Modes In Tokamaks Research Articles

Neoclassical tearing mode seeding by coupling with infernal modes in low-shear tokamaks

A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

Magnetohydrodynamic theory of the global structure and magnetic components of the geodesic acoustic continuum modes in tokamaks

Ideal magnetohydrodynamic (MHD) theory is used to investigate some of the fundamental properties of the geodesic acoustic continuum modes (GAMs) in tokamaks, including their global structure, their associated magnetic components both inside and outside the plasma, and effects of a non-circular cross section of the plasma. In addition to the well-known side-bands in the perturbed density and pressure of the (electrostatic) GAM, the MHD continuum GAM also includes a side-band in the perturbed toroidal magnetic field as well as side-bands in the perturbed density, pressure, poloidal flow and in the magnetic components and ( is the poloidal mode number). These side-bands exist within the whole plasma and the magnetic components also outside the plasma, and the magnitudes of these components in the vacuum region are calculated in the paper. It is shown that, for plasmas with a conducting wall not too far from the plasma surface, the perturbed magnetic field in the vacuum region is dominated by its poloidal component , with poloidal dependence , in agreement with experiments. Aspects of the plasma equilibrium that affect the magnitude of the perturbed magnetic field in the vacuum region are discussed in the paper. Furthermore, the influence of a non-circular plasma cross section on the GAM frequency and on the spectrum of the global, perturbed magnetic field is analysed. It is found that the only significant effect of a non-circular cross section on the GAM frequency comes from elongation and its variation across the plasma radius. However, higher-order shaping effects, as well as finite aspect ratio, induce other Fourier components than in the magnetic halo that surrounds the GAM surface.

Nonlinear Stability and Saturation of Ballooning Modes in Tokamaks.

The theory of tokamak stability to nonlinear "ballooning" displacements of elliptical magnetic flux tubes is presented. Above a critical pressure profile the energy stored in the plasma may be lowered by finite (but not infinitesimal) displacements of such tubes (metastability). Above a higher pressure profile, the linear stability boundary, such tubes are linearly and nonlinearly unstable. The predicted saturated flux tube displacement can be of the order of the pressure gradient scale length. Plasma transport from these displaced flux tubes may explain the rapid loss of confinement in some experiments.

RETRACTED ARTICLE: Edge-Localized Modes (ELM) Modification with Transport Barrier Control in Tokamak by Analytical Strategies

High confinement mode (H-mode) in tokamaks is characterized by the formation of a transport barrier at the edge of the plasma. The H-mode increases the plasma energy confinement time by around a factor of two compared to the Low confinement mode (L-mode). This result made a great step towards achieving the higher temperatures and pressures needed to create ignition conditions. The Grad–Shafranov Equation describes the magnetic flux distribution of plasma in an axisymmetric system like a tokamak. In this paper, we have calculated the magnetic flux surfaces in IR-T1 tokamak by two methods. An analytical solution of magnetic surfaces approximated by equilibrium calculation of GS equation based on first three (and then four) terms of expansion in flux function. Results of two methods are in good agreement with each other.

Influence of driven current on resistive tearing mode in Tokamaks

The influence of driven current on the m/n=2/1 resistive tearing mode is studied systematically using a three-dimensional toroidal magnetohydrodynamic code. A uniform driven current with Gaussian distribution in the radial direction is imposed around the unperturbed rational surface. It is found that the driven current can locally modify the profiles of the current and safety factor, such that the tearing mode becomes linearly stable. The stabilizing effect increases with the increase of the driven current Icd or the decrease of its width δcd, unless an excessively large driven current reverses the magnetic shear near the rational surface and drives other instabilities such as double or triple tearing modes. The stabilizing effect can be negligible or becomes reversed if the maximum driven current density is not at the unperturbed rational surface.

Electromechanical modelling and design for phase control of locked modes in the DIII-D tokamak

A basic nonlinear electromechanical model is developed for the interaction between a pre-existing near-saturated tearing-mode, a conducting wall, active coils internal to the wall, and active coils external to the wall. The tearing-mode is represented by a perturbed helical surface current and its island has a small but finite moment of inertia. The model is shown to have several properties that are qualitatively consistent with the experimental observations of mode-wall and mode-coil interactions. The main purpose of the model is to guide the design of a phase control system for locked modes (LMs) in tokamaks. Such a phase controller may become an important component in integrated disruption avoidance systems. A realistic feedback controller for the LM phase is designed and tested for the electromechanical model. The results indicate that a simple fixed-gain controller can perform phase control of LMs with a range of sizes, and at arbitrary misalignment relative to a realistically dimensioned background error field. The basic model is expected to be a useful minimal dynamical system representation also for other aspects of mode-wall-coil interactions.

Linear gyrokinetic particle-in-cell simulations of Alfvén instabilities in tokamaks

The linear dynamics of Alfvén modes in tokamaks is investigated here by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The model equations are shown and the local shear Alfvén wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfvén Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is described. In particular, a phase-shift in the poloidal angle is found to be present for modes whose frequency touches the continuum, whereas a radial symmetry is found to be characteristic of modes in the continuum gap.

Influence of toroidal rotation on resistive tearing modes in tokamaks

Influence of toroidal equilibrium plasma rotation on m/n = 2/1 resistive tearing modes is studied numerically using a 3D toroidal MHD code (CLT). It is found that the toroidal rotation with or without shear can suppress the tearing instability and the Coriolis effect in the toroidal geometry plays a dominant role on the rotation induced stabilization. For a high viscosity plasma (τR/τV ≫ 1, where τR and τV represent resistive and viscous diffusion time, respectively), the effect of the rotation shear combined with the viscosity appears to be stabilizing. For a low viscosity plasmas (τR/τV ≪ 1), the rotation shear shows a destabilizing effect when the rotation is large.

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities in order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.

Stabilization of resistive wall modes in tokamaks by drift kinetic effects combined with magnetic feedback

The synergetic effects of drift kinetic resonances, the resistive layer dissipation, the magnetic feedback, and the toroidal plasma flow on the stability of the resistive wall mode are numerically investigated using a full toroidal resistive magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503). It is found that the plasma resistivity, coupled with the favourable average curvature effect, can enlarge the stable domain predicted by the drift kinetic model. A synergy between the precessional drift resonance damping, the magnetic feedback and the plasma flow helps open two stability windows. The width of the inner stability window increases with the feedback gain, but decreases with the flow speed. In addition, optimization of the toroidal phase difference of the feedback gains between the upper and lower active coils can lead to a full suppression of the mode.

Global Sound Mode in Plasma with Sloshing Ions

In recent experiments on Gas Dynamic Trap (GDT), as well as in earlier experiments on the GOL-3 device, a new and interesting class of oscillations was observed. Its mode structure and frequency resemble that of a sound wave trapped in the mirror cell as a resonator. Such modes can strongly interact with the bounce motion of ions and thus affect the axial confinement in mirror traps. The modes are probably similar to the global acoustic modes (GAMs) in tokamaks. However, there are significant difficulties in reconciling the existence of such modes with conventional theory of plasma waves. In both GOL-3 and GDT in relevant regimes the electron temperature is far below the theoretical limit for existence (let alone weak Landau damping) of ion-sound waves in homogeneous plasma. We explore different models of inhomogeneous anisotropic non-Maxwellian plasma of a mirror trap in search for possible explanations of the observed phenomena.

The Coupling Structure Features Between (2,1) NTM and (1,1) Internal Mode in EAST Tokamak**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB103000, 2011GB101000 and 2013GB102000) and sponsored in part by National Natural Science Foundation of China (Nos. 10725523, 10990212 and 11205199)

In the discharge of EAST tokamak, it is observed that (2,1) neoclassical tearing mode (NTM) is triggered by mode coupling with a (1,1) internal mode. Using singular value decomposition (SVD) method for soft X-ray emission and for electron cyclotron emission (ECE), the coupling spatial structures and coupling process between these two modes are analyzed in detail. The results of SVD for ECE reveal that the phase difference between these two modes equals to zero. This is consistent with the perfect coupling condition. Finally, performing statistical analysis of r1/1, ξ1/1 and w2/1, we find that r1/1 more accurately represents the coupling strength than ξ1/1, and r1/1 is also strongly related to the (2,1) NTM triggering, where r1/1 is the width of (1,1) internal mode, ξ1/1 is the perturbed amplitude of (1,1) internal mode, and w2/1 denot es the magnetic island width of (2,1) NTM.

Kinetic modelling of material erosion and impurity transport in edge localized modes in EAST

The kinetic modelling of material erosion and impurity transport on divertor plates in edge localized modes (ELMs) in tokamaks has been performed using the SDPIC and ITCD codes. The kinetic information on impinging particles and background plasma such as incident angle and energy, electric potential and field during ELMs can be well treated by the SDPIC code; this is generally difficult to obtain in experiments and fluid simulations due to diagnostic and technical limitations. The heat flux modelled with the SDPIC code can well reproduce the experimental result in EAST. The major power delivered by ions results in a strong increase of the erosion rate for both carbon and tungsten substrates during ELMs. The variation of the incident angle of impinging particles can be interpreted by the change of the potential drop induced by fast electrons during ELMs. The time difference in the peak values of erosion rate between the carbon and tungsten substrates is determined by the particle flux and sputtering yield. The heat loads for present ELMs in EAST cannot cause the ablation and melting of surface material. The eroded tungsten species show different transport properties from the eroded carbon species due to the small mean free path of W atoms and consequent prompt redeposition. A W self-sputtering avalanche is not observed during ELMs, ascribed to the small kinetic energy carried by the redeposited W species.

Rotational stabilization of the resistive wall modes in tokamaks with a ferritic wall

The dynamics of the rotating resistive wall modes (RWMs) is analyzed in the presence of a uniform ferromagnetic resistive wall with μ̂≡μ/μ0≤4 (μ is the wall magnetic permeability, and μ0 is the vacuum one). This mimics a possible arrangement in ITER with ferromagnetic steel in test blanket modules or in future experiments in JT-60SA tokamak [Y. Kamada, P. Barabaschi, S. Ishida, the JT-60SA Team, and JT-60SA Research Plan Contributors, Nucl. Fusion 53, 104010 (2013)]. The earlier studies predict that such a wall must provide a destabilizing influence on the plasma by reducing the beta limit and increasing the growth rates, compared to the reference case with μ̂=1. This is true for the locked modes, but the presented results show that the mode rotation changes the tendency to the opposite. At μ̂>1, the rotational stabilization related to the energy sink in the wall becomes even stronger than at μ̂=1, and this “external” effect develops at lower rotation frequency, estimated as several kHz at realistic conditions. The study is based on the cylindrical dispersion relation valid for arbitrary growth rates and frequencies. This relation is solved numerically, and the solutions are compared with analytical dependences obtained for slow (s/dw≫1) and fast (s/dw≪1) “ferromagnetic” rotating RWMs, where s is the skin depth and dw is the wall thickness. It is found that the standard thin-wall modeling becomes progressively less reliable at larger μ̂, and the wall should be treated as magnetically thick. The analysis is performed assuming only a linear plasma response to external perturbations without constraints on the plasma current and pressure profiles.

Heat flux effects on the dispersion relation for geodesic modes in rotating plasmas

The MHD theory of the effect of toroidal and poloidal rotations on the dynamics of Zonal Flows - ZFs and Geodesic Acoustic Modes - GAMs in axisymmetric magnetic confinement configurations is revisited. The MHD model has an arbitrariness regarding the energy conservation equation and previous works on the effect of rotation on ZFs and GAMs adopted an adiabatic law, or other simplifying assumptions, to treat this problem. However, in fusion grade plasmas, the heat transport along the magnetic field lines is rather fast and, therefore, a somewhat more appropriate model is to assume isothermal flux surfaces. This implies to take into account the heat transport equation in the model and, in the presence of rotation, this leads to an increase in the degree of the dispersion relation for these modes, giving rise to a low-frequency third branch of these modes. This has been previously obtained by Elfimov, Galvão and Sgalla [1] employing a model of circular flux surfaces from the outset. In this paper, the theoretical development is generalized by using flux coordinates, following the method of Ilgisonis et al [2]. This allows a better assessment of the applicability of the results and to investigate the relevance of the low frequency mode in non-circular tokamaks. Specific results for the TCABR tokamak are presented.

Influence of energetic ions on tearing modes in a reversed field pinch

Tearing mode stability analysis in the presence of circulating energetic ions (CEI) is studied in the reversed field pinch (RFP) magnetic configuration. In contrast to the minimal effect of precessional drift of CEI on tearing modes in tokamaks, the effect of precessional drift of CEI on tearing modes is important in the RFP. It is found that the effects of CEI on tearing modes in RFP depend on their toroidal circulating direction, and have a strong relation to the pressure gradient of CEI. For co-CEI, tearing modes can be stabilized if the pressure gradient of energetic ions is sufficiently large, which is qualitatively consistent with experimental results in the Madison Symmetric Torus.

Enhanced confinement scenarios without large edge localized modes in tokamaks: control, performance, and extrapolability issues for ITER

Large edge localized modes (ELMs) typically accompany good H-mode confinement in fusion devices, but can present problems for plasma facing components because of high transient heat loads. Here the range of techniques for ELM control deployed in fusion devices is reviewed. Two strategies in the ITER baseline design are emphasized: rapid ELM triggering and peak heat flux control via pellet injection, and the use of magnetic perturbations to suppress or mitigate ELMs. While both of these techniques are moderately well developed, with reasonable physical bases for projecting to ITER, differing observations between multiple devices are also discussed to highlight the needed community R&D. In addition, recent progress in ELM-free regimes, namely quiescent H-mode, I-mode, and enhanced pedestal H-mode is reviewed, and open questions for extrapolability are discussed. Finally progress and outstanding issues in alternate ELM control techniques are reviewed: supersonic molecular beam injection, edge electron cyclotron heating, lower hybrid heating and/or current drive, controlled periodic jogs of the vertical centroid position, ELM pace-making via periodic magnetic perturbations, ELM elimination with lithium wall conditioning, and naturally occurring small ELM regimes.

Analysis of the nonlinear behavior of shear-Alfvén modes in tokamaks based on Hamiltonian mapping techniques

We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfvénic modes resonantly excited by energetic particles in tokamak plasmas and of the ensuing energetic particle transports. These phenomena are investigated by following the evolution of a test particle population in the electromagnetic fields computed in self-consistent MHD-particle simulation performed by the HMGC code. Hamiltonian mapping techniques are used to extract and illustrate several features of wave-particle dynamics. The universal structure of resonant particle phase space near an isolated resonance is recovered and analyzed, showing that bounded orbits and untrapped trajectories, divided by the instantaneous separatrix, form phase space zonal structures, whose characteristic non-adiabatic evolution time is the same as the nonlinear time of the underlying fluctuations. Bounded orbits correspond to a net outward resonant particle flux, which produces a flattening and/or gradient inversion of the fast ion density profile around the peak of the linear wave-particle resonance. The connection of this phenomenon to the mode saturation is analyzed with reference to two different cases: a Toroidal Alfvén eigenmode in a low shear magnetic equilibrium and a weakly unstable energetic particle mode for stronger magnetic shear. It is shown that, in the former case, saturation is reached because of radial decoupling (resonant particle redistribution matching the mode radial width) and is characterized by a weak dependence of the mode amplitude on the growth rate. In the latter case, saturation is due to resonance detuning (resonant particle redistribution matching the resonance width) with a stronger dependence of the mode amplitude on the growth rate.

Effect of Equilibrium Current Profiles on External Kink Modes in Tokamaks

Based on a linearized MHD model, the effect of equilibrium current profiles on external kink modes in tokamaks is studied by MARS code. Three types of equilibrium current profiles are adopted in this work. Firstly, a set of parabolic equilibrium current profiles are chosen. In these profiles the maximum current values in the center of the plasma are fixed, and the currents have different gradient and jump at the plasma boundary. The effects of the current gradient and jump on the growth rate of external kink mode are investigated. It is found that the current jump which causes the q profiles to change plays an important role in the external kink modes in tokamaks. Secondly, a set of step equilibrium current profiles with different jump positions are chosen. The effect of jump position on external kink modes is discussed. Thirdly, a set of parabolic equilibrium current profiles with current bumps are chosen for the case of off-axis heating. The effects of height, width and position of the current bumps on external kink modes are analyzed. The flat equilibrium current profiles are disadvantageous for the MHD stabilities of tokamaks, because of the large current jump at the plasma edge. The peaked equilibrium current profiles and a large and localized current bump near the plasma edge benefit the MHD stabilities of tokamaks.

Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas

A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an elongated mode structure along the magnetic field line.