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The kinetic effects of thermal particles and fast ions on internal kink (IK) mode are numerically investigated by the MHD-kinetic hybrid code MARS-K. It is shown that either thermal particles or fast ions have stabilizing influence on IK. However, the former can not fully stabilize IK, and the later can suppress the IK. In addition, the synergistic effect from thermal particles and fast ions induces more stronger damping on IK. The kinetic effects from particles significantly raise the critical value of poloidal beta () for driving IK in the toroidal plasma. This implies a method of controlling IK or sawtooth in the high-βp discharge scenario of tokamak. It is noted that, at the q = 1 rational surface, mode structure becomes more sharp due to the self-consistent modification by particles' kinetic effect. [ABSTRACT FROM AUTHOR]

Kinetic effects of both trapped thermal and energetic particles on the resistive wall mode (RWM) and on the fishbone-like mode (FLM) are investigated in theory. Here, the trapped thermal particles include both ions and electrons. The FLM is driven by trapped energetic particles. The results demonstrate that thermal particle collisions can either stabilize or destabilize the RWM, depending on the energetic particle pressure βh. Furthermore, the critical value of βh for triggering the FLM is increased when the thermal particle contribution is taken into account. The critical value sensitively depends on the plasma collision frequency. In addition, the plasma inertia is found to have a negligible influence on the FLM. [ABSTRACT FROM AUTHOR]

Electromagnetic effects of the kinetic geodesic acoustic modes (KGAMs) are numerically studied in low β(= plasma pressure/magnetic pressure) tokamak plasmas. The parallel component of the perturbed vector potential is considered along with the electrostatic potential perturbation. The finite Larmor radius and finite orbit width of the ions as well as electron parallel dynamics are all taken into account. Systematic harmonic and ordering analysis is performed for collisionless damping of the KGAMs, assuming β~(κρi)2, where κand ρiare the radial component of the KGAM wave vector and the Larmor radius of the ions, respectively. It is found that the electron parallel dynamics enhances the damping of the electrostatic KGAM modes when the safety factor q is high. In addition, the electromagnetic (finite β effect is revealed to enhance and weaken the damping of the modes in plasmas of low and high safety factor q~2.0 and 5.5, respectively. The harmonic features of the KGAMs are discussed as well. [ABSTRACT FROM AUTHOR]

The linear behaviors of the double tearing mode (DTM) mediated by parallel electron viscosity in cylindrical plasmas with reversed magnetic shear and thus two resonant rational flux surfaces is numerically investigated. The distance between the two surfaces is found to play an important role for modes with poloidal mode number m>1. Two modes, one of which is centered at the inner rational surface and the other is located between the two surfaces, are simultaneously unstable and the growth rates show the standard single tearing mode (STM) scaling as γ∝R-1/3 when the distance is large (here, the Reynolds number R≡τυ/τh, τυ, and τh are, respectively, the viscosity penetration time of the magnetic field and the Alfvén time for a plasma sheet of width a). The latter is unstable only and the growth rate transits to the standard DTM scaling as γ∝R-1/5 for low-m (e.g., m<4) modes and keeps the STM scaling γ∝R-1/3 for high-m (e.g., m∼10) modes, which are found dominant, when the distance is decreased. In contrast, two unstable modes extending from plasma center to the two rational surfaces, respectively, coexist and the growth rates always show the scaling of γ∝R-1/5, independent of the distance, when the poloidal mode number m=1. The DTMs mediated by electron viscosity are enhanced by plasma resistivity of the range where the growth rate of the mode induced by the latter alone is comparable with that mediated by the former alone and vice versa. Otherwise, the growth rate of the mode is equal to the higher of the modes mediated by resistivity or electron viscosity alone when both of them are taken into account. [ABSTRACT FROM AUTHOR]

The internal kink (fishbone) modes, driven by barely passing energetic ions (EIs), are numerically studied with the spatial distribution of the EIs taking into account. It is found that the modes with frequencies comparable to the toroidal precession frequencies are excited by resonant interaction with the EIs. Positive and negative density gradient dominating cases, corresponding to off- and near-axis depositions of neutral beam injection (NBI), respectively, are analyzed in detail. The most interesting and important feature of the modes is that there exists a second stable regime in higher βh (=pressure of EIs/toroidal magnetic pressure) range, and the modes may only be excited by the barely passing EIs in a region of βth1<βh<βth2 (βth is threshold or critical beta of EIs). Besides, the unstable modes require minimum density gradients and minimum radial positions of NBI deposition. The physics mechanism for the existence of the second stable regime is discussed. The results may provide a means of reducing or even preventing the loss of NBI energetic ions and increasing the heating efficiency by adjusting the pitch angle and driving the system into the second stable regime fast enough. [ABSTRACT FROM AUTHOR]

The three-dimensional characteristics of the geodesic acoustic mode zonal flows (GAMZFs) and the ambient turbulence (AT) at the edge of the HuanLiuqi-2A tokamak [Y. Liu et al., Nucl. Fusion 45, S203 (2005)] are investigated with Langmuir probe arrays and the results are presented in detail. The toroidal and poloidal symmetries, and the radial scale of the GAMZFs are simultaneously identified. The envelopes of the high frequency components of the AT in the presence of the GAMZFs are analyzed. The GAM frequency components (GAMFCs) of the coherent envelopes are also shown to have poloidal and toroidal symmetries, and similar radial scales as the GAMZF does. The correlation between the GAMFCs of the envelopes and the GAMs is high, with phase shifts between π/2 to π, indicating that the GAMZFs may regulate the AT and the regulation is embodied in the envelopes. Three-wave coupling between GAM and AT is found to be a plausible formation mechanism for the former, which acts on the whole spectra of the latter within its scale length. The temporal evolutions of the total fluctuation power, the GAM and the AT powers show that the AT power decreases when GAM power increases and vice versa, indicating possible regulating effects of the latter on the former. [ABSTRACT FROM AUTHOR]

Combined Thomson scattering (TS) and laser-induced fluorescence (LIF) diagnostics are being developed. The Thomson scattering and laser-induced fluorescence are laser diagnostics, with joint both probing and c-ollecting optical systems, which are the most complex and expensive parts of the diagnostic systems of large tokamaks, can be combined. Thomson scattering by free electrons is the use-proven diagnostic method for measuring profiles of important parameters of the plasma electron component (electron tempera-ture Te and electron density ne), which requires a minimum of model assumptions. Almost all existing tokamaks are equipped with one or more TS systems, and by now, considerable experience has been accumulated in practical methods for implementation of these systems. The use of laser-induced fluorescence for measuring parameters of ion and neutral plasma components is less common, also because it requires knowledge of electron parameters to calculate populations of excited levels. The joint diagnostics of the Thomson scattering and laser-induced fluorescence in divertor plasma will be used to simultaneously measure the plasma parameters necessary for fundamental understanding physics of plasma detachment from divertor plates. These parameters are: the local parameters of plasma electrons (Te, ne), ion temperature (Ti) measured from the data on emission of helium ions (HeII), as well as densities of helium atoms (na(He)) and hydrogen isotopes (na(H,D,T)). The measured parameters make it possible to calculate the following characteristics: (i) the ionization and recombination rates (using the data on Te, ne, Ti, and na(H, D, T)); (ii) the friction force of the plasma flow due to collisions with neutral particles (using the data on Ti, ni (assuming ni = ne), and na(H, D, T)); and (iii) the pressure of the oncoming plasma flow (using the data on Te, ne, Ti, and ni). The article discusses advantages of combining laser diagnostics and ways of further development of the joint diagnostcs, based on the experience of creating similar diagnostics for domestic tokamaks and the similar diagnostics developed for ITER. [ABSTRACT FROM AUTHOR]

An analytical formula systematically predicts the observed frequency of pressure relaxation limit cycle oscillations in the vicinity of the transition to high confinement in four tokamaks (JET, ASDEX Upgrade, COMPASS, Globus-M). The experimental dataset spans the widest available range of frequencies, machine sizes and plasma ion species. The machine size dependence is explained by the connection length scale of plasma flows parallel to the magnetic field. The model also explains the observed up-down poloidal current asymmetry and the impact of the plasma ion species mass and charge. [ABSTRACT FROM AUTHOR]

Transport and loss of beam injected energetic particles (EPs) due to three-dimensional perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about 10 − 2 . The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ∼2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits. [ABSTRACT FROM AUTHOR]

The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. This paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)]. [ABSTRACT FROM AUTHOR]

The effects of impurity ions on the trapped electron mode (TEM) in tokamak plasmas are numerically investigated with the gyrokinetic integral eigenmode equation. It is shown that in the case of large electron temperature gradient (ge), the impurity ions have stabilizing effects on the TEM, regardless of peaking directions of their density profiles for all normalized electron density gradient R=Lne. Here, R is the major radius and Lne is the electron density gradient scale length. In the case of intermediate and/or small ge, the light impurity ions with conventional inwardly (outwardly) peaked density profiles have stabilizing effects on the TEM for large (small) R=Lne, while the light impurity ions with steep inwardly (outwardly) peaked density profiles can destabilize the TEM for small (large) R=Lne. Besides, the TEM driven by density gradient is stabilized (destabilized) by the light carbon or oxygen ions with inwardly (outwardly) peaked density profiles. In particular, for flat and/or moderate R=Lne, two independent unstable modes, corresponding respectively to the TEM and impurity mode, are found to coexist in plasmas with impurity ions of outwardly peaked density profiles. The high Z tungsten impurity ions play a stronger stabilizing role in the TEM than the low Z impurity ions (such as carbon and oxygen) do. In addition, the effects of magnetic shear and collision on the TEM instability are analyzed. It is shown that the collisionality considered in this work weakens the trapped electron response, leading to a more stable TEM instability, and that the stabilizing effects of the negative magnetic shear on the TEM are more significant when the impurity ions with outwardly peaked density profile are taken into account. [ABSTRACT FROM AUTHOR]

The effects of impurity ions on the short wavelength ion temperature gradient (SWITG) driven instability in elongated tokamak plasmas are numerically investigated with the gyrokinetic integral eigenmode equation. It is found that for a moderate electron density gradient, the SWITG mode is first destabilized and then stabilized with increasing elongation κ, which is different from the conventional long wavelength ITG mode. For a large electron density gradient, the elongation can effectively stabilize the SWITG mode. Moreover, the low Z impurity ions with inwardly (outwardly) peaked density profiles have stabilizing (destabilizing) effects on the SWITG modes in elongated plasmas. Interestingly, the high Z tungsten impurity ions with inwardly peaked density profiles play a stronger stabilizing role in the SWITG modes than the low Z impurity ions (such as carbon and oxygen) do. In particular, the high Z tungsten impurity ions with a weakly outwardly peaked density profile still have a stabilizing effect. Finally, the critical threshold of impurity density gradient scale length for exciting impurity mode is also numerically obtained, indicating that the impurity mode is harder to be excited in elongated plasmas than in circular ones. [ABSTRACT FROM AUTHOR]

We report results of global resistive magnetohydrodynamic (MHD) simulations, which predict that wide-spread reconnecting instabilities may cause an internal disruption when 5 MW off-axis negative-ion-based neutral beam (N-NB) injection is used during the current ramp-up phase of a JT-60SA plasma. The simulations include fast ions as passive test particles and were initialized with plasma profiles obtained from an integrated transport simulation. The beam-driven current produces a nonmonotonic safety factor profile with three q = 2 rational surfaces. The resulting double or multiple kink-tearing instabilities redistribute both the bulk and fast particles in the inner half of the plasma. While the radial profiles appear to be flattened, the actual field topology and particle distributions are found to saturate in helical states. Moreover, because magnetic drifts are still large during the current ramp-up phase, there is a large difference between the topology of the magnetic field and 500 keV deuteron orbits. Fast ion phase space islands may thus appear and overlap at different times and in different regions than their magnetic counterparts. [ABSTRACT FROM AUTHOR]

Effects of toroidal plasma flow, magnetic drift kinetic damping as well as feedback control, on the resistive wall mode instability in HL-2M tokamak are numerically investigated, using the linear stability codes MARS-F/K (Liu et al 2000 Phys. Plasmas7 3681, Liu et al 2008 Phys. Plasmas15 112503). It is found that the precession drift resonance damping due to trapped thermal particles ensures a robust passive stabilization of the n  =  1 (n is the toroidal mode number) RWM in the 2 MA double-null advanced plasma scenario designed for HL-2M, provided that the toroidal flow speed is not too fast: . With two rows of magnetic control coils designed for HL-2M, the optimal poloidal location for the RWM stabilization is found to be . Toroidal modeling also shows that the plasma flow damping, drift kinetic damping and magnetic feedback can be arranged to synergistically stabilize the RWM in HL-2M, by tuning the feedback gain phase and/or including derivative actions in the control loop. The numerical results obtained by MARS-F/K are qualitatively well re-produced by an analytic single-pole model. [ABSTRACT FROM AUTHOR]

Radial wavenumber dependencies of the residual zonal potential for E × B flow in a circular, large aspect ratio tokamak is investigated by means of the collisionless gyrokinetic simulations of Rosenbluth–Hinton (RH) test and the semi-analytic approach using an analytic solution of the gyrokinetic equation Rosenbluth and Hinton (1998 Phys.Rev.Lett.80 724). By increasing the radial wavenumber from an ion Larmor radius scale to an electron Larmor radius scale , the well-known level is retained, while the level remains O(1) when the wavenumber is decreased from the electron to the ion Larmor radius scale, if physically same adiabatic assumption is presumed for species other than the main species that is treated kinetically. The conclusion is not modified by treating both species kinetically, so that in the intermediate scale between the ion and electron Larmor radius scale it seems difficult to determine the level uniquely. The toroidal momentum conservation property in the RH test is also investigated by including an initial parallel flow in addition to the perpendicular flow. It is shown that by taking a balance between the initial parallel flow and perpendicular flows which include both E × B flow and diamagnetic flow in the initial condition, the mechanical toroidal angular momentum is approximately conserved despite the toroidal symmetry breaking due to the finite radial wavenumber zonal modes. Effect of electromagnetic potentials is also investigated. When the electromagnetic potentials are applied initially, fast oscillations which are faster than the geodesic acoustic modes are introduced in the decay phase of the zonal modes. Although the residual level in the long time limit is not modified, this can make the time required to reach the stationary zonal flows longer and may weaken the effectiveness of the turbulent transport suppression by the zonal flows. [ABSTRACT FROM AUTHOR]

Generation of coherent radial electric fields in plasma by drift-wave turbulence driven by plasma inhomogeneities is ab initio studied using gyro-kinetic particle simulation for conditions of operational tokamaks. In particular, the effect of the electron-to-ion mass ratio ϵ on the entire evolution of the plasma is considered. It is found that the electric field can be increased, and the turbulence-induced particle transport reduced, by making ϵ smaller, in agreement with many existing experimental observations. [ABSTRACT FROM AUTHOR]

The present vision for a plasma–material interface in the tokamak is an axisymmetric poloidal magnetic X-point divertor. Four tasks are accomplished by the standard poloidal X-point divertor: plasma power exhaust; particle control (D/T and He pumping); reduction of impurity production (source); and impurity screening by the divertor scrape-off layer. A low-temperature, low heat flux divertor operating regime called radiative detachment is viewed as the main option that addresses these tasks for present and future tokamaks. Advanced magnetic divertor configuration has the capability to modify divertor parallel and cross-field transport, radiative and dissipative losses, and detachment front stability. Advanced magnetic divertor configurations are divided into four categories based on their salient qualitative features: (1) multiple standard X-point divertors; (2) divertors with higher order nulls; (3) divertors with multiple X-points; and (4) long poloidal leg divertors (and also with multiple X-points). This paper reviews experiments and modeling in the area of radiative detachment in the advanced magnetic divertor configurations. [ABSTRACT FROM AUTHOR]

The ion temperature gradient (ITG) modes in transport barriers (TBs) of tokamak plasmas are numerically studied with a code solving gyrokinetic integral eigenvalue equations in toroidal configurations. It is found that multiple ITG modes with conventional and unconventional ballooning mode structures can be excited simultaneously in TBs with steep gradients of ion temperature and density. The characteristics of the modes, including the dependence of the mode frequencies, growth rate and structure on plasma parameters, are systematically investigated. Unconventional modes with large mode-number (where denotes a certain parity and peak number in ballooning space) dominate in the large region (), while the conventional mode with dominates in the medium region (), and unconventional modes with small mode-number dominate in the small region (). Thus, the spectra of these conventional and unconventional modes at steep gradients are qualitatively different from those of the conventional ITG modes at small or medium gradients, in which the growth rate of the only ITG mode with reaches maximum at the medium value . Through scanning ion temperature gradient and density gradient separately, it is proven that the synergetic effect of and , rather than alone, drives the unconventional ITG modes in TBs. Moreover, it is found that the critical value of for driving the unconventional ITG modes with large l number increases with increasing . In addition, the effects of magnetic shear on conventional and unconventional ITG modes in the high confinement regime (H-mode) are analyzed in detail, and compared with equivalent effects on conventional modes in the low and intermediate gradient regimes (L- and I- modes). Finally, the effects of the poloidal wave number and gradients of ion temperature and density on radial transport are analyzed based on quasi-linear mixing length estimations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Energetic ion excited non-resonant fishbone-like modes (FLMs) of m / n  >  1 is investigated for reversed magnetic shear configurations. It is found that the mode can be destabilized by trapped fast ions with a similar excitation mechanism as m / n  =  1 fishbones but with a local interchange-like mode structure, which is in agreement with previous experiments (Toi et al 1999 Nucl. Fusion39 1929). The dispersion relation of the mode is derived for m / n  >  1. The radial mode structure is then studied by numerically solving the eigenvalue equation. Effects of on/off-axis heating, the width of the particle distribution, the beam energy and the energy distribution on the mode are discussed in detail. Nonlinear analysis of the mode is also carried out by a modified predator–prey model. [ABSTRACT FROM AUTHOR]

Starting from the Braginskii equations, relevant for the tokamak edge region, a complete set of nonlinear equations for the geodesic acoustic modes (GAM) has been derived which includes collisionality, plasma beta and external sources of particle, momentum and heat. Local linear analysis shows that the GAM frequency increases with collisionality at low radial wave number and decreases at high . GAM frequency also decreases with plasma beta. Radial profiles of GAM frequency for two Tore Supra shots, which were part of a collisionality scan, are compared with these calculations. A discrepancy between experiment and theory is observed, which seems to be explained by a finite for the GAM when flux surface averaged density and temperature are assumed to vanish. It is shown that this agreement is incidental and self-consistent inclusion of and responses enhances the disagreement more with at high . So the discrepancy between the linear GAM calculation and experiment, (which also persist for more ‘complete’ linear models such as gyrokinetics) can probably not be resolved by simply adding a finite . [ABSTRACT FROM AUTHOR]

Fast ion beta scaling of non-resonant modes (NRMs) with a safety factor profile close to but above unity ( 1) in tokamak plasmas with a reversed magnetic shear configuration, particularly those with a weak shear ( ~ 0) of around , are analysed in this study. It is found that, in three different regimes of magnetic shear configuration, the fast ion beta scaling of the NRM growth rate are: (1) in the small but finite regime, (2) , in the = 0 regime, and (3) in an almost flat q-profile regime. The scalings suggest that the growth rate of the mode is related to the fast ion beta and weakens as the q-profile is flattened. The dispersion relation of NRM in the = 0 regime is then derived and analysed. [ABSTRACT FROM AUTHOR]

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

The identification of the magnetic island structure in the HL-2A tokamak is presented. First, the perturbation current as a source for the perturbation flux can be determined by using Mirnov probe measurements. By superposing the perturbation flux and the equilibrium flux reconnected by equilibrium fitting, the structure and the width of the magnetic islands can be estimated. The method has been used in the HL-2A experiments. [ABSTRACT FROM AUTHOR]