Poloidal Symmetry Research Articles

Helical streamers guided by surface electromagnetic standing waves

The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment, in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube. The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory. The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.

Mechanism of low-temperature helical streamer discharge driven by pulsed electromagnetic field

Under the condition of specific pulsed discharge parameters, the discharge mode conversion of the low-temperature plasma jet discharge channel that originally propagates along a straight line will occur, forming a three-dimensional helical plasma channel. Unlike the traditional helical wave discharge, there are no factors such as an external constant magnetic field that destroys the poloidal symmetry of the dielectric tube, and the chiral direction of the helical streamer will change with the discharge parameters. In order to understand in depth the electromagnetic mechanism of the helical structure in the plasma jet, and the source and influencing factors of the poloidal electric field that leads to the helical shape and determines the chirality in this new type of discharge, we analyze the complex characteristics and electromagnetic mechanism of the helical streamer, such as the chiral direction, pitch, branching, by establishing a self-consistent plasma theoretical model. It is found that the phase of the poloidal wave mode has an effect on the chiral selection of the helical streamer, that the electron density has an influence on the pitch of the streamer, and that the repetition frequency has an effect on the bifurcation point. The above discharge characteristics and their influencing factors are of scientific significance in exploring the interaction mechanism of electromagnetic wave and plasma, and also in providing experimental and theoretical support for the chiral application of low-temperature plasma.

Global simulations of energetic electron excitation of beta-induced Alfvén eigenmodes

The energetic electron (EE) excitation of beta-induced Alfvén eigenmodes is investigated by using the newly developed global eigenvalue code MAS, which is based on a hybrid model that consists of Landau fluid bulk plasma and drift kinetic EE. Specifically, the bulk plasma kinetic effects such as finite Larmor radius, diamagnetic drifts and Landau dampings, and the EE adiabatic fluid response of convection and non-adiabatic kinetic response of precessional drift resonance are incorporated in the simulations. The global eigenmode equation is solved for e-BAE mode structure and linear dispersion relation in tokamak non-perturbatively. The radial width of e-BAE mode structure becomes narrower as the toroidal mode number increases, which can be explained by the change of Alfvén continuous spectra that interact with kinetic Alfvén waves for corresponding eigenmode formation. The e-BAE growth rate exhibits a non-monotonic variation with toroidal mode number for precessional drift resonance destabilization, while the e-BAE real frequency is close to the continuum accumulation point that almost remains the same. The parametric dependence of e-BAE stability on EE density and that on temperature are analyzed by MAS non-perturbative simulations, which shows that the EE density can affect e-BAE real frequency and thus changes the resonance condition, resulting in e-BAE stabilization in the strong EE drive regime. Further, the EE non-perturbative effect on the symmetry breaking of e-BAE mode structure is reported. The poloidal symmetry breaking characterized by the ‘boomerang’ shape two-dimensional (2D) structure can be greatly enhanced by increasing EE temperature, together with the large radial variation of the poloidal phase angle of dominant principal poloidal harmonic. The radial symmetry breaking of e-BAE mode structure arises when EE density/temperature drive is not symmetric with respect to corresponding rational surface, which can lead to a net volume-averaged value of e-BAE parallel wave number which drives plasma intrinsic rotation. These results are helpful in understanding the e-BAE dynamics observed in recent experiments.

Identity of the JET M-mode and the ASDEX Upgrade I-phase phenomena

An H-mode plasma state free of edge-localized mode (ELM), close to the L-H transition with clear density and temperature pedestal has been observed both at the Joint European Torus (JET) and at the ASDEX Upgrade (AUG) tokamaks usually identified by a low frequency (LFO, 1–2 kHz), m = 1, n = 0 oscillation of the magnetics and the modulation of pedestal profiles. The regime at JET is referred to as M-mode while at AUG as intermediate phase or I-phase. This contribution aims at a comparative analysis of these phenomena in terms of the density and temperature pedestal properties, the magnetic oscillations and symmetries. Lithium beam emission spectroscopy (Li-BES) and reflectometer measurements at JET and AUG show that the M-mode and the I-phase modulates the plasma edge density. A high frequency oscillation of the magnetics and the density at the pedestal is also associated with both the M-mode and the I-phase, and its power is modulated with the LFO frequency. The power modulation happens simultaneously in every Mirnov coil signal where it can be detected. The bursts of the magnetic signals and the density at the pedestal region are followed by the flattening of the density profile, and by a radially outward propagating density pulse in the scrape-off layer (SOL). The analysis of the helium line ratio spectroscopy (He-BES) signals at AUG revealed that the electron temperature is modulated in phase with the density, thus the I-phase modulates the pressure profile gradient. This analysis gave opportunity to compare Li-BES and He-BES density profiles at different locations suggesting a toroidal and poloidal symmetry of the density modulation. The presented results indicate that the regimes, the AUG I-phase and the JET M-mode, exhibit similar characteristics, which leads to the conclusion that the regimes are likely the same.

Three-dimensional effect of particle motion on plasma filament dynamics

It is shown for the first time with the three-dimensional (3D) electrostatic particle-in-cell simulation that the plasma particle motion influences plasma filament dynamics three-dimensionally. If we assume that the filament size on the cross section is a few times as large as ρemi/me and that the ion temperature is higher than the electron temperature, the poloidal symmetry of filament propagation is broken and the propagation velocity has the non-negligible poloidal component, where ρe is the electron Larmor radius. Then, it is observed that such propagation dynamics depend on the position on the magnetic field line, i.e., in the toroidal direction. As the ion temperature increases beyond the electron temperature, the perpendicular electric field in a filament varies greatly according to the toroidal position. Such a variation might arise from the presheath potential drop on the potential hill side in a filament. Thus, the toroidal dependence of the propagation dynamics appears.

Magnetic configuration effects on the Reynolds stress in the plasma edge

Breaking the poloidal symmetry of the magnetic shear induced tilt of turbulent structures, by either divertor X-point resistivity or limiter positions, can lead to a finite (residual) contribution to the flux-surface averaged radial-binormal Reynolds stress. This residual stress supports or works against the radial electric field at the plasma edge of a tokamak. The impact of divertor geometry on the poloidal pattern of the Reynolds stress is studied by flux-coordinate-independent fluid simulations. Clear modifications of the Reynolds stress are found due to the magnetic shear in the confined region. The impact of different poloidal limiter positions on the radial electric field and the Reynolds stress is studied by means of magnetic field aligned gyrofluid simulations. Only if the limiter is close to the outer midplane can its position have a substantial effect on the radial electric field.

Microscopic Effect on Filamentary Coherent Structure Dynamics in Boundary Layer Plasmas

This study has demonstrated kinetic behaviors on the plasma filament propagation with the three-dimensional (3D) Particle-in-Cell (PIC) simulation. When the ion-to-electron temperature ratio T i / T e is higher, the poloidal symmetry breaking in the filament propagation occurs. The poloidal symmetry breaking is thought to be induced by the unbalanced potential structure that arises from the effect of the gyro motion of plasma particles.

Limiter observations during W7-X first plasmas

During the first operational phase (referred to as OP1.1) of the new Wendelstein 7-X (W7-X) stellarator, five poloidal graphite limiters were mounted on the inboard side of the vacuum vessel, one in each of the five toroidal modules which form the W7-X vacuum vessel. Each limiter consisted of nine specially shaped graphite tiles, designed to conform to the last closed field line geometry in the bean-shaped section of the standard OP1.1 magnetic field configuration (Sunn Pedersen et al 2015 Nucl. Fusion 55 126001). We observed the limiters with multiple infrared and visible camera systems, as well as filtered photomultipliers. Power loads are calculated from infrared (IR) temperature measurements using THEODOR, and heating patterns (dual stripes) compare well with field line mapping and EMC3-EIRENE predictions. While the poloidal symmetry of the heat loads was excellent, the toroidal heating pattern showed up to a factor of 2× variation, with peak heat loads on Limiter 1. The total power intercepted by the limiters was up to ~60% of the input ECRH heating power. Calorimetry using bulk tile heating (measured via post-shot IR thermography) on Limiter 3 showed a difference between short high power discharges, and longer lower power ones, with regards to the fraction of energy deposited on the limiters. Finally, fast heating transients, with frequency >1 kHz were detected, and their visibility was enhanced by the presence of surface coatings which developed on the limiters by the end of the campaign.

Investigation of zonal flows by using the collective scattering measurement of density fluctuations

The poloidal rotation velocities in the core plasma region are studied using the instantaneous frequency method (IFM) with the density fluctuations measured by the CO2 laser collective scattering diagnostics on the HT-7 tokamak. A coherent mode is observed in the fluctuations of poloidal velocities with the mode frequency from 10 to 20 kHz. It is identified as geodesic acoustic mode (GAM) zonal flow with poloidal symmetry (m = 0) and its mode frequency coinciding with the theoretical expected GAM frequency. The nonlinear interactions are investigated by applying the envelope analysis on the density fluctuations. The results confirm that the envelope modulation in the high frequency density fluctuations only comes from the shearing by GAM. The comparison between IFM and envelope analysis is also discussed.

RCD Large Aspect-Ratio Tokamak Equilibrium with Magnetic Islands: a Perturbed Approach

Solutions of Grad-Shafranov (GS) equation with Reversed Current Density (RCD) profiles present magnetic islands when the magnetic flux is explicitly dependent on the poloidal angle. In this work it is shown that a typical cylindrical (large aspect-ratio) RCD equilibrium configuration perturbed by the magnetic field of a circular loop (simulating a divertor) is capable of generate magnetic islands, due to the poloidal symmetry break of the GS equilibrium solution.

The influence of finite Larmor radius effects on the radial interchange motions of plasma filaments

The influence of finite Larmor radius (FLR) effects on the perpendicular convection of isolated particle density filaments driven by interchange motions in magnetized plasmas is investigated using a two-moment gyrofluid model. By means of numerical simulations on a two-dimensional, bi-periodic domain perpendicular to the magnetic field, it is demonstrated that the radial velocities of the blob-like filaments are roughly described by the inertial scaling, which prescribes a velocity proportional to the square root of the summed electron and ion pressures times the square root of the blob width. Due to FLR effects, the poloidal up-down symmetry in the particle density field observed in the zero Larmor radius limit is broken. The symmetry breaking implies a poloidal motion of the blobs in the B×∇B direction. At later times, the direction of the poloidal motion is reversed when the blob is decelerated. It is shown that the spatial structure of the blobs depends on the ratio of the ion gyroradius to the initial filament size ρi/σ. Blobs with ρi/σ≳0.2 remain coherent as they move through the scrape-off layer, whereas blobs with ρi/σ≲0.1 form plume-like structures that loose their coherence and eventually become fragmented. After having traveled approximately five times their initial widths, coherent blobs carry ∼2–3 times the particle density of fragmented blobs. It is shown that FLR effects reduce mixing, stretching, and generation of small spatial scales in the particle density field by setting up a sheared flow surrounding the blob.

Plasma torque and nonambipolar transport

Poloidal symmetry breaking in toroidal plasmas causes a damping of poloidal rotation and toroidal symmetry breaking a damping of toroidal rotation. These torques are transmitted by the magnetic field to the outside world. An upper limit exists on the torque that can be transmitted by magnetic asymmetries. This limit is enforced by shielding asymmetries from the plasma, which can be an important effect for toroidal asymmetries. The torque interaction of plasmas with magnetic fields can be either through an anisotropic pressure or by the drive for magnetic islands. The physics of both types of interactions are considered and paradoxical effects are clarified.

3D modelling of edge parallel flow asymmetries

The issue of parallel flows asymmetries in the edge plasma is tackled with a new first principle transport and turbulence code. TOKAM-3D is a 3D full-torus fluid code that can be used both in diffusive and turbulent regimes and covers either exclusively closed flux surfaces or both open and closed field lines in limiter geometry. Two independent mechanisms susceptible to lead to large amplitude asymmetric parallel flows are evidenced. Global ExB drifts coupled with the presence of the limiter break the poloidal symmetry and can generate large amplitude parallel flows even with poloidally uniform transport coefficients. On the other hand, turbulent transport in the edge exhibits a strong ballooning of the radial particle flux generating an up-down m = 1, n = 0 structure on the parallel velocity. The combination of both mechanisms in complete simulations leads to a poloidal and radial distribution of the parallel velocity comparable to experimental results.

Variational derivation of the dispersion relation of kinetic coherent modes in the acoustic frequency range in tokamaks

In the present paper, we compare two modes with frequencies belonging to the acoustic frequency range: the geodesic acoustic mode (GAM) and the Beta Alfvén eigenmode (BAE). For this, a variational gyrokinetic energy principle coupled to a Fourier sidebands expansion is developed. High order finite Larmor radius and finite orbit width effects are kept. Their impact on the mode structures and on the Alfvén spectrum is calculated and discussed. We show that in a local analysis, the degeneracy of the electrostatic GAM and the BAE dispersion relations is verified to a high order and based in particular on a local poloidal symmetry of the two modes. When a more global point of view is taken, and the full radial structures of the modes are computed, differences appear. The BAE structure is shown to have an enforced localization, and to possibly connect to a large magnetohydrodynamic structure. On the contrary, the GAM is seen to have a wavelike, nonlocalized structure, as long as standard slowly varying monotonic profiles are considered.

On the Physics of Improved Confinement During Pulsed Poloidal Current Drive in MST Reversed-Field Pinch

Reduction of core-resonant magnetic fluctuations and improved confinement in the Madison Symmetric Torus reversed-field pinch (MST RFP) have been routinely achieved by applying the surface poloidal electric field. The created inductive poloidal electric field drives current in plasma which leads to the improved confinement. To study the effect we developed a relatively simple 1-D model in cylindrical geometry which assumes poloidal and axial symmetry during the drive. We use resistive magnetohydrodynamics model with realistic plasma parameters and assume that there is a vacuum gap between plasma boundary and conducting wall of the vessel. Evolution of plasma density is taken into account and plasma boundary moves self-consistently with momentum equation. We start from an initial unstable equilibrium and examine stability of plasma configuration at intermediate moments of time during the drive. For this we calculate the growth rates of unstable eigenmodes in the plasma. Our results show that the modifications to the plasma current profile during the drive are stabilizing. The initial stabilization is due to the direct modification of the current profile near the edge. It enhances later in time due to the flattening of λ profile in the core region as plasma and magnetic field compress inward during the drive.

Observation and identification of zonal flows in a basic physics experiment

The role of self-generated zonal flows (ZF) in transport regulation in magnetic confinement devices via its shear is a potent concept and a physics issue. However, as the experimental evidence of its existence in tokamaks is meagre, a basic physics experimental study of ZF associated with ion temperature gradient (ITG) drift modes has been performed in the Columbia Linear Machine. The difficult problem of detection of ZF has been solved via a novel diagnostic using the paradigm of frequency modulation (FM) in radio transmission. Using this and discrete short time Fourier transform, we find a power spectrum peak at ITG (‘carrier’) frequency of ∼120 kHz and FM sidebands at frequency of ∼2 kHz, which is identified as a ZF. It has all the signatures of a ZF: a potential at near zero frequency and poloidal symmetry (m = 0), toroidal symmetry (k‖ = 0) and radial variations only. The results roughly agree with theoretical estimates given here.

Characterization of the density profile collapse of type I ELMs in ASDEX Upgrade with high temporal and spatial resolution reflectometry

This paper characterizes the density profile dynamics during edge localized modes (ELMs), using high temporal and spatial resolution reflectometry, with main emphasis on the dynamics of type I ELMs. Qualitatively, the density profile dynamics of both type I and type III ELM ASDEX Upgrade tokamak discharges shows the same characteristic behaviour. The analysis of the behaviour of the density at the plasma edge allows the identification of three phases of the ELM event: precursor, collapse and recovery phases. For the three phases, the effect of ELMs is analysed both on the high-field side (HFS) and the low-field side (LFS) of the plasma at the ASDEX Upgrade. Asymmetries of the ELM event when comparing the HFS and LFS are found. The ELM event is associated with a sudden loss of particles from the main plasma (inside the last closed flux surface) to the scrape-off layer and then to the divertor. For type I ELMs the relative particle losses (to the pedestal particle content), assuming poloidal symmetry, was found to be of ∼10% using LFS measurements and of ∼5% using the HFS measurements. The type I ELM affected depths are about ∼25% and ∼15% of the plasma minor radius for the LFS and HFS profiles mapped to the outer midplane, respectively.

Measurements of the plasma radiative loss profile in the M-11M tokamak with the help of a tangential-view AXUV photodiode array

The plasma radiative loss profile in the T-11M tokamak operating with a lithium limiter was measured using a sixteen-channel absolute extreme-ultraviolet photodiode array. The field of view of the detector was set in a vertical plane tangential to the plasma column axis. The radiative loss profile was recovered by solving an inverse problem under the assumption of toroidal and poloidal symmetry of the plasma column. A stable algorithm is developed for solving the problem with this geometry, and the possible errors of the method are evaluated. The radiative loss profiles and their evolution in various tokamak regimes are derived.

Patterns of ELM impacts on the JET wall components

Numerical analysis of the images in visible light from the JET tangential camera show that the edge localised mode (ELM) events are characterised by impacts on the low-field side components. The increase of emission is not restricted to the components closest to the plasma. One finds also that the deposition on the low-field side components does not exhibit any poloidal or toroidal symmetry and varies from ELM to ELM. Conversely the increase of emission on the divertor baffles, or the top protection tiles, is close to axisymmetric.

Edge convection driven by externally applied potentials

A theoretical model of convection in collisional tokamak edge and scrape-off-layer plasmas is described. In the linear theory, any mechanism for poloidal and toroidal symmetry breaking of the equilibrium will drive E×B flows; this result stems from the parallel thermal and pressure forces in Ohm’s law. In the nonlinear theory, the quadratic coupling of the perturbations leads to quasilinear-type fluxes in the vorticity, density, and temperature equations. If the convection is strong enough, these fluxes lead to an ambipolarity constraint on the equilibrium electric field and to increased transport of particles and energy. The theory shows qualitative agreement with some tokamak experiments in which potential perturbations are externally driven by radio frequency antennas.