Shear Alfven Research Articles

Effects of zonal fields on energetic-particle excitations of reversed shear Alfvén eigenmode: Simulation and theory

Abstract Employing both nonlinear gyrokinetic simulation and analytical theory, we have investigated the effects of zonal (electromagnetic) fields on the energetic particle's drive of reversed shear Alfv'en eigenmodes in tokamak plasmas. Contrary to the conventional expectation, simulations with zonal fields turned on and off in the energetic particle dynamics while keeping the full nonlinear dynamics
of the thermal plasma indicate that zonal fields further enhance the instability drive and lead, thus, to a higher saturation level. These puzzling simulation results can be understood analytically in terms of the general fishbone-like dispersion relation with the correspondingly different energetic-particle phase-space structures induced by the zonal fields. Analytical expressions for the zonal fields beat driven by the reversed shear Alfv'en eigenmodes are also derived, and shown to be in good agreement with the simulation results.

Current status and prospects of burning plasma physics in magnetically confined fusion

Current status and challenges of key physics related to high-confinement operational scenarios and energetic particle confinement are briefly reviewed from the perspective of design and operation of tokamak-based fusion reactors. In the past few decades, significant progress has been made in the research on high-confinement mode physics, i.e. the main stability and confinement constraints on operational window of a fusion reactor have been identified, and some control methods for adjusting plasma kinetic profiles to optimize performance have been developed. Several operational scenarios, including inductive, hybrid and steady-state <i>etc</i>, which are potentially applicable for future reactors, have been developed. In the conditions that fusion alpha particle self-heating is predominant and shear Alfvén wave (SAW) instabilities potentially dominate fusion alpha particle transport, the SAW linear stability properties and excitation mechanisms are understood in depth, and the SAW instabilities nonlinear saturation, alpha particle confinement, and the influence of the heating deposition and the micro-turbulence regulation on fusion profile are under extensive investigation. The magnetically confined fusion research has entered a new stage of ignition and burning plasma physics, and new challenges that are faced are addressed, including whether efficient self-heating of plasmas by fusion alpha particles can be achieved, how the plasma stability and high-confinement can be maintained through the active control of key plasma profiles under the condition of dominant alpha particle heating, and whether it is possible to establish accurate models to predict long time scale complex dynamical evolution of fusion plasmas <i>etc</i>. Solving these key problems will lay a solid scientific foundation for designing and operating future fusion reactors as well as promote the development of plasma science.

The Potential Role of Modified Electron Acoustic Wave and Nonlinear Mode Coupling in Mono‐Energetic Aurora

AbstractResults from a 1D kinetic simulation, for the first time, reveal the important role of modified electron acoustic wave (MEAW) in auroral electron acceleration. Parallel electric fields, generated due to the mode coupling between kinetic Alfven waves (KAWs) and MEAWs in the transition region from the magnetosphere and the ionosphere, can be sustained by continuous energy input carried by Alfven waves from the magnetosphere. Under the incidence of long‐period Alfven waves carrying upward field‐aligned currents, a parallel potential drop can be formed in the transition region, leading to mono‐energetic electron acceleration. Such a mechanism provides a possible link between shear Alfven waves and the mesoscale mono‐energetic auroral electron acceleration.

Generation of an obliquely propagating shear alfven wave in dusty plasma by an ion beam

AbstractIon beam‐dusty plasma interaction leads to significant changes in the dispersion relation of shear Alfven wave depending on the beam, dust grain, and plasma parameters. Hydrogen ion beam particles interact with the shear Alfven wave via cyclotron interaction when they counter‐propagate with the wave and they can also interact with the co‐propagating wave via Cerenkov interaction. The interaction causes beam as well as plasma density fluctuations and gives rise to perpendicular currents. We have analytically obtained the dispersion relation and the growth/damping rate expressions for obliquely propagating shear Alfven waves in dusty plasma. The effect of beam velocity, magnetic field, wave number, dust particle density, and dust charge fluctuations are discussed. It is shown that both the wave frequency and the maximum growth rate decrease with an increase in beam velocity and the variations are different for parallel and perpendicular wave numbers. The dust particles enhance the frequency and maximum growth rate while the dust charge fluctuations induce damping. The results are in good agreement with the experimental observations.

Nonlinear gyrokinetic simulations of reversed shear Alfven eigenmodes in DIII-D tokamak

Nonlinear gyrokinetic simulations of reversed shear Alfven eigenmodes in DIII-D tokamak

3-D global hybrid simulations of magnetospheric response to foreshock processes

It has been suggested that ion foreshock waves originating in the solar wind upstream of the quasi-parallel (Q-||) shock can impact the planetary magnetosphere leading to standing shear Alfvén waves, i.e., the field line resonances (FLRs). In this paper, we carry out simulations of interaction between the solar wind and terrestrial magnetosphere under radial interplanetary magnetic field conditions by using a 3-D global hybrid model, and show the properties of self-consistently generated field line resonances through direct mode conversion in magnetospheric response to the foreshock disturbances for the first time. The simulation results show that the foreshock disturbances from the Q-|| shock can excite magnetospheric ultralow-frequency waves, among which the toroidal Alfvén waves are examined. It is found that the foreshock wave spectrum covers a wide frequency range and matches the band of FLR harmonics after excluding the Doppler shift effects. The fundamental harmonic of field line resonances dominates and has the strongest wave power, and the higher the harmonic order, the weaker the corresponding wave power. The nodes and anti-nodes of the odd and even harmonics in the equatorial plane are also presented. In addition, as the local Alfvén speed increases earthward, the corresponding frequency of each harmonic increases. The field-aligned current in the cusp region indicative of the possibly observable aurora is found to be a result of magnetopause perturbation which is caused by the foreshock disturbances, and a global view substantiating this scenario is given. Finally, it is found that when the solar wind Mach number decreases, the strength of both field line resonance and field-aligned current decreases accordingly.

Effect of arbitrary temperature degeneracy and ion magnetization on shear Alfven waves in electron‐positron‐ion plasmas

AbstractLinear properties of low‐frequency electromagnetic shear Alfven waves (SAWs) are studied in quantum electron‐positron‐ion plasmas with effect of arbitrary temperature degeneracy for magnetized () and unmagnetized ( ) ions by using the quantum hydrodynamic model. Dispersion relations are derived for nearly degenerate () and nearly non‐degenerate () plasmas. Bohm potential due to density correlation and temperature degeneracy due to Fermi–Dirac statistics of electron–positron, and their effects on the dispersion of SAWs are studied in detail both analytically and numerically. The relevance of the work regarding dense astrophysical plasmas is highlighted.

Solitary dispersive Alfven wave in a plasma with hot electrons, cold positrons and ions

The dispersion relation and the nonlinear behaviour of dispersive Alfven waves (DAWs) in a plasma, which is composed by hot electrons, cold positrons and ions, are studied from the multi-component fluid theory. It can be indicated from the linear dispersion relation that the coupling of positron acoustic waves with shear Alfven waves results from the effect of the finite ion gyroradius. In our mode, the pressure and the inertia of the positron acoustic wave are, respectively, provided by the hot electrons and the cold positrons, which are different from the ones in a plasma consisting of two-group positrons with different temperatures. Furthermore, the existence and properties of DAW solitons are analysed from the Sagdeev pseudopotential equation, which indicates the existence of super-Alfvenic or sub-Alfvenic solitary DAWs, as well as the amplitude and width of DAW solitons depend on the positron concentration and the electron temperature. When the effects of cold positrons can’t be neglected, there may coexist the compressive and rarefactive DAW solitons. When the concentration of positron is negligibly small, the properties of DAW solitons in our model are similar to the ones of kinetic Alfven wave solitons in a plasma composed by hot electrons and cold ions.

Dynamic charging effect on electromagnetic wave in low $\beta $ plasmas

Low beta plasma system is chosen for the study of low frequency electromagnetic Shear Alfven waves exhibiting dynamical charging of micron/sub micron size dust particles. A semi classical Quantum Hydrodynamic Model (QHD) is employed which includes the quantum effects for plasma electrons in the terms of statistical degenerate pressure, Landau quantization, exchange-correlation potential, and tunneling potential. The low beta plasma characteristics provides the opportunity for the usage of two potential theory in order to derive a complex equation of dispersion of the shear Alfven wave in quantum dusty magneto plasmas. Analytical simplification of dispersion equation provides the damping rate of the Shear Alfven wave which is verified graphically for a typical set of parameters. It is noticed that the damping rate depends upon the quantum properties of Landau quantization, exchange-correlation, and tunneling potential in addition to the dust radius which modifies the floating potential of the dust particles. This work may seek its applications in the astrophysical objects in general, and in the semiconductor laboratory plasmas for particular dust size and magnetic field.

Nonlinear simulation and energy analysis of the EAST coherent mode

The EAST coherent modes (CMs) during the inter-ELM phase are simulated by the electromagnetic six-field two-fluid module in BOUT++ framework. The fluctuation level of the electrostatic potential, electron pressure and density perturbations are comparable to the experiments, and the simulated electrostatic perturbation is around two orders of magnitude larger than the magnetic one in EAST CM. The frequency and poloidal wave number are consistent with experiments in the simulations of EAST CM equilibriums. The energy transfer between three-wave coupling indicates that the energy tends to transfer from medium-n to low-n modes in the early nonlinear phase, and the modes coupling effect in the nonlinear saturation phase is larger than that in the early nonlinear phase. Both the energy transfer and bispectral analysis show that the Ni fluctuation tends to generate the ‘single-mode’ coupling and Te tends to be ‘multiple-mode’, which indicates that the collapse of the density profile is larger than the electron temperature. The relative phase analysis is applied to evaluate whether the turbulence can extract the energy from density and temperature profiles. The result indicates that the density profile provides much more energy to drive the turbulence than electron temperature. The kinetic and magnetic energy transfer rates are used to understand the instability and turbulence driving mechanisms of the EAST CM. In the linear phase of the nonlinear simulation, the instability is driven by the peeling-ballooning mode and drift-Alfven wave (DAW), and the radial electric field and shear Alfven wave have large suppressing effects. The turbulence of EAST CM is a predominantly electrostatic mode, which corresponds to the Reynolds stress seven times larger than Maxwell stress. In addition, the effect of the electrostatic part in DAW is much larger than the electromagnetic one.

The Alfven Wave Zoo

It has been shown that a variety of names are assigned to the original MHD Alfven wave derived originally by Hannes Alfven in the 40s (Nature 150, 405-406 (1942)), and those names are used due to the different magnetic geometries where the target plasma could be confined, that is, in laboratory, in fusion, in space, and in astrophysics, where one could use as working geometry systems such as cartesian, cylindrical, toroidal, dipolar, and even more complex ones. We also show that different names with no new dramatic new physics induce misleading information on what is new and relevant and what is old related to the considered wave mode. We also show that changing the confining geometry and the background plasma kinetic properties, the Alfven wave dispersion properties change accordingly and this change “induces” all types of non-necessary swarm of names for the same MHD shear Alfven wave derived previously by Alfven.

Theory of Alfvén-slow frequency gaps and discovery of Alfvén-slow eigenmodes in tokamaks

An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfvén wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfvén Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfvén m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfvén m harmonic continuous spectrum to be uplifted from the uncoupled Alfvén spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfvén-slow (AS) mode continuous spectrum is broken up into two Alfvén-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfvén m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfvén-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfvén-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfvén Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

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.

Shear Alfvén and acoustic continuum in general axisymmetric toroidal geometry

The equations describing the continuous spectrum of shear Alfvén and ion sound waves propagating along magnetic field lines are introduced and solved in the ballooning space for general geometry in the ideal MHD limit. This approach is equivalent to earlier analyses by Chu et al. 1992 [Phys. Fluids B 4, 3713 (1992)], but the present formulation in the ballooning space allows us to readily extend it to include gyrokinetic and three-dimensional equilibrium effects. In particular, following Chen and Zonca 2017 [Phys. Plasmas 24, 072511 (2017)], the MHD limit is adopted to illustrate the general methodology in a simple case, and the equations are solved within the framework of Floquet and Hill's equation theory. The connection of shear Alfvén and ion sound wave continuum structures to the generalized plasma inertia in the general fishbonelike dispersion relation is also illustrated and discussed. As an application, the continuous frequency spectrum is calculated for a reference equilibrium of the Divertor Tokamak Test facility. The results are compared with those obtained by the MARS code adopting the standard methodology, demonstrating excellent agreement.

Shear Alfvén Waves in a Magnetized Electron–Positron Plasma

A theoretical investigation of high-frequency shear Alfven waves is made in a magnetized relativistic rotating electron–positron (e–p) plasma. The derivative nonlinear Schrodinger equation (DNSE) is derived by employing the reductive perturbation technique. A stationary solitary solution of DNSE is derived, which is used to analyze the basic properties (amplitude, width, etc.) of shear e–p Alfven (SEPA) solitons. Different intrinsic plasma parameters (namely, positrons thermal energy to electrons thermal energy ratio and relativistic effects, etc.) are seen to influence the basic properties of SEPA waves significantly. It is found that the SEPAs have new features with high time and small length scales. The phase speed of the waves is seen to increase with the relativistic parameter while it decreases with the increase of positron-to-electron (p–e) thermal energy ratio. It is also observed that both the soliton’s amplitude and width increase with the increase of p–e thermal energy ratio, which are independent of rotational frequency. Our findings are useful to understand e–p plasma in the rotational astrophysical object.

Zonal structure effect on the nonlinear saturation of reverse shear Alfven eigenmodes

A gyrokinetic ion/fluid electron hybrid model is used to study the nonlinear evolution of reverse shear Alfven eigenmodes (RSAE) driven by energetic particles. When only the energetic particle nonlinear effects are included, the saturation amplitude of a single-n RSAE follows the trapping scaling, δB/B∼(γ/ω)2. When the nonlinear effects of thermal ions and electrons are included, zonal structures are force generated but do not affect the saturation amplitude for γ/ω≤0.03. No spontaneous generation of zonal structures is observed, in contrast to ion-temperature-gradient-driven modes. At larger energetic particle drive, the effects of zonal structures cause a significant reduction in the RSAE saturation amplitude. The reduction is not caused by the zonal flow shearing of the RSAE, but by the force-generated n = 0 component in the thermal ion distribution function and the electron density. These n = 0 perturbations lead to nonlinear evolution of the RSAE mode structure and enhance damping.

Numerical study of the existence criterion for the reversed shear Alfven eigenmode in the presence of a parallel equilibrium current

We have re-visited the existence criterion of the reverse shear Alfven eigenmodes (RSAEs) in the presence of the parallel equilibrium current by numerically solving the eigenvalue equation using a fast eigenvalue solver code KAES. The parallel equilibrium current can bring in the kink effect and is known to be strongly unfavorable for the RSAE. We have numerically estimated the critical value of the toroidicity factor Qtor in a circular tokamak plasma, above which RSAEs can exist, and compared it to the analytical one. The difference between the numerical and analytical critical values is small for low frequency RSAEs, but it increases as the frequency of the mode increases, becoming greater for higher poloidal harmonic modes.

Kinematics of coronal rain in a transversely oscillating loop: Ponderomotive force and rain-excited oscillations

Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at sub-ballistic speeds, which is not well-understood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed sub-ballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a onedimensional shear Alfven wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one in-depth comparison with an observation that shows rain with up-and down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured sub-ballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding sub-ballistic motion, but it plays a role in cases of large loop oscillations. The appearance of rain causes the excitation of small-amplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.

Study of Reversed Shear Alfvén Eigenmodes with Down Sweeping Frequency in HL-2A Experiment atqmin∼ 1

The reserved shear Alfven eigenmodes (RSAEs) whose frequencies sweep down have been observed in HL-2A plasmas at qmin ∼ 1 during current ramp-up and NBI+ECRH recently. The kinetic Alfven eigenmode code (KAEC), which is a non-perturbative kinetic/magnetohydrodynamic eigenvalue code for calculating kinetic damping of shear Alfven eigenmodes, is used to investigate the modes according to the experimental data. It is found that the kinetic reversed shear Alfven eigenmodes (KRSAEs) with downsweeping frequency and localized radial structure would appear, which are consistent with the observations. The theoretical analysis for the existence of the mode and the scaling of the mode width are provided. It is shown that the mode width of KRSAEs is proportional to the square root of thermal ion Larmor radius.

Observation of an Alfvén Wave Parametric Instability in a Laboratory Plasma

A shear Alfvén wave parametric instability is observed for the first time in the laboratory. When a single finite ω/Ω_{i} kinetic Alfvén wave (KAW) is launched in the Large Plasma Device above a threshold amplitude, three daughter modes are produced. These daughter modes have frequencies and parallel wave numbers that are consistent with copropagating KAW sidebands and a low frequency nonresonant mode. The observed process is parametric in nature, with the frequency of the daughter modes varying as a function of pump wave amplitude. The daughter modes are spatially localized on a gradient of the pump wave magnetic field amplitude in the plane perpendicular to the background field, suggesting that perpendicular nonlinear forces (and therefore k_{⊥} of the pump wave) play an important role in the instability process. Despite this, modulational instability theory with k_{⊥}=0 has several features in common with the observed nonresonant mode and Alfvén wave sidebands.