High Mode Number Research Articles

Modeling of ion cyclotron resonance frequency heating of proton-boron plasmas in EHL-2 spherical tokamak

Ion cyclotron resonance heating (ICRH) stands out as a widely utilized and cost-effective auxiliary method for plasma heating, bearing significant importance in achieving high-performance discharges in p-11B plasmas. In light of the specific context of p-11B plasma in the EHL-2 device, we conducted a comprehensive scan of the fundamental physical parameters of the antenna using the full-wave simulation program TORIC. Our preliminary result indicated that for p-11B plasma, optimal ion heating parameters include a frequency of 40 MHz, with a high toroidal mode number like to heat the majority H ions. In addition, we discussed the impact of concentration of minority ion species on ion cyclotron resonance heating when 11B serves as the heavy minority species. The significant difference in charge-to-mass ratio between boron and hydrogen ions results in a considerable distance between the hybrid resonance layer and the tow inverted cyclotron resonance layer, necessitating a quite low boron ion concentration to achieve effective minority heating. We also considered another method of direct heating of hydrogen ions in the presence of boron ion minority. It is found that at appropriate boron ion concentrations ( ), the position of the hybrid resonance layer approaches that of the hydrogen ion cyclotron resonance layer, thereby altering the polarization at this position and significantly enhancing hydrogen ion fundamental absorption.

Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability

Accretion disks are highly unstable to magnetic instabilities driven by shear flow, where classically, the axisymmetric, weak-field magnetorotational instability (MRI) has received much attention through local WKB approximations. In contrast, discrete nonaxisymmetric counterparts require a more involved analysis through a full global approach to deal with the influence of the nearby magnetohydrodynamic (MHD) continua. Recently, rigorous MHD spectroscopy identified a new type of ultralocalized, nonaxisymmetric instability in global disks with super-Alfvénic flow. These super-Alfvénic rotational instabilities (SARIs) fill vast unstable regions in the complex eigenfrequency plane with (near eigen)modes that corotate at the local Doppler velocity and are radially localized between Alfvénic resonances. Unlike discrete modes, they are utterly insensitive to the radial disk boundaries. In this work, we independently confirm the existence of these unprecedented modes using our novel spectral MHD code Legolas, reproducing and extending our earlier study with detailed eigenspectra and eigenfunctions. We calculate the growth rates of SARIs and MRI in a variety of disk equilibria, highlighting the impact of field strength and orientation, and find correspondence with analytical predictions for thin, weakly magnetized disks. We show that nonaxisymmetric modes can significantly extend instability regimes at high mode numbers, with maximal growth rates comparable to those of the MRI. Furthermore, we explicitly show a region filled with quasi-modes whose eigenfunctions are extremely localized in all directions. These modes must be ubiquitous in accretion disks, and play a role in local shearing box simulations. Finally, we revisit recent dispersion relations in the appendix, highlighting their relation to our global framework.

Efficient multimode Wigner tomography.

Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.

Compact high-Q Ka-band sapphire distributed Bragg resonator

In a class of high quality (Q-) factor dielectric resonators with low radiative losses, including popular whispering-gallery mode (WGM) resonators with high azimuthal mode numbers, due to high confinement of modal field in dielectric, the Q-factor is limited by the value of inverse dielectric loss tangent of dielectric material. Metal enclosures necessary for device integration only marginally affect the Q-factor while eliminating the residual radiative loss and allowing the optimization of input and output coupling. While very high Q-factors ∼200000 are available in sapphire WGM resonators in X-band, at millimeter wave frequencies increasing dielectric loss limits the Q-factor to much smaller values, e.g. ∼50000 and ∼25000 for quasi-TE and quasi-TM modes, correspondingly, at 36 GHz. The use of distributed Bragg reflection (DBR) principle allows to push modal energy outside dielectric while also isolating it from Joule losses in metallic enclosure walls. Very high Q∼600000>tgδ has been demonstrated in X-band [C. A. Flory and R. C. Taber, IEEE Trans. Ultrason., Ferroelectr., Freq. Control 44, 486–495 (1997).] at the expense of impractically large dimensions. In this work, we report on the assembly and testing of a compact Ka-band sapphire distributed Bragg reflector cavity characterized with Q-factor seven times larger than one predicted by the material’s dielectric loss at the frequency of interest. An intrinsic Q-factor of ∼200000 is demonstrated at 36 GHz for the lowest order TM-mode of a sapphire DBR. The resonator has 50 cm3 volume, smaller than previously demonstrated DBRs.

Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids

In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.

A pressure-free long-time stable reduced-order model for two-dimensional Rayleigh-Bénard convection.

The present work presents a stable proper orthogonal decomposition (POD)-Galerkin based reduced-order model (ROM) for two-dimensional Rayleigh-Bénard convection in a square geometry for three Rayleigh numbers: 104 (steady state), 3×105 (periodic), and 6×106 (chaotic). Stability is obtained through a particular (staggered-grid) full-order model (FOM) discretization that leads to a ROM that is pressure-free and has skew-symmetric (energy-conserving) convective terms. This yields long-time stable solutions without requiring stabilizing mechanisms, even outside the training data range. The ROM's stability is validated for the different test cases by investigating the Nusselt and Reynolds number time series and the mean and variance of the vertical temperature profile. In general, these quantities converge to the FOM when increasing the number of modes, and turn out to be a good measure of accuracy. However, for the chaotic case, convergence with increasing numbers of modes is relatively difficult and a high number of modes is required to resolve the low-energy structures that are important for the global dynamics.

Influence of lower hybrid wave injection on peeling-ballooning modes

The high-confinement mode (H-mode) significantly enhances the energy and particle confinement in fusion plasma compared with the low-confinement mode (L-mode), and it is the basic operation scenario for ITER and CFETR. Edge localized mode (ELM) often appears in H-mode, helping to expel impurities to maintain a longer stable state. However, the particle burst and energy burst from ELM eruptions can severely damage the first wall of fusion device, so, it is necessary to control the ELM. Experiments on EAST tokamak and HL-2A tokamak have been conducted with ELM mitigation by lower hybrid wave (LHW), confirming the effect of LHW on ELMs, but the physical mechanism of ELM mitigation by LHW is still not fully understood. In this paper, the influences of LHW injection on the linear and nonlinear characteristics of peeling-ballooning mode (P-B mode) are investigated in the edge pedestal region of H-mode plasma in tokamak by using the BOUT++ code. The simulations take into consideration both the conventional main plasma current driven by LHW and the three-dimensional perturbed magnetic field generated by the scrape-off layer helical current filament (HCF) on the P-B mode. The linear results show that the core plasma current driven by LHW moves the linear toroidal mode spectrum towards higher mode numbers and lower growth rates by reducing the normalized pressure gradient and magnetic shear of the equilibrium. Nonlinear simulations indicate that due to the broadening of the linear mode spectrum, the core current driven by LHW can reduce the pedestal energy loss caused by ELM through globally suppressing different toroidal modes of the P-B mode, and the three-dimensional perturbed magnetic field generated by LHW-driven HCF can reduce the energy loss caused by ELMs through promoting the growth of modes other than the main mode and enhancing the coupling between different modes. It is found in the study that the P-B mode promoted by the three-dimensional perturbed magnetic field generated by HCF has a mode number threshold, and when the dominant mode of the P-B mode is far from the mode number threshold driven by the three-dimensional perturbed magnetic field, the energy loss due to ELMs is more significantly reduced. These results contribute to a more in-depth understanding of the physical mechanism in ELM control experiment by LHW.

Topological elastic interface states in hyperuniform pillared metabeams

Topological states have been receiving a great deal of interest in various wave problems, such as photonic, acoustic, and elastic waves. However, few studies of topological elastic waves in non-periodic systems have been reported. Recently, hyperuniform systems suppressing long-range order while partly maintaining short-range order have provided new opportunities to control waves. In this work, we study the elastic topological interface states appearing between two Su–Schrieffer–Heeger (SSH)-like pillared metabeams where each metabeam, is constituted by a mirror symmetric hyperuniform structure. The SSH-like model is constructed by combining two hyperuniform metabeams with inverted configurations. We demonstrate that this structure could open new bandgaps at low frequencies, of which some are nontrivial and can support topological interface modes. We further show that the number of low-frequency bandgaps supporting the topological modes increases with the level of randomness, hence providing a high number of interface modes in the same structure. The robustness of the topological interface states against random perturbations in the pillars’ positions is further verified. Our work offers a reliable platform for studying topological properties and hyperuniform metamaterials and designing wave control devices for low-frequency wave attenuation and robust energy localization.

Tungsten transport due to the neoclassical toroidal viscosity induced by resonant magnetic perturbation in the EAST tokamak

The impact of neoclassical toroidal viscosity (NTV) induced by resonant magnetic perturbations (RMPs) on tungsten has been studied in EAST. Modeling results from NTVTOK show that the NTV effect on low charge state tungsten ions is greater than that on high charge state tungsten ions, and the effective transport coefficient of W20+ is only on the order of 10−4–10−3 m2/s, while the effective transport coefficient of W1+ can reach 0.1–1 m2/s, which is close to the 2D neoclassical diffusion coefficient of W1+. The flux of W1+ exhibits a clear phase dependence on the RMP spectrum, and the W1+ flux obtained from NTVTOK is higher at low toroidal mode numbers compared to high toroidal mode numbers of RMPs, which is qualitatively consistent with EAST experiments.

Toroidal Alfvén eigenmodes observed in low power JET deuterium–tritium plasmas

The Joint European Torus recently carried out an experimental campaign using a plasma consisting of both deuterium (D) and tritium (T). We observed a high-frequency mode using a reflectometer and an interferometer in a D-T plasma heated with low power neutral beam injection, . This mode was observed at a frequency and was located at major radii . The observed mode was identified as a toroidal Alfvén eigenmode (TAE) using the linear MHD code, MISHKA. Beam ions and fusion-born alpha particles were modelled using the full orbit particle tracking code LOCUST, which produces smooth distribution functions suitable for stability calculations without analytical fits or the use of moments. We calculated the stability of the 21 candidate modes using the HALO code. These calculations revealed that beam ions can drive TAEs with toroidal mode numbers with linear growth rates , while TAEs with n < 8 are damped by the beam ion population. Alpha particles drive modes with significantly smaller linear growth rates, due to the low alpha power generated almost exclusively by beam-thermal fusion reactions. Non-ideal effects were calculated using complex resistivity in the CASTOR code, leading to an assessment of radiative, collisional, and continuum damping for all 21 candidate modes. Ion Landau damping was modelled using Maxwellian distribution functions for bulk D and T ions in HALO. Radiative damping, the dominant bulk damping mechanism, suppresses modes with high toroidal mode numbers. Comparing the drive from energetic particles with damping from thermal particles, we find all but one of the candidate modes are damped. The single net-driven n = 9 TAE with a net growth rate matches experimental observations with a lab frequency and location . The TAE was driven by co-passing particles through the resonance. Both co- and counter-passing alpha particles drive the TAE through the resonance. Additional sideband resonances contribute significant drive for both beam and alpha particles.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes (NDTMs) in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics (MHD) equations. Cases with different separations Δ rs = |r s2–r s1| between the two same rational surfaces are considered. In the small Δ rs cases, the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase. Moreover, the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation, forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence. As a result, the profiles of safety factors also enter a nonlinear oscillation phase. In the intermediate Δ rs case, the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces, because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces. In the large Δ rs case, through destabilizing the outer islands significantly, the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.

Enhanced secrecy in optical communication using speckle from multiple scattering layers.

We study the secrecy of an optical communication system with two scattering layers, to hide both the sender and receiver, by measuring the correlation of the intermediate speckle generated between the two layers. The binary message is modulated as spatially shaped wavefronts, and the high number of transmission modes of the scattering layers allows for many uncorrelated incident wavefronts to send the same message, making it difficult for an attacker to intercept or decode the message and thus increasing secrecy. We collect 50,000 intermediate speckle patterns and analyze their correlation distribution using the Kolmogorov-Smirnov (K-S) test. We search for further correlations using the K-Means and Hierarchical unsupervised classification algorithms. We find no correlation between the intermediate speckle and the message, suggesting a person-in-the-middle attack is not possible. This method is compatible with any digital encryption method and is applicable for codifications in optical wireless communication (OWC).

Convergent Richtmyer–Meshkov instability on two-dimensional dual-mode interfaces

We report the first shock-tube experiments on two-dimensional dual-mode air–SF $_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

High Number of Transport Modes: A Requirement for Contact Resistance Reduction to Atomically Thin Semiconductors

Electrical contacts to atomically thin 2-D semiconductors are considered as the hindering aspect of electronic devices based on these materials. The high resistance of such contacts stems from their Schottky nature in contrast to the desired low-resistance Ohmic contacts. This issue of Schottky contacts is thus one of the major inhibitors to the integration of 2-D materials into mainstream technology. In this work, we explore contact resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula> ) to atomically thin 2-D semiconductors in terms of the injected current through the Schottky barrier (SB) by using the Landauer-Büttiker formalism as well as experimental measurements and technology computer aided design (TCAD) simulations. We show that the SB height and width, which are determined by the metal–semiconductor interface and the number of charge carriers in the semiconductor channel, respectively, affect <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula> when it is relatively high ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}} &gt;$ </tex-math></inline-formula> 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{k}\Omega \cdot \mu \text{m}$ </tex-math></inline-formula> ). However, the number of transport modes for carrier injection is the limiting factor for aggressive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula> lowering ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}} &lt; $ </tex-math></inline-formula> 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{k}\Omega \cdot \mu \text{m}$ </tex-math></inline-formula> ), even for near-zero SB height. Our results show that to reduce <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {C}}$ </tex-math></inline-formula> below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100~\Omega \cdot \mu \text{m}$ </tex-math></inline-formula> , large number of transport modes are required, which can be accomplished through raising the number of channel carriers above 5. 1013 cm-2 by means of heavy doping or gating. Our conclusions offer insight for future contact engineering and can explain recently published state-of-the-art results.

Torsional vibration of Timoshenko-Gere non-circular nano-bars

The displacement field and governing equation completely depend on the cross-section shape in the torsion of nano-bars. Due to the torsion of structure and warping of its cross-section, axial strain is created. A review of the literature demonstrates that the effect of the normal strain in the torsional analysis of nanostructures with non-circular cross-sections is ignored for the sake of simplicity and causes a computational error. While in the torsion of short nano-bars due to the great warping of the cross-section the normal strain appears and it shouldn’t be ignored. Therefore, for the first time, the effect of normal strain based on the torsion of Timoshenko-Gere theory is considered in this research. In this theory, the twist rate of non-circular sections in the axial direction is not considered constant, unlike studies in the literature. The governing equation of torsional vibration is extracted using the Hamilton principle, and the nonlocal strain gradient theory is used to show the size-dependent effects. The fundamental frequency is calculated for the arbitrary cross-section shape by using Galerkin’s method. The effect of parameters such as size effects, the thickness of nano-bar, mode number, and dimensions changes of cross-section versus natural frequency of nano-bar for both the Timoshenko-Gere and typical theories are investigated. Results indicate that neglecting normal strain due to warping the cross-section causes a significant error in the short nano-bars, especially at higher mode numbers. Also, a comparison is made between the obtained natural frequencies and those of the results reported in the literature.

Gregory-Laflamme encounters Superradiance

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

Comparison of the Characteristics of Internal Wave Propagation under Two Surface-Boundary Conditions in Continuously Density-Stratified Oceans

Zhang, H.-s.; He, L.; Zhang, Z.-h., and Zhang, Y., 2023. Comparison of the characteristics of internal wave propagation under two surface boundary-conditions in continuously density-stratified oceans. Journal of Coastal Research, 39(2), 303–316. Charlotte (North Carolina), ISSN 0749-0208. Complete theoretical solutions were developed for the propagation of internal waves (IWs) with small amplitudes in a continuously density-stratified ocean under the free surface-boundary condition and rigid lid assumption. Additionally, a numerical model was established for the propagation of IWs under the free surface-boundary condition. In the proposed model, the Euler equations are employed as the governing equations and are discretized with an improved SIMPLE algorithm. In waters with a constant depth, a comparison between the numerical and theoretical results proved the reasonability and accuracy of the proposed method. Additionally, the numerical results under the free surface-boundary condition were compared with those under the rigid lid assumption to analyse the differences between the calculated velocities and density fields. Herein, the influences of characteristic parameters, including the period and amplitude of the incident waves and the coefficient of density and the mode number on the velocity fields under the two surface-boundary conditions, are discussed thoroughly. In the waters with nonuniform varied depths, numerical simulations on the IWs propagation were performed under the two surface-boundary conditions. Differences between the calculated physical fields of IWs in front of and behind the submerged dike are discussed. The detailed analyses showed that differences exist between the calculation results under the two surface-boundary conditions. In particular, they were obvious for the cases with high mode number and variable topography. The results are significant considering the propagation mechanism of IWs under different surface-boundary conditions in a continuously density-stratified ocean.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 2.07 m with the normalized minor radius 0.2 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

Multi-scale structures of electric current generated by collisionless trapped-electron-mode turbulence

The spatial structure and amplitude of the current induced by collisionless trapped-electron-mode (CTEM) turbulence are investigated by gyrokinetic simulations. It is shown that the barely passing electrons play a crucial role in determining the magnitude and direction of the current density. Two characteristic radial scales of the current density are found. The fine structure (a few ion Larmor radius) of the turbulence-induced current is observed near the rational surfaces. Furthermore, the mesoscale structure (tens of ion Larmor radii) of the turbulence-induced current related to the zonal flow shear is confirmed, especially for the high toroidal mode number (n) CTEM. For the strongly driven CTEM, the zonal flow shear effect on the turbulence-induced current is significant, while it is not visible for the weakly driven CTEM. We show that the magnitude of the CTEM turbulence-induced current density features a moderate local magnitude comparable to the bootstrap current density near rational surfaces, as demonstrated by nonlinear simulations with multi-n modes.