Perpendicular Wavenumber Research Articles

Experimental study of the effect of 2/1 classical tearing mode on (intermediate, small)-scale microturbulence in the core of an EAST L mode plasma

In this paper, we report an experimental study of the effect of a m/n = −2/−1 (m, n being poloidal and toroidal mode number, separately) classical tearing mode on (intermediate, small)-scale microturbulence (see the definition in section ) in the core of an EAST L mode plasma discharge. The microturbulence at different scales k⊥ = 10, 18 and 26 cm−1 (i.e., , 3.6 and 5.2, respectively. Here, is the ion gyroradius and k⊥ is the perpendicular wavenumber) were measured simultaneously by the EAST multi-channel tangential CO2 laser collective scattering diagnostics. Experimental results confirm that the decrease of microturbulent Doppler shift (), inversely correlated to the increase of microturbulent mean frequency (defined in equation ()), is due to the 2/1 tearing mode. Temporal evolution of frequency-integrated spectral power Stot of microturbulence, found to be correlated with the width of 2/1 magnetic island, suggests the modulation effect on microturbulence by the tearing mode beyond Doppler shift effect. Modulation effects on microturbulence by the tearing mode are further demonstrated by the correlation between microturbulent envelope and magnetic fluctuations.

Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas

Density fluctuations in the large-density-gradient region of improved confinement Madison Symmetric Torus reversed field pinch (RFP) plasmas exhibit multiple features that are characteristic of the trapped-electron mode (TEM). Core transport in conventional RFP plasmas is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes. Using inductive current profile control, these tearing modes are reduced, and global confinement is increased to that expected for comparable tokamak plasmas. Under these conditions, new short-wavelength fluctuations distinct from global tearing modes appear in the spectrum at a frequency of f ∼ 50 kHz, which have normalized perpendicular wavenumbers k⊥ρs≲0.2 and propagate in the electron diamagnetic drift direction. They exhibit a critical-gradient threshold, and the fluctuation amplitude increases with the local electron density gradient. These characteristics are consistent with predictions from gyrokinetic analysis using the Gene code, including increased TEM turbulence and transport from the interaction of remnant tearing magnetic fluctuations and zonal flow.

Density variation effect on multi-ions with kinetic Alfven wave around cusp region—a kinetic approach

The kinetic Alfven waves in the presence of homogeneous magnetic field plasma with multi-ions effect are investigated. The dispersion relation and normalised damping rate are derived for low- $\beta$ plasma using kinetic theory. The effect of density variation of $\text{H}^{+}$ , $\text{He}^{+}$ and $\text{O}^{+}$ ions is observed on frequency and damping rate of the wave. The variation of frequency ( $\omega$ ) and normalised damping rate ( $\gamma / \varOmega_{H^{ +}} $ ) of the wave are studied with respect to $k_{ \bot} \rho_{j}$ , where $k_{ \bot} $ is the perpendicular wave number, $\rho_{j}$ is the ion gyroradius and $j $ denotes $\text{H}^{+}$ , $\text{He}^{+}$ and $\text{O}^{+}$ ions. The variation with $k_{ \bot} \rho_{j}$ is considered over wide range. The parameters appropriate to cusp region are used for the explanation of results. It is found that with hydrogen and helium ions gyration, the frequency of wave is influenced by the density variation of $\text{H}^{+}$ and $\text{He}^{+}$ ions but remains insensitive to the change in density of $\text{O}^{+}$ ions. For oxygen ion gyration, the frequency of wave varies over a short range only for $\text{O}^{+}$ ion density variation. The wave shows damping at lower altitude due to variation in density of lighter $\text{H}^{+}$ and $\text{He}^{+}$ ions whereas at higher altitude only heavy $\text{O}^{+}$ ions contribute in wave damping. The damping of wave may be due to landau damping or energy transfer from wave to particles. The present study signifies that the both lighter and heavier ions dominate differently to change the characteristics of kinetic Alfven wave and density variation is also an important parameter to understand wave phenomena in cusp region.

Driving magnetic turbulence using flux ropes in a moderate guide field linear system

We present a series of experiments on novel, line-tied plasma geometries as a study of the generation of chaos and turbulence in line-tied systems. Plasma production and the injection scale for magnetic energy is provided by spatially discrete plasma guns that inject both plasma and current. The guns represent a technique for controlling the injection scale of magnetic energy. A two-dimensional (2-D) array of magnetic probes provides spatially resolved time histories of the magnetic fluctuations at a single cross-section of the experimental cylinder, allowing simultaneous spatial measurements of chaotic and turbulent behaviour. The first experiment shows chaotic fluctuations and self-organization in a hollow-current line-tied screw pinch. These dynamics is modulated primarily by the applied magnetic field and weakly by the plasma current and safety factor. The second experiment analyses the interactions of multiple line-tied flux ropes. The flux ropes all exhibit chaotic behaviour, and under certain conditions develop an inverse cascade to larger scales and a turbulent inertial range with magnetic energy ($E$) related to perpendicular wave number ($k_{\bot }$) as $E\propto k_{\bot }^{-2.5\pm 0.5}$.

The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar convection by leading-order 2D Elsässer fluctuations, with critical balance being achieved when Alfvén wave sweeping balances passive scalar convection by leading-order 2D Elsässer fluctuations. Besides yielding predictions of 2D and slab spectra for Elsässer fluctuations, NI MHD shows that density fluctuations are advected by the majority or dominant incompressible velocity fluctuations. In the case of β ∼ 1 or ≪ 1, the density spectrum is Kolmogorov in the perpendicular wave number, thus providing a possible explanation for the observed extended Kolmogorov-like power law spectrum for electron density fluctuations in the interstellar medium.

Spontaneous emission of Alfvénic fluctuations

Low-frequency fluctuations are pervasively observed in the solar wind. The present paper theoretically calculates the steady state spectra of low-frequency electromagnetic (EM) fluctuations of the Alfvénic type for thermal equilibrium plasma. The analysis is based upon a recently formulated theory of spontaneously emitted EM fluctuations in magnetized thermal plasmas. It is found that the fluctuations in the magnetosonic mode branch is constant, while the kinetic Alfvénic mode spectrum is dependent on a form factor that is a function of perpendicular wave number. Potential applicability of the present work in the wider context of heliospheric research is also discussed.

An eight-channel Doppler backscattering system in the experimental advanced superconducting tokamak.

Doppler backscattering system can measure the perpendicular velocity and fluctuation amplitude of the density turbulence with intermediate wavenumber. An eight-channel Doppler backscattering system has been installed in the Experimental Advanced Superconducting Tokamak (EAST), which can probe eight different radial locations simultaneously by launching eight fixed frequencies (55, 57.5, 60, 62.5, 67.5, 70, 72.5, 75 GHz) into plasma. The quasi-optical system consists of circular corrugated waveguide transmission, a fixed parabolic mirror, and a rotatable parabolic mirror which are integrated with quasi-optics front-end of the profile reflectometer inside the vacuum vessel. The incidence angle can be chosen from 5° to 12°, and the wavenumber range is 2-15/cm with the wavenumber resolution Δk/k≤0.21. Ray tracing simulations are used to calculate the scattering locations and the perpendicular wavenumber. The dynamic range of this new eight-channel Doppler backscattering system can be as large as 40 dB in the EAST. In this article, the hardware design, the ray tracing, and the preliminary experimental results in the EAST will be presented.

X mode Doppler reflectometry k-spectral measurements in ASDEX Upgrade: experiments and simulations

The perpendicular density fluctuation spectrum in the tokamak ASDEX Upgrade was measured with Doppler reflectometry. In this paper, extensive plasma turbulence and microwave propagation simulations with the gene gyro-kinetic code and the ipf-fd3d full-wave code were undertaken to explain the observed spectral shape. It was shown that in this case the X-mode polarisation suffers both from a large nonlinear saturation effect at low-to-intermediate probed wavenumbers, and a super-linear enhancement effect at large wavenumbers. With these effects, we were able to explain the observed discrepancies between the gene perpendicular wavenumber spectra and the Doppler reflectometry derived wavenumber spectra. While the agreement is not perfect, the simulations give guidance on how to interpret X-mode Doppler reflectometry spectra.

Effects of temperature anisotropy on electrostatic ion-cyclotron (EIC) wave in multi-component plasma around polar cusp region-particle aspect approach

Particle aspect analysis is used to describe electrostatic ion-cyclotron (EIC) wave with multi-ion plasma (H+, He+ and O+) around polar cusp region. Variations of resonant energy and growth rate with general loss-cone distribution function and temperature anisotropy with perpendicular wave number are studied. The whole plasma is considered to consist of resonant and non-resonant particles. The resonant particles participate in energy exchange with wave, while non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate obliquely to the static magnetic field. It is found that the temperature anisotropy enhances the transverse, parallel resonant energies of particles and growth rate of the wave. Distribution indices also enhance the growth rate and parallel resonant energy and reduce the perpendicular resonant energy. The study may explain the EIC waves observed in polar cusp region. The results are interpreted for the space plasma parameters appropriate to the polar cusp region in the earth’s magnetosphere.

O–X mode conversion in a non-symmetric torus at electron cyclotron frequencies

Previous work on this topic, [Weitzner, Phys. Plasmas 11, 866 (2004)], applicable in a system with toroidal symmetry, is extended to the case of a non-symmetric background equilibrium state. Maxwell's equations with the cold plasma dielectric tensor are used to represent the plasma-electromagnetic wave interaction. Away from the mode conversion region, geometrical optics adequately characterizes the wave propagation. A new, simpler derivation of the wave equations in the mode conversion region is given. Aside from one very special case in which a general plasma equilibrium behaves like a stratified medium, the previous results apply and highly effective mode conversion is found. The matching of the mode conversion solution to the geometrical optics solution, not previously examined, is discussed. A relatively weak condition on the perpendicular wave number near the resonance layer is found. Provided that the perpendicular wave number is small, it tends to zero at the mode conversion layer and the solutions match effectively.

A Model for Dissipation of Solar Wind Magnetic Turbulence by Kinetic Alfvén Waves at Electron Scales: Comparison with Observations

Abstract In hydrodynamic turbulence, it is well established that the length of the dissipation scale depends on the energy cascade rate, i.e., the larger the energy input rate per unit mass, the more the turbulent fluctuations need to be driven to increasingly smaller scales to dissipate the larger energy flux. Observations of magnetic spectral energy densities indicate that this intuitive picture is not valid in solar wind turbulence. Dissipation seems to set in at the same length scale for different solar wind conditions independently of the energy flux. To investigate this difference in more detail, we present an analytic dissipation model for solar wind turbulence at electron scales, which we compare with observed spectral densities. Our model combines the energy transport from large to small scales and collisionless damping, which removes energy from the magnetic fluctuations in the kinetic regime. We assume wave–particle interactions of kinetic Alfvén waves (KAWs) to be the main damping process. Wave frequencies and damping rates of KAWs are obtained from the hot plasma dispersion relation. Our model assumes a critically balanced turbulence, where larger energy cascade rates excite larger parallel wavenumbers for a certain perpendicular wavenumber. If the dissipation is additionally wave driven such that the dissipation rate is proportional to the parallel wavenumber—as with KAWs—then an increase of the energy cascade rate is counterbalanced by an increased dissipation rate for the same perpendicular wavenumber, leading to a dissipation length independent of the energy cascade rate.

DIRECT AND INVERSE CASCADES IN THE ACCELERATION REGION OF THE FAST SOLAR WIND

ABSTRACT Alfvén waves are believed to play an important role in the heating and acceleration of the fast solar wind emanating from coronal holes. Nonlinear interactions between the dominant waves and minority waves have the potential to transfer wave energy either to smaller perpendicular scales (“direct cascade”) or to larger scales (“inverse cascade”). In this paper we use reduced magnetohydrodynamic (RMHD) simulations to investigate how the cascade rates depend on perpendicular wavenumber and radial distance from the Sun center. For models with a smooth background atmosphere, we find that an inverse cascade ( ) occurs for the dominant waves at radii between 1.4 and and dimensionless wavenumbers in the inertial range ( ), and a direct cascade ( ) occurs elsewhere. For a model with density fluctuations, there are multiple regions with an inverse cascade. In both cases, the cascade rate varies significantly with perpendicular wavenumber, indicating that the cacsade is a highly nonlocal process. As a result of the inverse cascades, the energy dissipation rates are much lower than expected from a phenomenological model and are insufficient to maintain the temperature of the background atmosphere. We conclude that RMHD models are unable to reproduce the observed properties of the fast solar wind.

Linear global gyrokinetic simulations of toroidal Alfven eigenmodes in KSTAR plasmas

Excitation of toroidal Alfven eigenmodes (TAEs) in KSTAR tokamak plasmas has been studied by using the GENE code. Verification and benchmark analysis are performed for Alfven eigenmodes (AEs) excited by the energetic particles (EPs) in comparison with the AEs from the GYGLES code, and excellent agreements are found. In addition, the threshold value of the EP density gradient to destabilize the TAE has been investigated. For the plasma equilibrium of KSTAR discharge (10574), TAEs of n = 2 are found to be excited by coupling of adjoining poloidal harmonics (5, 6), (6, 7), and (7, 8). The dependence of the growth rate and frequency of the TAE on the EP density gradient is examined. It is found that the threshold value of EP density gradient increases with the higher poloidal mode coupling, of which location moves outward in the radial direction. The growth rates of TAEs with higher poloidal mode numbers are smaller than those with lower poloidal mode numbers, indicating that perpendicular wavenumbers play an...

The I-mode confinement regime at ASDEX Upgrade: global properties and characterization of strongly intermittent density fluctuations

Properties of the I-mode confinement regime on the ASDEX Upgrade tokamak are summarized. A weak dependence of the power threshold for the L-I transition on the toroidal magnetic field strength is found. During improved confinement, the edge radial electric field well deepens. Stability calculations show that the I-mode pedestal is peeling-ballooning stable. Turbulence investigations reveal strongly intermittent density fluctuations linked to the weakly coherent mode in the confined plasma, which become stronger as the confinement quality increases. Across all investigated structure sizes (–12 cm−1, with the perpendicular wavenumber of turbulent density fluctuations), the intermittent turbulence bursts are observed. Comparison with bolometry data shows that they move poloidally toward the X-point and finally end up in the divertor. This might be indicative that they play a role in inhibiting the density profile growth, such that no pedestal is formed in the edge density profile.

A high-accuracy Eulerian gyrokinetic solver for collisional plasmas

We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker–Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order conservative upwind scheme is used to permit high-accuracy electromagnetic simulation even in the limit of very high plasma β and vanishingly small perpendicular wavenumber, k⊥→0. To our knowledge, this is the first pseudospectral implementation of the collision operator in a gyrokinetic code. We show that the new solver agrees closely with GYRO in the limit of weak Lorentz collisions, but gives a significantly more realistic description of collisions at high collision frequency. The numerical methods are also designed to be efficient and scalable for multiscale simulations that treat ion-scale and electron–scale turbulence simultaneously.

Kinetic Alfvén waves in three‐dimensional magnetic reconnection

AbstractAlfvénic waves are believed to be fundamentally important in magnetic reconnection. Kinetic dynamics of particles can break the Alfvén speed limit in the evolution and propagation of perturbations during reconnection. In this paper, the generation and signatures of kinetic Alfvén waves (KAWs) associated with magnetic reconnection in a current sheet is investigated using a three‐dimensional (3‐D) hybrid code under a zero or finite guide field. In order to understand the wave structures in the general cases of multiple X line reconnection, cases with a single X line of various lengths are examined. The KAWs are identified using the wave dispersion relation, electromagnetic polarization relations, as well as spectral analysis. In the cases in which the X line is so long to extend through the entire simulation domain in the current direction, quasi 2‐D configurations of reconnection are developed behind a leading flux/plasma bulge. KAWs with perpendicular wave number k⊥ρi∼1 (with ρi being the ion Larmor radius) are found throughout the transient plasma bulge region and propagate outward along magnetic field lines with a slightly super‐Alfvénic velocity. These KAWs are generated from the X line and coexist with the whistler structure of the ion diffusion region under a small guide field. In the cases in which the X line has a finite length 2ξ ∼ 10di, with ξ being the half length of the X line and di the ion inertial length, the KAWs originated from the X line are of 3‐D nature. Under a finite guide field, KAWs propagate along the oblique magnetic field lines into the unperturbed regions in the current direction, carrying parallel electric field and Poynting fluxes. The critical X line length for the generation of 3‐D‐like structures is found to be 2ξc≤30di. The structure, propagation, energy, spectrum, and damping of the KAWs are examined. Dependence of the structure of KAWs on the guide field is also investigated.

Study of electric and magnetic field fluctuations from lower hybrid drift instability waves in the terrestrial magnetotail with the fully kinetic, semi-implicit, adaptive multi level multi domain method

The newly developed fully kinetic, semi-implicit, adaptive multi-level multi-domain (MLMD) method is used to simulate, at realistic mass ratio, the development of the lower hybrid drift instability (LHDI) in the terrestrial magnetotail over a large wavenumber range and at a low computational cost. The power spectra of the perpendicular electric field and of the fluctuations of the parallel magnetic field are studied at wavenumbers and times that allow to appreciate the onset of the electrostatic and electromagnetic LHDI branches and of the kink instability. The coupling between electric and magnetic field fluctuations observed by Norgren et al. [“Lower hybrid drift waves: Space observations,” Phys. Rev. Lett. 109, 055001 (2012)] for high wavenumber LHDI waves in the terrestrial magnetotail is verified. In the MLMD simulations presented, a domain (“coarse grid”) is simulated with low resolution. A small fraction of the entire domain is then simulated with higher resolution also (“refined grid”) to capture smaller scale, higher frequency processes. Initially, the MLMD method is validated for LHDI simulations. MLMD simulations with different levels of grid refinement are validated against the standard semi-implicit particle in cell simulations of domains corresponding to both the coarse and the refined grid. Precious information regarding the applicability of the MLMD method to turbulence simulations is derived. The power spectra of MLMD simulations done with different levels of refinements are then compared. They consistently show a break in the magnetic field spectra at k⊥di∼30, with di the ion skin depth and k⊥ the perpendicular wavenumber. The break is observed at early simulated times, Ωcit<6, with Ωci the ion cyclotron frequency. It is due to the initial decoupling of electric and magnetic field fluctuations at intermediate and low wavenumbers, before the development of the electromagnetic LHDI branch. Evidence of coupling between electric and magnetic field fluctuations in the wavenumber range where the fast and slow LHDI branches develop is then provided for a cluster magnetotail crossing.

Are there two regimes in strongly rotating turbulence?

We describe numerical experiments of freely decaying, rapidly rotating turbulence in which the Rossby number varies from Ro = O(1) down to Ro ∼ 0.02. Our central premise is that there exists two distinct dynamical regimes; one for Ro > 0.3 → 0.4, which is typical of most laboratory experiments, and another corresponding to Ro < 0.3, which covers most previous numerical studies. The case of Ro > 0.3 → 0.4 is reported in Baqui and Davidson [“A phenomenological theory of rotating turbulence,” Phys. Fluids 27, 025107 (2015)] and is characterised by: (i) a growth of the parallel integral scale according to l|| ∼ l⊥Ωt; (ii) a dissipation law which is quite different from that predicted by weak-turbulence theories, specifically ε = βu3/l|| where the pre-factor β is a constant of order unity; and (iii) an inertial-range energy spectrum for both the parallel and perpendicular wavenumbers which scales as k−5/3, a scaling that has nothing to do with Kolmogorov’s law in non-rotating turbulence. (Here, l|| is the integral length-scale parallel to the rotation vector Ω, l⊥ the integral length-scale perpendicular to Ω, u the integral scale velocity, and ε the viscous dissipation rate per unit mass.) By contrast, in the low-Ro regime, we find that l|| ∼ l⊥Ωt is replaced by l|| ∼ ut and there is no power-law scaling of the inertial range energy spectrum. While the dissipation law ε = βu3/l|| continues to hold at low Ro, at least approximately, the value of β now depends on Ro. It appears, therefore, that the dynamics of these two regimes are very different, and this may help explain why experimentalists and theoreticians sometimes present rather different interpretations of rotating turbulence.

ALFVÉNIC WAVE HEATING OF THE UPPER CHROMOSPHERE IN FLARES

ABSTRACT We have developed a numerical model of flare heating due to the dissipation of Alfvénic waves propagating from the corona to the chromosphere. With this model, we present an investigation of the key parameters of these waves on the energy transport, heating, and subsequent dynamics. For sufficiently high frequencies and perpendicular wave numbers, the waves dissipate significantly in the upper chromosphere, strongly heating it to flare temperatures. This heating can then drive strong chromospheric evaporation, bringing hot and dense plasma to the corona. We therefore find three important conclusions: (1) Alfvénic waves, propagating from the corona to the chromosphere, are capable of heating the upper chromosphere and the corona, (2) the atmospheric response to heating due to the dissipation of Alfvénic waves can be strikingly similar to heating by an electron beam, and (3) this heating can produce explosive evaporation.

Ray Tracing for Doppler Backscattering System in the Experimental Advanced Superconducting Tokamak**supported by National Natural Science Foundation of China (Nos. 10990211 and 11105146) and the ITER-CN Project, 973 Program of China (No. 2013GB106002)

The Doppler backscattering system has been widely used for turbulence measurements, and the microwave beam will be backscattered near the cut-off layer when the Brag condition is fulfilled. In tokamak, the ray-tracing code is used to obtain the radial position and perpendicular wave number of the scattering layer for turbulence velocity measurement and the WKB (Wentzel-Kramers-Brillouin) approximation should be satisfied for optical propagation. To calculate the backscattering location and wave number at the cut-off layer only, a single ray tracing in the cross section is enough, while for spatial and wave number resolution calculation, multiple rays reflecting the microwave beam size should be used. Considering the angle between the wave vector and the magnetic field, a three-dimension quasi-optical Gaussian ray tracing is sometimes needed.