovered from line-integrated spectroscopic measurements, but an independent measurement of the radial velocity is necessary to complete the temperature inversion. The extension of this technique to handle the radial velocity is relevant for magnetic reconnection and merging compression devices where temperature inversion from spectroscopic measurements is desired. A simulation demonstrates the effects of radial velocity on the determination of ion temperature. [ABSTRACT FROM AUTHOR]

A phenomenon is analyzed, which is observed at some laboratory-scale tokamaks and seems to be unexplained: a strong drop in the soft x-ray radiation (SXR) after it passed through the 'thick' Be foils (the pit in the SXR spectrum). This phenomenon becomes more pronounced as the foil thickness increases and the plasma electron density decreases. The explanation for this phenomenon is proposed, which involves the assumption that the Maxwellian electron velocity distribution becomes 'depleted' in the range of velocities that are 3–5 times higher than the thermal one. The anomalous electron heat transport along the weakly perturbed toroidal magnetic field of the tokamak (the 'magnetic flutter' model) seems to be the most probable reason for this depletion. Thus, the 'SXR—Pit' can be a new tool for studying the physical nature of the anomalous electron transport in tokamaks. [ABSTRACT FROM AUTHOR]

In this article, we report the latest results for the impacts of the isotope mass and the plasma heating scenario on the spatiotemporal characteristics of the low-frequency zonal flow (ZF)-like electrostatic oscillation found in the plasma edge of the TJ-II stellarator. The radial profile of the toroidal cross-coherence in low-frequency floating potential fluctuations (1 < f < 25 kHz), known as long-range correlations (LRCs), was explored along the plasma boundary region by a dual Langmuir probe system. The study was performed using electron cyclotron resonance heating (ECRH)- and neutral beam injection (NBI)-heated plasmas with two different isotope concentrations: pure hydrogen plasmas and plasmas dominated by deuterium (). The highest toroidal coherence levels are detected for floating potential oscillations at less than 10 kHz in hydrogen and deuterium plasmas, in both the ECRH and NBI heating schemes. The radial extent of the LRC profile is clearly larger in the ECRH than in the NBI-heated plasma scenarios. While the maximum amplitude of the LRC does not show a significant dependence on isotope mass, the relation between the LRCs' radial sizes in plasmas and different isotope masses increases with the isotope mass in NBI-heated scenarios. These results provide the first experimental observation of ZFs with a larger radial size in deuterium than in hydrogen plasmas. [ABSTRACT FROM AUTHOR]

The penetration properties of the n = 1 resonant magnetic perturbations (RMPs) with toroidal rotation are systematically studied by the upgraded three-dimensional toroidal magnetohydrodynamic code CLTx, through both linear and nonlinear simulations. It is found that in the presence of toroidal plasma rotation, the saturation state for high resonant harmonics is obtained in linear simulations due to the mode becoming unlocked from the internal magnetic islands. In nonlinear simulations, nonlinear effects become important when the toroidal plasma rotation is not included. The zonal component resulting from the nonlinear mode coupling is necessary for the saturation of the whole system including the internal kink mode and the m /n = 2/1 tearing mode. The simulations of RMP penetration demonstrate that the mode coupling is associated with the toroidal effect rather than nonlinear effects. With a low resistivity close to the experimental value, the single-harmonic-RMP is hard to penetrate the mode-rational surface because of the plasma screening effects, resulting in a truncation of the radial mode structure. On the other hand, the non-resonant components in the multiple-harmonic-RMP could largely reduce the effect of the plasma shielding, which leads to that the RMP is able to penetrate deeply into the central plasma region through the poloidal harmonic coupling. [ABSTRACT FROM AUTHOR]

Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. This structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori. [ABSTRACT FROM AUTHOR]

The high plasma temperatures expected at reactor conditions in magnetic confinement fusion toroidal devices suggest that near-marginal operation could be a reality in future devices and reactors. By near-marginal it is meant that the plasma profiles might wander around the local critical thresholds for the onset of instabilities. Self-organized criticality (SOC) was suggested in the mid 1990s as a more proper paradigm to describe the dynamics of tokamak plasma transport in near-marginal conditions. It advocated that, near marginality, the evolution of mean profiles and fluctuations should be considered simultaneously, in contrast to the more common view of a large separation of scales existing between them. Otherwise, intrinsic features of near-marginal transport would be missed, that are of importance to understand the properties of energy confinement. In the intervening 20 years, the relevance of the idea of SOC for near-marginal transport in fusion plasmas has transitioned from an initial excessive hype to the much more realistic standing of today, which we will attempt to examine critically in this review paper. First, the main theoretical ideas behind SOC will be described. Secondly, how they might relate to the dynamics of near-marginal transport in real magnetically confined plasmas will be discussed. Next, we will review what has been learnt about SOC from various numerical studies and what it has meant for the way in which we do numerical simulation of fusion plasmas today. Then, we will discuss the experimental evidence available from the several experiments that have looked for SOC dynamics in fusion plasmas. Finally, we will conclude by identifying the various problems that still remain open to investigation in this area. Special attention will be given to the discussion of frequent misconceptions and ongoing controversies. The review also contains a description of ongoing efforts that seek effective transport models better suited than traditional equations to capture SOC dynamics. Most of these models, based on the use of fractional transport equations and related concepts, could prove useful both in reactor operation and experiment control and design. [ABSTRACT FROM AUTHOR]

The primary function of the ITER glow discharge cleaning (GDC) system will be the preparation of in-vessel component surfaces prior to the machine start-up. It may also contribute to tritium removal in the nuclear phase. In GDC, conditioning efficiency is strongly dependent on the homogeneity of the flux of ions impinging onto wall surfaces. In order to assess the wall particle flux distribution in ITER, a novel 2D multi-fluid model, described in a companion paper, has recently been developed and is benchmarked here against both experimental glow discharge data obtained in a small laboratory chamber with cylindrical geometry and from two large toroidal devices: the JET tokamak and the RFX reverse field pinch. In the laboratory plasma, simulated and measured plasma electron density and temperature are in a good agreement in the negative glow region, while discrepancies exist in the anode glow, where the fluid description of the model is inaccurate due to long mean free paths of electrons. Calculated and measured ion flux distribution profiles in RFX are found in good agreement, whereas in JET comparison it is more difficult, due to the complex geometry of the first wall which leads to local inhomogeneities in the measured flux. Simulations of H2-GDC for ITER with one or two anodes indicate fairly homogeneous plasma parameters and wall ion flux in the negative glow at 0.5 Pa, a commonly used gas pressure for GDC in existing fusion devices. Although the axisymmetric geometry in the model does not allow all seven ITER anodes to be powered simultaneously in the simulations, the results can be extrapolated to the full system and predict ion current densities on wall surfaces close to the simple expectation of total anode current divided by wall surface area (0.21 A m−2), which is relevant to GDC in JET and other machines. [ABSTRACT FROM AUTHOR]

Anomalous transport due to large coherent structures, or coherent events, is studied experimentally in a magnetized toroidal discharge plasma. The present analysis emphasizes anomalous plasma losses as well as transport of electron thermal energy density across magnetic field lines. The experiment was carried out in the Blaamann device at the University of Tromsř. The diagnostics are based on data for potential, density and electron temperature variations as detected by Langmuir probes. Most of the data analysis uses conditional sampling. The flux of thermal energy density can be broken down into several components which are analyzed separately. Experimental means for obtaining the space-time variation of the complete polarization drifts are demonstrated, and the results compared with the fluctuating -velocities. For the present conditions these polarization drifts contribute only little to the plasma losses, but for other discharge parameters in heavier gases they can be important. Our results show that while the density, the potential and the electric field variations are dominated by large scales, the vorticity of the -flow as well as the ion polarization drifts are strongly intermittent. [ABSTRACT FROM AUTHOR]

Ideal magnetohydrodynamic (MHD) properties depending on the plasma pressure are considered for axisymmetric equilibrium magnetoplasma configurations in the Galatea trap with three ring current-carrying conductors embedded in plasma. The study of ideal MHD modes with different toroidal wave numbers takes into account the plasma compressibility with an adiabatic index of 5/3 in the perturbed potential energy functional in the framework of the energy principle. The stability calculations are performed in the presence of a vacuum layer between the plasma and the vacuum chamber. The limiting pressure values corresponding to stable multiply connected plasma configurations without an assumption of nested magnetic surfaces are estimated. [ABSTRACT FROM AUTHOR]

Anisotropy and some limiting toroidal flow effects on the stability of nearly resonant ideal magnetohydrodynamic modes in hybrid shaped tokamak plasmas are investigated within the ideal MHD infernal mode framework. Such effects are found to alter the plasma magnetic well/hill, which can be interpreted as imparing the average curvature, and the strength of mode coupling. In line with previous results, it is found that better stability properties are achieved through deepening the magnetic well by special cases of uniform toroidal flow and parallel plasma anisotropy. Plasma shaping provides additional modifications to the magnetic well depth, whose global stabilising or destabilising effect depends on the mutual interplay of elongation, triangularity and toroidicity. Further stabilisation is achieved by weakening the mode drive in vertically elongated plasmas. [ABSTRACT FROM AUTHOR]

The 1-dimensional reaction-diffusion-convection code TOMATOR-1D describes plasma production by RF waves inside a tokamak using the Braginskii continuity and heat balance equations. The model simulates self-consistent radial density and temperature profiles for magnetised plasma mixtures of hydrogen and helium. The model reproduces the density profiles of X2 electron cyclotron resonance heating (ECRH) plasmas on TCV and proposes a Bohm-like poloidal magnetic field dependent scaling for anomalous diffusion and a convection scaling that results from drifts in the toroidal magnetic field configuration. A relation is proposed between the anomalous diffusion and the outward convection in toroidal plasmas. It is found that the EC absorption efficiency decreases at higher power, which is understood from the acceleration of electrons beyond the optimal energy for the electron impact ionisation of helium. A dramatic increase of the absorption efficiency is seen at intermediate vertical magnetic field values of which results in the highest density plasmas. Losses along the field lines in the vertical direction become dominant at higher fields which effectively reduces the plasma density in these discharges. To arrive at predictive capabilities towards ECRH plasmas on JT-60SA and ITER, the proposed scalings, subsuming dependencies on the torus major radius and the toroidal field strength, need to be validated in a multi-machine study. [ABSTRACT FROM AUTHOR]

The coupling between the poloidal distribution and the collisional flux of impurities can be exploited to derive a simplified analytical model covering toroidal rotation and electrostatic potential asymmetry effects, valid in the Pfirsh-Schlüter regime. This model is compared with earlier works and with the drift-kinetic code NEO, which includes the full Fokker-Planck collision operator. The low computational cost of the model, compared to NEO, is particularly adapted for fast integrated simulation purposes. [ABSTRACT FROM AUTHOR]

Fast-particle driven Alfvén Eigenmodes have been observed in low-collisionality discharges with off-axis neutral beam injection (NBI), electron cyclotron resonance heating (ECRH) and a reduced toroidal magnetic field. During NBI and ECRH, toroidicity induced Alfvén Eigenmodes (TAEs) appear in frequency bands close to 200 kHz and energetic-particle-induced geodesic acoustic modes (EGAMs) are observed at about 40 and 80 kHz. When turning off ECRH in the experiment, those beam-driven modes disappear which can be explained by a modification of the fast-ion slowing down distribution. In contrast, coherent fluctuations close to the frequency of the beam-driven TAEs are present throughout the experiment. The modes are even observed during ohmic plasma conditions, which clearly demonstrates that they are not caused by fast particles and suggests an alternative drive, such as turbulence. The mode-induced fast-ion transport has been found to be weak and marginal in terms of the fast-ion diagnostic sensitivities. Measurements of the plasma stored energy, neutron rates, neutral particle fluxes and fast-ion D-alpha spectroscopy show good agreement with neoclassical modelling results from TRANSP. This is further supported by a similarly good agreement between measurement and modelling in cases with and without ECRH and therefore with and without the modes. Instead, a significant level of charge exchange losses are predicted and observed which generate a bump-on-tail fast-ion distribution function that can provide the necessary free energy to EGAMs. [ABSTRACT FROM AUTHOR]

Investigation of helicon wave heating and current drive (CD) in toroidal plasma has been carried out with the ray-tracing code GENRAY. The wave trajectories, profiles of power deposition and driven-currents are presented. It is shown that increasing the poloidal launch angle does not change the absorption rate of the wave, but moves the peak of the wave deposition toward the plasma core. Wave frequencies in the range of our interest (460 MHz ∼ 480 MHz) do not change the absorption of the wave. Under low parameter plasmas, we find that both the peak position and magnitude of the wave power deposition are dependent on the launched parallel refractive index n||. With increasing the refractive index, the driving efficiency first increases and then decreases. The parallel refractive index figure of merit for mid-plane launching in HL-2M configuration is 3.2. With high plasma parameters, both the position and magnitude of the driving current are weakly dependent on n||. The magnitude of the driven current is determined by both the absorption rate and the value of ξe, which is related to n||. It is also demonstrated that driven current increases with increase of the core plasma temperature and decrease of the core plasma density. The plasma ohmic current seems do not significantly affect the helicon CD efficiency, but moves the driven current toward the plasma core region and narrows the width of the driven current profile. In addition, the preliminary calculations including scrape-off-layer (SOL) suggest that the power absorption rate loss in SOL is about 5%–20%. These results provide a reference and theoretical basis for the design and construction of HL-2M helicon wave system. [ABSTRACT FROM AUTHOR]

Quasi-analytical equilibrium solutions for plasmas rotating in the toroidal direction are presented. The formalism provides control of the plasma shape (aspect ratio, elongation and triangularity) and allows to independently set the values of the rotation velocity (Mach number) and the plasma current and β. Explicit expressions for the shape coefficients and examples of equilibria calculated with this method are presented. [ABSTRACT FROM AUTHOR]