Poloidal Mode Research Articles

A new explanation of the sawtooth phenomena in tokamaks

The ubiquitous sawtooth phenomena in tokamaks are so named because the central temperature rises slowly and falls rapidly, similar to the blades of a saw. First discovered in 1974, it has so far eluded a theoretical explanation that is widely accepted and consistent with experimental observations. We propose here a new theory for the sawtooth phenomena in auxiliary heated tokamaks, which is motivated by our recent understanding of “magnetic flux pumping.” In this theory, the role of the (m,n)=(1,1) mode is to generate a dynamo voltage, which keeps the central safety factor, q0, just above 1.0 with low central magnetic shear. When central heating is present, the temperature on axis will increase until at some point, and the configuration abruptly becomes unstable to ideal MHD interchange modes with equal poloidal and toroidal mode numbers, m=n>1. It is these higher order modes and the localized magnetic stochasticity they produce that cause the sudden crash of the temperature profile, not magnetic reconnection. Long time 3D MHD simulations demonstrate these phenomena, which appear to be consistent with many experimental observations.

Magnetohydrodynamics-induced internal crash near density limit in ohmic discharge on experimental advanced superconducting tokamak

The magnetohydrodynamics (MHD)-induced internal crash (IC) is one of the most fundamental dynamics of a tokamak discharge. Study of IC and the consequent formation of seed island (for neo-classical tearing modes) are still attractive in both experimental and numerical studies. In this work, a set of MHD-induced sawtooth like crashes (SLCs) have been observed in experimental advanced superconducting tokamak (EAST) ohmic discharge near density limit. With the tomography of high-resolution upgraded soft x-ray imaging system, it is observed that m/n = 2/1 tearing mode converts to a m/n = 1/1 instability, and it then triggers crash in the plasma core, here, m is the poloidal mode number and n is the toroidal mode number. Similar to sawtooth crash (SC), the crash of SLC here is due to m/n = 1/1 mode nonlinear dynamic. An extended MHD simulation code M3D is used to understand of the dynamics of m/n = 1/1 internal kink mode in SC in torus. A complex SC is reproduced from M3D nonlinear simulation under EAST realistic magnetic flux equilibrium and experimental resistivity. The rapid growth of unstable m/n = 1/1 kink and interaction with its higher harmonics, are responsible for SC. The simulation results show an existence of annular chaos belt outside q = 1 surface during SC. Furthermore, magnetic islands with higher poloidal mode number are found after SC. The formation of island after SC make plasma current profile flat in the core.

Two modes of ion-ion hybrid waves in magnetospheric plasma

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

The effect of resonant magnetic perturbation on the electron density threshold of runaway electron generation during disruptions on J-TEXT

The generation of runaway electrons (REs) during disruptions is a key issue for the safe operation of large tokamaks. For better design, a reliable scenario to suppress RE generation and for the investigation of RE generation during disruptions is highly essential. On J-TEXT, RE generation is strongly dependent on the pre-disruption electron density, toroidal magnetic fields (B T ) and magnetic perturbations. RE generation can be avoided in discharges with a low B T or a high electron density. For discharges with a high B T , a high electron density threshold is required to suppress RE generation. However, this threshold decreases with the application of resonant magnetic perturbations (RMP) which is applied before the thermal quench. The enhancement of magnetic perturbation increases the RE loss during disruptions, leading to robust runaway suppression in the discharges with a relatively low electron density. The electron density threshold required for RE suppression reduces with the increase of RMP strength and the m/n = 2/1 mode RMP is more efficient than the m/n = 3/1 mode RMP for the reduction of density threshold, where m and n are the poloidal and toroidal mode numbers, respectively. The NIMROD simulation is applied to investigate the transport of REs during disruptions, which indicates that the 2/1 mode RMP can create stronger magnetic perturbations during a disruption, resulting in a high loss ratio of RE seeds. All results provide evidence of the significant effect of RMP mode and amplitude on the electron density threshold for RE generation, which might give an insight into future large reactor tokamak operation with high electron densities.

Pc4‐5 Poloidal ULF Wave Observed in the Dawnside Plasmaspheric Plume

AbstractA localized Pc4‐5 ultralow‐frequency (ULF) wave event associated with a plasmaspheric plume was observed by THEMIS‐E on the dawnside near L = 6, which was identified as a second harmonic poloidal wave. The plume was identified as a sudden density enhancement during an outbound pass. The charged particle populations in the plume have a variety of periodic modulation characteristics at different energies. First, there is an antiphase relationship between magnetic field Br and particle flux across a wide energy range both for ions and electrons (~50 keV to 1 MeV). Second, there is a 180° phase shift in the modulated ion flux within an energy range of ~2–6 keV, with negative slope dispersions of ion pitch angle distributions at ~2–6 keV and ~50–75 keV, which are characteristic of drift‐bounce resonances. Third, the lower‐energy (<32 eV) ion flux is modulated at double the wave frequency, which are the result of E × B effect. Considering the generation mechanism of this poloidal mode wave within the plume, we find that it is likely generated by drift‐bounce resonance from an unstable population of ions, due to an inward radial phase space density gradient. We suggest that the localization of waves to the plume is because the high plasma density reduces the local poloidal mode eigenfrequency, enabling a match to the drift‐bounce frequencies of these ions, and resonant energy transfer from these particles to the eigenfunction at this location. This generates the Pc4‐5 second harmonic poloidal waves at a much lower L region than would otherwise be expected.

Kinetic infernal modes for Wendelstein 7-X-like -profiles

We show analytically that for $\unicode[STIX]{x1D704}$ -profiles similar to the one of the Wendelstein 7-X stellarator, where $\unicode[STIX]{x1D704}$ is the rotational transform of the equilibrium magnetic field, a highly conducting toroidal plasma is unstable to kinetically mediated pressure-driven long-wavelength reconnecting modes, of the infernal type. The modes are destabilized either by the electron temperature gradient or by a small amount of current, depending on how far from unity the average value of $\unicode[STIX]{x1D704}$ is, which is assumed to be slowly varying. We argue that, for W7-X, a broad mode with toroidal and poloidal mode numbers $(n,m)=(1,1)$ can be destabilized due to the strong geometric side-band coupling of the resonant kinetic electron response at locations where $\unicode[STIX]{x1D704}$ is rational for harmonics that belong to the mode family of the $(n,m)=(1,1)$ mode itself. In many regimes, the growth rate is insensitive to the plasma density, thus it is likely to persist in high performance W7-X discharges. For a peaked electron temperature, with a maximum of $T_{e}=5~\text{keV}$ , larger than the ion temperature, $T_{i}=2.5~\text{keV}$ , and a density $n_{0}=10^{19}~\text{m}^{-3}$ , instability is found in regimes which show plasma sawtooth activity, with growth rates of the order of tens of kiloHertz. Frequencies are either electron diamagnetic or of the ideal magnetohydrodynamic type, but sub-Alfvénic. The kinetic infernal mode is thus a good candidate for the explanation of sawtooth oscillations in present-day stellarators and poses a new challenge to the problem of stellarator reactor optimization.

ICRF coupling in ASDEX upgrade magnetically perturbed 3D plasmas

The RF properties of the four ion cyclotron range of frequencies (ICRF) antennas in the ASDEX Upgrade tokamak are characterized in H-mode magnetically perturbed 3D discharges. An n = 2 magnetic perturbation (MP) field is applied and rigidly rotated, which allows diagnosing the separatrix displacement and consequent coupling change. We find the antenna loading resistance to be coherently modified by the resulting non-axisymmetric plasma equilibria, thus becoming a function of the applied MP field poloidal mode spectra. We perform a detailed statistical analysis, which correlates the change in loading resistance to the fast wave R-cutoff layer movements. From it, a 1D scaling is derived that differs from previous studies evaluated in pure axisymmetric plasma conditions. This experimentally derived scaling is used to predict the average loading resistance change of the ITER ICRF antenna under applied MPs. ICRF coupling simulations using measured 1D density profiles are performed with the RAPLICASOL code, in order to investigate the predictive capabilities of numerical state of the art tools. We find that both 1D conventional scaling laws and 1D numerical simulations fail to capture the 3D physics, and can substantially overestimate the measured loading resistance change up to a factor of ∼3.

Numerical study of linear plasma dynamics in a spherical tokamak

The magnetohydrodynamic equilibrium is the starting point to study macro- instabilities in a confined plasma; for the particular case, where the system is axially symmetric, the static and stationary equilibrium is due by the Grad-Shafranov equation. We present the equilibrium state for a toroidal plasma confined by a spherical Tokamak with aspect ratio A ∼1.6, total plasma current 1.3 MA and beta parameter β ∼0.35. The Grad-Shafranov equation is solved numerically in a rectangular region of the poloidal plane, using the finite differences method under a successive over-relaxation scheme. Profiles of poloidal magnetic flux, pressure, safety factor and magnetic field are presented. Subsequently, by using the resistive magnetohydrodynamic model, said equilibrium is subjected to perturbations in the velocity to study the dynamics of the plasma in the linear regime. The plasma dynamics simulation is carried out under a fourth order finite difference scheme for the spatial derivatives and implementing the Runge-Kutta algorithm as a temporal integrator. The results show that the perturbations are located in the plasma outer edge; however, some poloidal modes move toward the central zone around the magnetic axis.

Experimental characterization of a quasi-coherent turbulent structure in the edge plasma in Wendelstein 7-X

A quasi-coherent mode (QCM) near the plasma edge is characterized experimentally by measuring the density fluctuation via a poloidal correlation reflectometer (PCR) in Wendelstein 7-X. This QCM frequency descends from 25 kHz near the separatrix to 10 kHz as the cutoff position penetrates toward the core. A similar mode structure is also observed in the spectra of electron cyclotron emission edge channels and Mirnov coil signals, which shows a clear correlation with respect to the PCR measurement. The mode evaluation yields a range for the poloidal mode number of , and for the normalized mode scale , which suggest a drift type instability. The QCM structure appears in the standard and narrow-mirror configurations (both with the rotational transform in the boundary), but is absent in the high- configuration (boundary ). The impact of plasma parameters on the QCM is discussed. It is observed that the QCM frequency and amplitude can be affected by the edge magnetic topology and plasma parameters. The shifts upward during the negative and non-stellarator-symmetric control coil current scans, which may be attributed to the effect of the shear, Er, and ne in the plasma edge region.

Recent Doppler backscattering applications in Globus-M tokamak

Recently, a four-frequency Doppler backscattering (DBS) system was installed on the Globus-M tokamak. In addition to the classical DBS application for determining the mean plasma rotational velocities, DBS was used for the investigation of different plasma oscillatory processes in the spherical Globus-M tokamak. Application of various DBS data processing allowed us to reveal and investigate plasma oscillations, such as geodesic acoustic mode, limit cycle oscillations and Alfvén modes. It has been shown that DBS also allows registering filament like structures, which manifest as quasi-coherent oscillations in signals of various DBS channels. The multi-frequency DBS system makes it possible to localize plasma oscillations, their poloidal and radial sizes and mode structure. The main results of the DBS application for the study of these oscillations are presented. A comparison of the DBS data with the data of other diagnostics is also given.

The effects of the misalignment of Mirnov coils in mode analysis based on the phase detection method

Mirnov coils (MCs) are used to identify the toroidal and poloidal mode number of tearing mode instabilities in the KSTAR tokamak. The mode number is analyzed by accumulating the phase of MC signals from a Morlet wavelet transform. There is ambiguity in identification of the poloidal mode number due to the phase distortion in the MC measurements. The extreme case is so-called phase folding. Although the phase distortion caused by the eddy currents in the in-vessel components and by the coupling of multimodes has been studied intensively, little attention is given to the effect of the orientation of MCs. The poloidal MCs are not aligned to the plasma shape but to the vacuum vessel. The effect of this misalignment is quantitatively analyzed by simulating the MC measurements of magnetic field fluctuations in a tokamak with mathematical modeling of perturbed current filaments on rational surfaces. The maximum MC response to a perturbed current filament occurs when the current filament is located at an angle different from the geometric installation angle of the MC. This angle is defined as the effective angle. The characteristics of the effective angle are investigated depending on the plasma shape, mode number, and distribution of the perturbed currents. The ambiguity in the identification of the poloidal mode number is reduced when the MC measurements are analyzed in the effective angular coordinate instead of the geometric coordinate. The only requirement for the calculation of the effective angles is an equilibrium reconstruction to identify the rational q surfaces.

Alteration of Particle Drift Resonance Dynamics Near Poloidal Mode Field Line Resonance Structures

AbstractWe examine the effect on drift‐resonant particle dynamics of a strongly peaked internally driven poloidal mode field line resonance (FLR; with specified frequency ω in the Pc5 range and azimuthal mode number m≫1). Using an analytic magneto‐hydrodynamic model in a dipole field to describe the ultra low frequency wave mode, we use the bounce‐averaged formalism of Northrop (1963) to obtain equations of motion for charged particles in the wave frame and find an analytic solution for the case of a temporally constant ultra low frequency wave amplitude profile. Focusing on equatorially mirroring electrons in this study, we demonstrate that, for sufficiently peaked radial profiles, multiple drift resonances appear that are associated with the FLR peak. These are in addition to the well‐known zeroth‐order drift resonance location, occurring when the unperturbed drift speed satisfies the resonance condition ( ). The additional resonances arise because the strongly peaked FLR wave field components provide sufficiently strong perturbations to the azimuthal drift speed to cause multiple zero crossings in the resonance condition. These additional resonances have trapping periods much lower than that of the zeroth‐order resonance and considerably complicate the electron dynamics. Further properties of these resonances and their measurable effect on electron dynamics are discussed. For example, their effect on observations of energetic electron flux on board satellites in the vicinity of an FLR is calculated and shown to significantly distort the typical signature associated with drift resonance (modulations in electron flux at the wave frequency with a 180° phase change across the resonant energy).

Reduced models for parallel magnetic field fluctuations and their impact on pressure gradient driven MHD instabilities in axisymmetric toroidal plasmas

It is well known that parallel magnetic field fluctuations are connected with finite plasma beta effects. It can therefore be expected that Reduced Models that simplify or neglect the parallel magnetic field may not capture the salient physics of all types of pressure gradient driven instabilities. This is particularly true in axisymmetric toroidal plasmas in which pressure driven MHD instabilities are always associated with toroidicty and the coupling of the poloidal mode harmonics. This contribution examines the distinct role of parallel magnetic field perturbations on short and long wavelength pressure driven MHD instabilities, and investigates quantitatively the impact of reduced electromagnetic models frequently deployed in fluid and gyrokinetic codes.

Numerical study of transition between even and odd toroidal Alfvén eigenmodes on EAST

Linear simulations of toroidal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on the experimental measurement. The “slowing down” distribution is adopted for modeling the equilibrium distribution of the energetic ions from the deuterium neutral beam injection on EAST. The frequency, the dominant poloidal mode number, the radial location and the detailed 2D mode structure of the TAE/RSAE (Reverse Shear Alfvén Eigenmode)/EPM (energetic particle mode) modes are consistent between the eigenvalue analysis and the NIMROD simulation. As the β fraction of EP increases, a transition between even and odd TAEs occurs, along with that between the ballooning and antiballooning mode structures. When the β fraction of EP is close to the transition threshold, both types of TAEs coexist.

Destabilization of field-line localized density fluctuation with a 1/1 internal kink mode in the EAST tokamak

A high frequency (HF) density fluctuation, ranging from 100 kHz to 400 kHz, is locally destabilized with an m/n = 1/1 internal kink mode before a sawtooth crash in the experimental advanced superconducting tokamak (EAST). The location is just around the region with a high electron pressure gradient due to the flux compression from the 1/1 mode. And this HF fluctuation can be triggered at both the low field side and high field side. This fluctuation has a poloidal wave number (kθ) from 3 to 5 cm−1, corresponding to a poloidal mode number (m) of 36–60. A threshold of the local electron pressure gradient (|∇p e|) exists for the stimulation of the HF fluctuation, and its amplitude increases with |∇p e|. The results could be beneficial for the understanding of a sawtooth crash, and also physics in 3D equilibrium.

Constraints on the resistivity of the oceanic lithosphere and asthenosphere from seafloor ocean tidal electromagnetic measurements

SUMMARY The electromagnetic (EM) field generated by ocean tidal flow is readily detectable in both satellite magnetic field data, and in ocean-bottom measurements of electric and magnetic fields. The availability of accurate charts of tidal currents, constrained by assimilation of modern satellite altimetry data, opens the possibility of using tidal EM fields as a source to image mantle electrical resistivity beneath the ocean basins, as highlighted by the recent success in defining the globally averaged lithosphere–asthenosphere boundary (LAB) with satellite data. In fact, seafloor EM data would be expected to provide better constraints on the structure of resistive oceanic lithosphere, since the toroidal magnetic mode, which can constrain resistive features, is a significant component of the tidal EM field within the ocean, but is absent above the surface (in particular in satellite data). Here we consider this issue in more detail, using a combination of simplified theoretical analysis and 1-D and 3-D numerical modelling to provide a thorough discussion of the sensitivity of satellite and seafloor data to subsurface electrical structure. As part of this effort, and as a step toward 3-D inversion of seafloor tidal data, we have developed a new flexible 3-D spherical-coordinate finite difference scheme for both global and regional scale modelling, with higher resolution models nested in larger scale solutions. We use the new 3-D model, together with Monte Carlo simulations of errors in tidal current estimates, to provide a quantitative assessment of errors in the computed tidal EM signal caused by uncertainty in the tidal source. Over the open ocean this component of error is below 0.01 nT in Bz at satellite height and 0.05 nT in Bx on the seafloor, well below typical signal levels. However, as coastlines are approached error levels can increase substantially. Both analytical and 3-D modelling demonstrate that the seafloor magnetic field is most sensitive to the lithospheric resistance (the product of resistivity and thickness), and is more weakly influenced (primarily in the phase) by resistivity of the underlying asthenosphere. Satellite data, which contain only the poloidal magnetic mode, are more sensitive to the conductive asthenosphere, but have little sensitivity to lithospheric resistance. For both seafloor and satellite data’s changes due to plausible variations in Earth parameters are well above error levels associated with source uncertainty, at least in the ocean interior. Although the 3-D modelling results are qualitatively consistent with theoretical analysis, the presence of coastlines and bathymetric variations generates a complex response, confirming that quantitative interpretation of ocean tidal EM fields will require a 3-D treatment. As an illustration of the nested 3-D scheme, seafloor data at five magnetic and seven electric stations in the northeastern Pacific (41○N, 165○W) are fit with trial-and-error forward modelling of a local domain. The simulation results indicate that the lithospheric resistance is roughly 7 × 108 Ωm2. The phase of the seafloor data in this region are inconsistent with a sharp transition between the resistive lithosphere and conductive asthenosphere.

Observation of toroidal acoustic mode in a current-less toroidal plasma

The existence of a Toroidal Acoustic Mode (TAM) in a nearly collisionless, magnetized current-less toroidal plasma is demonstrated experimentally. The mode is found to be a discrete, global, axisymmetric mode with measured frequency nearly three times that of 2cs/(2πR), where cs=Te/Mi, Te is the local electron temperature, and Mi is the ion mass. The observed frequency is found to be independent of the radial location. The mode is found to be driven by the nonlinear interaction of a finite frequency acoustic-like mode with itself. The TAM is a discrete, global mode and is found to exhibit (m = 1, n = 0) symmetry in density fluctuations and (m ≥ 0, n = 0) symmetry in potential fluctuations, where m and n are the poloidal and toroidal mode numbers, respectively. It is found that the TAM mode interacts with the background fluctuations. The observed frequency of both the TAM mode and the driver mode is found to scale linearly with 1/Mi, where Mi is the ion mass, but with their slopes different by a factor of 2. This mode is found to have characteristics similar to Geodesic Acoustic Modes often found in Tokamaks.

High frequency mode generation by toroidal Alfvén eigenmodes

Nonlinear generation of high frequency modes (HFMs) by the toroidal Alfvén eigenmode (TAE) observed in the HL-2A tokamak is analyzed using nonlinear gyrokinetic theory. It is found that the HFM can be dominated by |nq−m|=1 perturbations with predominantly ideal magnetohydrodynamic polarization if the two primary TAEs are copropagating, while the HFM can be characterized by nq − m = 0 electrostatic perturbations if the two primary TAEs are counter-propagating. Here, n and m are the toroidal and poloidal mode numbers, respectively, and q is the safety factor. The nonlinear process is sensitive to the equilibrium magnetic geometry of the device.

Observation of filament-like structures in ELMy H-mode plasma with a VUV imaging system developed on the EAST tokamak

On the EAST tokamak, filament-like structures have been observed in ELMy H-mode discharges with a high-speed vacuum ultraviolet (VUV) imaging system. The topos, chronos and their weight can be obtained simultaneously by performing the so-called singular value decomposition (SVD) analysis of raw VUV imaging data. The fluctuation amplitude is observed to be suppressed and enhanced gradually in the edge localized mode (ELM) crash and pedestal recovery phase in the chronos, respectively, while filament-like structures can only be found in the pedestal recovery phase on the topos. The mode structure, i.e. m/n = 36/9 (m and n are the poloidal and toroidal mode number, respectively) with = 0.95, = 0.07 ( and denote the mode location and mode width, respectively) is derived by a comparison of the synthetic images and the experimental imaging data.

Impurity effects on ion temperature gradient driven multiple modes in transport barriers

The impurity effects on ion temperature gradient (ITG) driven instability in transport barriers (TBs) are numerically investigated with the gyrokinetic integral eigenmode equations in tokamak plasmas. In particular, the effects of temperature and density gradients of the main ions ( and ) are analyzed independently to understand the physical mechanisms better, instead of keeping their ratio as carried out in previous works, when the parameters of impurity ions vary. It is found that the effect of impurity ions with outwardly peaked density profiles on ITG modes depends on the competition between the destabilizing effect of the impurity density gradient and the stabilizing effect induced by the dilution of main ions from impurity ions when is fixed, which is in significant contrast with the results for a fixed . The destabilizing effects include enhancement of ITG modes and coupling to the impurity mode (IM) in weak ITGs (big ) and strong impurity density gradient regimes. In addition, the stability boundaries for ITG modes, including high-order modes, are discussed in detail, and compared with previous works (Fröjdh et al 1992 Nucl. Fusion 32 419). Furthermore, the impurity ions with either inwardly or slightly outwardly peaked density profiles have weaker and stronger stabilizing effects on small and big poloidal wave vector modes, respectively. However, the impurity ions with steeper outwardly peaked density profiles have stronger stabilizing effects on big modes. Moreover, the inwardly peaked impurity ion density profiles are beneficial for main ion confinement and impurity decumulation, due to the main (impurity) ions flowing inwardly (outwardly). Finally, analyses of eigenmode structure and the quasi-linear particle flux are performed in detail. The results show that impurity ions have non-negligible effects, especially on higher-order ITG modes.