The evolution of a linearly-polarized, long-wavelength Alfvén wave --propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow-- is here studied by means of two-dimensional hybrid Vlasov-Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations (Malara {\it et al.}, Phys. Rev. E 97, 053212), this avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moderate amplitude Alfvén wave, in order to separate linear wave-shear flow couplings from kinetic effects, the latter being more relevant for larger wave amplitudes. The phase-mixing generated by the shear flow modifies the initial perturbation, leading to the formation of small-scale transverse fluctuations at scales comparable with the proton inertial length. By analyzing both the polarization and group velocity of perturbations in the shear regions, we identify them as Kinetic Alfvén Waves (KAWs). In the moderate amplitude run, kinetic effects distort the proton distribution function in the shear region. This leads to the formation of a proton beam, at the Alfvén speed and parallel to the magnetic field. Such a feature, due to the parallel electric field associated with KAWs, positively compares with solar-wind observations of suprathermal ions' populations, suggesting that it may be related to the presence of ion-scales KAW-like fluctuations.
The possibility of fast dynamo action by collisionless kinetic Alfven Wave turbulence is demonstrated. The irreversibility necessary to lock in the generated field is provided by electron Landau damping, so the induced electric field does not vanish with resistivity. Mechanisms for self-regulation of the system and the relation of these results to the theory of alpha quenching are discussed. The dynamo-generated fields have symmetry like to that of zonal flows, and thus are termed zonal fields.
The linear non-modal kinetic theory of the kinetic drift-Alfven instability of plasma shear flows reveals the temporal non-modal growth with growing with time growth rate. The turbulent scattering of the sheared modes on ions accelerates this growth. The instability ceases its growth when the coupling of the drift and Alfven waves violates due to the changing with time frequencies of the drift and Alfven waves in shear flow.
The magnetic energy of nonlinear Alfven waves in compressible plasmas may be ponderomotively coupled only to ion-acoustic quasi-modes which modulate the wave phase velocity and cause wave-front steepening. In the collisionless plasma with $β\not=0$, the dynamics of nonlinear Alfven wave is also affected by the resonant particle-wave interactions. Upon relatively rapid evolution (compared to the particle bounce time), the quasi-stationary wave structures, identical to the so called (Alfvenic) Rotational Discontinuities, form, the emergence and dynamics of which has not been previously understoo…
An experimental investigation of nonlinear interactions between shear Alfvén waves in a laboratory plasma is presented. Two Alfvén waves, generated by a resonant cavity, are observed to beat together, driving a low frequency nonlinear psuedo-mode at the beat frequency. The psuedo-mode then scatters the Alfvén waves, generating a series of sidebands. The observed interaction is very strong, with the normalized amplitude of the driven psuedo-mode comparable to the normalized magnetic field amplitude ($δB/B$) of the interacting Alfvén waves.
General nonlinear equations describing reversed shear Alfven eigenmode (RSAE) self-modulation via zero frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow (ZF) and electromagnetic zonal current (ZC) can be preferentially excited by finite amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfven wave continuum is evaluated using the derived saturation level of ZC, which …
A novel channel for fuel ions heating in tokamak core plasma is proposed and analyzed using nonlinear gyrokinetic theory. The channel is achieved via spontaneous decay of reversed shear Alfven eigenmode (RSAE) into low frequency Alfven modes (LFAM), which then heat fuel ions via collisionless ion Landau damping. The conditions for RSAE spontaneous decay are investigated, and the saturation level and the consequent fuel ion heating rate are also derived. The channel is expected to be crucial for future reactors operating under reversed shear configurations, where fusion alpha particles are gene…
The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. The combined effects of both wave nonlinearity and Landau damping result in the evolutionary formation of stationaryOA S- and arc-polarized directional and rotational discontinuities. These waveforms are freqently observed in the interplanet…
In this work we used Particle-In-Cell simulations to study the interaction of circularly polarised Alfvén waves with one dimensional plasma density inhomogeneities transverse to the uniform magnetic field (phase mixing) in collisionless plasmas. In our preliminary work we reported discovery of a new electron acceleration mechanism, in which progressive distortion of the Alfvén wave front, due to the differences in local Alfvén speed, generates an oblique (nearly parallel to the magnetic field) electrostatic field. The latter accelerates electrons through the Landau resonance. Here we report a …
The drift-Alfven instabilities in the magnetic field aligned (parallel) sheared flow of a finite beta plasma with comparable inhomogeneous ion temperature and homogeneous electron temperature are examined. The development of instabilities are quantitatively discussed on the basis of numerical solution of a set of equations for the electrostatic and electromagnetic potentials. It is found that the accounting for the electromagnetic ion kinetic response, which has been ignored usually in existing discussions of the drift-Alfven instabilities of a steady plasma, reveals new drift-Alfven instabili…
Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an eXtended version of Hybrid Magnetohydrodynamics Gyrokinetic Code (XHMGC) to study thermal ion kinetic effects on Alfvénic modes driven by energetic particles, such as kinetic beta induced Alfvén eigenmodes in tokamak fusion pl…
High-order plasma shaping (mainly elongation and shift, as opposed to low-order toroidicity) is shown, under certain conditions, to open gaps in the coupled shear-Alfvén and acoustic continua at frequencies significantly above the values predicted by previous theories. Global eigenmodes in these gaps, which lie between those of geodesic acoustic modes (GAMs) and toroidicity-induced Alfvén eigenmodes (TAEs), are found unstable to hot-ion populations typical of tokamak operation, whilst their fundamental resonances with circulating particles are shown to take place at velocities near the geometr…
This comment clarifies the relation of the research in a recently published article [Phys. Plasmas 14, 042503 (2007)] to other prior publications addressing the inclusion of electromagnetic and drift-kinetic electron physics in gyrokinetic simulation, raises a concern related to the inclusion of kinetic electrons in a system with magnetic shear, and discusses alternatives in the face of an important limitation on the general applicability of the algorithm described therein.
Using a 2D Viscoresistive Reduced MagnetoHydroDynamic (VR-RMHD) model, the magnetic island coalescence problem is studied in the presence of in-plane, parallel shear flows. Extending the analytical work of Waelbroeck et al [33] and Throumoulopoulos et al [34] in the sub-Alfvénic flow shear regime for Fadeev equilibrium, the super-Alfvénic regime is studied for the first time numerically. A wide range of values of shear flow amplitudes and shear scale lengths have been considered to understand the effect of sub-Alfvénic and super-Alfvénic flows on the coalescence instability and its nonlinear f…
The radial structure of the continuous spectrum of shear Alfven waves is calculated in this paper within the separatrix of a magnetic island. Geometrical effects due to the noncircularity of the flux surface's cross section are retained to all orders. On the other hand, we keep only curvature effects responsible for the beta-induced gap in the low-frequency part of the continuous spectrum. Modes with different helicity from that of the magnetic island are considered. The main result is that, inside a magnetic island, there is a continuous spectrum very similar to that of tokamak plasmas, where…
In this work, the FALCON code is adopted for illustrating the features of shear Alfvén and continuous spectra in toroidal fusion plasmas. The FALCON codes employs the local Floquet analysis discussed in [Phys. of Plasmas \textbf{26} (8), 082502 (2019)] for computing global structures of continuous spectra in general toroidal geometry. As particular applications, reference equilibria for the Divertor Tokamak Test and ASDEX Upgrade plasmas are considered. In particular, we illustrate the importance of mode polarization for recognizing the physical relevance of the various branches of the continu…
A new analytic expression is derived for the resonant drive of high n Alfvenic modes by particles accelerated to high energy by Ion Cyclotron Resonance Heating. This derivation includes finite orbit effects, and the formalism is completely non-perturbative. The high-n limit is used to calculate the complex particle response integrals along the orbits explicitly. This new theory is applied to downward sweeping Alfven Cascade quasimodes completing the theory of these modes, and making testable predictions. These predictions are found to be consistent with experiments carried out on the Joint Eur…
The radial structure of the continuous spectrum of shear Alfven modes is calculated in the presence of a magnetic island in tokamak plasmas. Modes with the same helicity of the magnetic island are considered in a slab model approximation. In this framework, with an appropriate rotation of the coordinates the problem reduces to 2 dimensions. Geometrical effects due to the shape of the flux surface's cross section are retained to all orders. On the other hand, we keep only curvature effects responsible of the beta induced gap in the low-frequency part of the continuous spectrum. New continuum ac…
Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using two-dimensional full particle simulations, it is shown, that the ion temperature component perpendicular to the shock magnetic field at the shock foot region is proportional to the square of the Alfven Mach number divided by the plasma beta. This result is also explained by a simple analytical argument, in which the reflected ions get energy from upstream plasma flow. By comparing our analytic and numerical results, it is also confirmed that the fraction of the reflected ions hardly depends …
The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfvén Eigenmode (MAE) gap and the Helicity-induced Alfvén Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfvén Eigenmode (TAE) gap into t…
A new technique for manipulation and control of gradient-driven instabilities through nonlinear interaction with Alfvén waves in a laboratory plasma is presented. A narrow field-aligned density depletion is created in the Large Plasma Device (LAPD), resulting in coherent unstable fluctuations on the periphery of the depletion. Two independent kinetic Alfvén waves are launched along the depletion at separate frequencies, creating a nonlinear beat-wave response at or near the frequency of the original instability. When the beat-wave has sufficient amplitude, the original unstable mode is suppres…
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 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 metho…
Following the analysis on linear spectra of shear Alfvén fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfvén eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. …
In the previous works harmonic, phase-mixed, Alfven wave dynamics was considered both in the kinetic and magnetohydrodynamic regimes. Up today only magnetohydrodynamic, phase-mixed, Gaussian Alfven pulses were investigated. In the present work we extend this into kinetic regime. Here phase-mixed, Gaussian Alfven pulses are studied, which are more appropriate for solar flares, than harmonic waves, as the flares are impulsive in nature. Collisionless, phase-mixed, dispersive, Gaussian Alfven pulse in transversely inhomogeneous plasma is investigated by particle-in-cell (PIC) simulations and by a…
A pair of nonlinear diffusion equations in Fourier space} is used to study the dynamics of strong Alfvén-wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is …
Recent observations reveal that magnetic turbulence in the nearly colisionless solar wind plasma extends to scales smaller than the plasma microscales, such as ion gyroradius and ion inertial length. Measured breaks in the spectra of magnetic and density fluctuations at high frequencies are thought to be related to the transition from large-scale hydromagnetic to small-scale kinetic turbulence. The scales of such transitions and the responsible physical mechanisms are not well understood however. In the present work we emphasize the crucial role of the plasma parameters in the transition to ki…
Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and nonlinear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizin…
The outflow velocity of jets produced by collisionless magnetic reconnection is shown to be reduced by the ion exhaust temperature in simulations and observations. We derive a scaling relationship for the outflow velocity based on the upstream Alfvén speed and the parallel ion exhaust temperature, which is verified in kinetic simulations and observations. The outflow speed reduction is shown to be due to the firehose instability criterion, and so for large enough guide fields this effect is suppressed and the outflow speed reaches the upstream Alfvén speed based on the reconnecting component o…
We report the first experimental evidence of Alfvenic ion temperature gradient (AITG) modes in HL-2A Ohmic plasmas. A group of oscillations with $f=15-40$ kHz and $n=3-6$ is detected by various diagnostics in high-density Ohmic regimes. They appear in the plasmas with peaked density profiles and weak magnetic shear, which indicates that corresponding instabilities are excited by pressure gradients. The time trace of the fluctuation spectrogram can be either a frequency staircase, with different modes excited at different times or multiple modes may simultaneously coexist. Theoretical analyses …
Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length $d_p$ and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the…
With first-principles kinetic simulations, we show that a large-scale Alfvén wave (AW) propagating in an inhomogeneous background decays into kinetic Alfvén waves (KAWs), triggering ion and electron energization. We demonstrate that the two species can access unequal amounts of the initial AW energy, experiencing differential heating. During the decay process, the electric field carried by KAWs produces non-Maxwellian features in the particle VDFs, in accordance with space observations. The process we present solely requires the interaction of a large-scale AW with a magnetic shear and may be …
A novel 2D nonlinear dynamical paradigm is constructed to interpret the fast and repetitive frequency chirping and amplitude oscillation of Alfvén eigenmodes excited by energetic particles in fusion plasmas as observed in global gyrokinetic simulations. In this non-perturbative paradigm of the collisionless phase-space dynamics, wave-particle resonant interactions cause the phase-space structure to continuously twist and fold, leading to the repetitive excitation and decay of the Alfvén eigenmode. The radial (perpendicular to the dominant wave-particle interaction) dependence of the mode ampli…
Nonlinear set of equations for inertial or slow shear Alfven wave (SSAW) in ideal electron-positron-ion (e-p-i) plasmas are presented. The analytical solution for arbitrary amplitude SSAW in such multi-component plasmas is obtained using Sagdeev potential approach. The numerical solutions for several different cases have also been presented for illustrative purpose. It is found that the electron density dips of SSAW are formed in the super Alfvenic region. The amplitude and the width of the nonlinear shear Alfven wave reduces with the increase in the concentration of positrons in electron-ion …
We calculate the disruption scale $λ_{\rm D}$ at which sheet-like structures in dynamically aligned Alfvénic turbulence are destroyed by the onset of magnetic reconnection in a low-$β$ collisionless plasma. The scaling of $λ_{\rm D}$ depends on the order of the statistics being considered, with more intense structures being disrupted at larger scales. The disruption scale for the structures that dominate the energy spectrum is $λ_{\rm D}\sim L_\perp^{1/9}(d_eρ_s)^{4/9}$, where $d_e$ is the electron inertial scale, $ρ_s$ is the ion sound scale, and $L_\perp$ is the outer scale of the turbulence…
Compressional plasma perturbations may cause thermal misbalance between plasma heating and cooling processes. This misbalance significantly affects the dispersion properties of compressional waves providing a feedback between the perturbations and plasmas. It has been shown that Alfvén waves may induce longitudinal (compressional) plasma motions. In the present study, we analyze the effects of thermal misbalance caused by longitudinal plasma motions induced by shear Alfvén waves. We show that thermal misbalance leads to appearance of exponential bulk flows, which itself modifies the Alfvén ind…
Newton-Raphson method in complex space is used to numerically solve the transcendental dispersion relation of low frequency shear Alfven waves in fusion plasmas. The equation exhibits several physically relevant basins of attraction. The method is shown to be efficient and fast in solving this equation, with very small portion of non-converging points.
On shear Alfvén wave-induced energetic ion transport in optimized stellarators
Columbia University（哥伦比亚大学）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Cornell University（康奈尔大学）；Oak Ridge National Laboratory（橡树岭国家实验室）
In ideal MHD, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic fu…
In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of Reversed Shear Alfvén Eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with Energetic Particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It…
We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-beta, collisionless plasma. The key feature of such turbulence is the interplay between local wave--wave interactions between the fluctuations in the cascade and the non-local wave-particle interactions associated with kinetic micro-instabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion-cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic hi…
We study in a fully kinetic framework the generation of seed magnetic fields through the Weibel instability driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and its saturation when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated seed fields on key parameters…
The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfven eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as alpha-induced toroidal Alfven eigenmodes (alpha-TAE); that is, bound states trapped between pressure-gradient-induced potential barriers of the Schroedinger equation for shear Alfven waves. Using numerical tools, we examine in detail the effect of kinet…
Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes $δB_{\perp}/B_{0}\gtrsim β^{\,-1/2}$ (where $β$ is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-sc…
We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear Particle-in-Cell (PIC) simulations. We focus on the Alfvén-ion-cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distributio…
