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The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition. [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]

Stability of the internal kink (IK) mode is numerically investigated with inclusion of the anisotropic thermal transport effect and the toroidal plasma flow. It is found that anisotropic thermal transport, in combination with plasma flow, stabilizes the IK in two ways. One is direct stabilization of the mode synergistically with plasma flow. The other, indirect stabilization involves generation of a finite mode frequency in static plasmas by thermal transport, which in turn invokes wave-wave resonance damping of the mode via interaction with stable shear Alfvén waves. This second IK stabilization mechanism is further corroborated by examining the eigenmode structure, which peaks at the radial locations where the mode frequency matches that of the shear Alfvén wave. Finally, two branches of unstable IK are identified, with mode conversion occurring at certain plasma flow speed and thermal transport level. These findings provide new physics insights in the IK stability in tokamak fusion plasmas. [ABSTRACT FROM AUTHOR]

The influence of negative triangularity (NT) of the plasma shape on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability has been numerically investigated, with results compared to that of the positive triangularity (PT) counterpart. By matching the safety factor profile for a series of toroidal equilibria, several important plasma parameters, including the triangularity, the plasma equilibrium pressure, the plasma resistivity as well as the toroidal rotation, have been varied. The TM localized near the plasma edge is found to be more unstable in the NT plasmas as compared to the PT counterpart. The fundamental reason for this difference is the lack of favorable average curvature stabilization in NT configurations. Direct comparison of the Mercier index corroborates this conclusion. For the core-localized mode, where the difference in the local triangularity between NT and PT becomes small and the curvature stabilization is significantly reduced, larger Shafranov shift in the plasma core associated with the NT configuration results in more stable TM. The plasma toroidal flow generally stabilizes the TM in plasmas with both NTs and PTs. The flow stabilization is however weaker in the case of negative triangularity with finite plasma pressure. [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 successful application of three-dimensional (3D) magnetohydrodynamic (MHD) spectroscopy enables us to identify the multi-mode eigenvalues in DIII-D and KSTAR tokamak experiments with stable plasmas. The temporal evolution of the multi-modes' stabilities have been detected. The new method is numerically efficient allowing the real time detection of MHD modes' stabilities during the discharge. The method performs active detection of the plasma stability by utilizing the upper and lower rows of internal non-axisymmetric coils to apply a wide variety of 3D fields. Multi-mode eigenvalues are extracted using subspace system identification of the plasma response measured by 3D-field magnetic sensors distributed at different poloidal locations. The equivalence of this new method with the one introduced by Wang (2019 Nucl. Fusion 59 024001) has been numerically corroborated. The more robust and efficient calculation developed here will enable real time monitoring of the plasma stability based on the extracted eigenvalues of stable modes. [ABSTRACT FROM AUTHOR]

Removal of helium ash and the anomalous transport of deuterium (D) and tritium (T) ions driven by collisionless trapped electron mode (CTEM) turbulence in tokamak plasmas with weak magnetic shear are studied. We derive the eigenvalue of CTEM with helium ash, and calculate the quasi-linear turbulent fluxes of helium ash, D and T ions simultaneously. Based on the analytical results, the parametric dependence of CTEM instability as well as the anomalous transport of helium ash and D-T ions is investigated, in order to explore the parameter region that is favorable for expelling more helium ash than D and T ions. It is found that helium ash with higher temperature and steeper density profile plays a role of destabilizing CTEM instability, and has higher transport level than that of T ions. We also find that increasing electron temperature and flattening electron density profile are favorable for exhausting helium ash. Isotopic effects (i.e. increasing the fraction of T ions) enhance the transport of both helium ash and D-T ions. Moreover, the trend of stronger transport level of helium ash than that of D-T ions is enhanced by raising electron temperature and flattening electron density profile as well as isotopic effects. Besides, the diffusivity is much larger than the convection. This indicates that the CTEM turbulence driven helium ash transport is favorable for removing helium ash under the parameter region used in the present paper. The possible relevance of our theoretical results to experimental observations is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influences of shear flows on dynamic evolutions of the m/n = 2/1 double tearing mode (DTM), using three-dimensional, toroidal, and nonlinear resistive magnetohydrodynamic code CLT. It is found that weak shear flows can lead to the decoupling of tearing modes on the two resonant surfaces, reducing the linear growth rate of DTMs. When the two tearing modes grow to large amplitudes at the nonlinear stage, they start to lock with each other. Consequently, DTMs with weak shear flows exhibit almost the same behavior as those without shear flows, i.e. weak shear flow can significantly reduce the linear growth rate of the DTM and delay a pressure crash, but has almost no influence on the time and the amplitude of the pressure crash. It is also found that the linear growth rates of the modes can become even larger than those without shear flows when the shear flow exceeds a critical value, due to Kelvin–Helmholtz (KH)-like instability. This KH-like instability can broaden the spectrum of the modes and then form a broad region with stochastic magnetic fields. Therefore, strong shear flows might be even more destructive in relation to plasma confinement. [ABSTRACT FROM AUTHOR]

The sawtooth activity is investigated for an EU DEMO reference plasma, including kinetic effects from both thermal particles and fusion-born alphas. Kinetic effects are studied in conjunction with modification of the magnetic shear near the q= 1 surface (q is the safety factor) due to local current drive. Kinetic stabilization on the internal kink mode is found by both the non-perturbative MHD-kinetic hybrid code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) and the perturbative semi-analytic Porcelli model. The latter predicts full stabilization of the mode, when the local magnetic shear s1 at the q= 1 surface is less than 1 (e.g. s1 ∼ 0.6 as is the case for the target EU DEMO plasma without local current drive). By increasing the local magnetic shear with local current drive up to s1 ∼ 2.8, one of the Porcelli sawtooth crash criteria can be satisfied, by accessing the ion-kinetic regime. Direct MARS-K non-perturbative eigenvalue computations, on the other hand, predict less kinetic stabilization of the internal kink and more robust triggering of the sawtooth crash in EU DEMO. The general trend of the predicted results remains similar though, between the MARS-K model and the Porcelli model. [ABSTRACT FROM AUTHOR]

The effect of electron cyclotron current drive (ECCD) on the multi-helicity neo-classical tearing modes (2/1 and 3/2 NTMs) in tokamak plasmas is numerically studied by adopting a reduced magnetohydrodynamic (MHD) model. It is found that the control process of certain single helicity NTM by ECCD can be influenced by nonlinear multi-helicity interaction. In the case without plasma rotation, the 'phase flip' of 2/1 NTM, which happens in the control of single helicity situation, has been modified by multi-helicity interaction and consequently behaves periodicity. And the 'phase flip' of 3/2 NTM disappears. When plasma rotation is considered, the direct control of 3/2 NTM becomes difficult. Moreover, a dual role of 5/3 mode is found in the multi-helicity interaction between 2/1 and 3/2 modes. The nonlinear mode coupling among 2/1 and 3/2 modes through the 5/3 mode will increase the difficulty of the suppression of 3/2 mode by ECCD, while the competition effect between multi-helicity NTMs leads to the relatively weak amplitude of 2/1 mode. In addition, investigations of multiple ECCDs are also carried out. The numerical results indicate that the control strategy for controlling multi-helicity NTMs by ECCD in experiments may require well-designed aiming to gain high effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

The explosive bursts, induced by self-organized double tearing modes (DTMs) in reversed magnetic shear tokamak plasmas, are numerically investigated based on a set of reduced two-fluid equations. It is found that the diamagnetic drift has a destabilizing effect on the mode in the Rutherford phase but can effectively stabilize the explosive burst of the mode in the following nonlinear phase. The plasma viscosity µ is found to have an important effect on the critical ion skin depth for completely suppressing the explosive bursts. In the low viscosity regime (i.e. , where is the critical viscosity), increases with increasing µ, because the increase of µ can effectively reduce the velocity difference of islands between the two rational surfaces, which mainly result from zonal flow and electron diamagnetic flow. In the high viscosity regime (i.e. ), however, decreases with increasing µ, because the increase of µ can greatly stabilize the DTM instability. In addition, the dependences of critical viscosity on viscosity and resistivity are obtained and the relevant mechanisms are analyzed. [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]

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]

This report summarizes the contributions to, and discussions at, the 6th Asia-Pacific Transport Working Group (APTWG) meeting, held on 21–25 June 2016 at Korea University, Seoul, Republic of Korea. The objective of the meeting was to develop an integrated understanding of transport phenomena in magnetically confined plasmas. To accomplish this objective, four technical working groups were organized under the headings: (1) turbulence suppression and transport bifurcation, (2) effect of magnetic topology on transport and magnetohydrodynamics-turbulence interaction, (3) nonlocality and non-diffusive transport, and (4) Energetic particles and particle/impurity transport. A summary is also given of the three plenary review talks on impurity transport, the magnetohydrodynamics relaxation process in reversed field pinch, and recent experimental and modelling results on the quiescent H-mode operation. [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]

The modified dispersion relation of qs  =  m/n double tearing modes (DTMs) with trapped energetic ions is derived by the matching procedure of mode structures in the ideal region and resistive layer. It is found that a mode transition between the DTM and the fishbone-like mode can be triggered, depending on fast ion driving, which provides a possible explanation for the observation of experiments (Günter et al 1999 Nucl. Fusion39 1793; Maget et al 2006 Nucl. Fusion46 797). The resistivity scaling of DTMs is changed significantly by on/off-axis heating beams. The effects of beam energy, electron inertia, magnetic shear and plasma resistivity on the stability of the mode and mode transition are discussed in detail. [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]

A generalized dispersion relation for fishbone instability is obtained by considering Gaussian distributions of spatial density and pitch angle of energetic electrons (EEs). The fishbone modes excited by trapped EEs are analysed in detail based on the HL-2A tokamak electron cyclotron resonant heating (ECRH) experiment. Numerical results show that the calculated time evolution of the mode real frequency is in reasonable agreement with the observations in ECRH experiment. Density gradient of the EEs plays an important role in excitation of the modes via resonant interaction between the modes and EEs. The modes are excited at the positions of maximum EE density gradient. The frequency of the mode in the case of on-axis heating is higher than that in the case of off-axis heating. The background plasma tends to prohibit excitation of the fishbone instabilities. The numerical results show that there is a cut-off background plasma density (or background plasma-β) for the fishbone instabilities. In addition, the toroidal magnetic field Bt has to be higher than a critical value in order to excite the mode, and the real frequency of the modes decreases with increasing Bt. [ABSTRACT FROM AUTHOR]