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In this study, we introduce the concept of a renormalized plasma equilibrium, dubbed zonal state (ZS), in the presence of a finite level of electromagnetic fluctuations. Our approach involves deriving governing equations for ZS through a comprehensive full $f$/$\delta f$ mixed formulation for the distribution function. By utilizing a CGL (Chew Goldberger Low) description, we consistently separate the microscale structures from macro-/meso- scale components of this equilibrium. We illustrate the method's generality by using the derived equations to describe the physics of GAM/EGAM (Geodesic Acoustic Modes).~This study builds upon previous research regarding Phase Space zonal Structures (PSZS) and contributes to the development of a general phase space transport theory for characterizing nonlinear dynamics in weakly collisional plasmas.

Using electron drift wave (eDW) as a paradigm model, we have investigated analytically direct wave-wave interactions between a test DW and ambient toroidal Alfv\'en eigenmodes (TAE) in toroidal plasmas, and their effects on the stability of the eDW. The nonlinear effects enter via scatterings to short-wavelength electron Landau damped kinetic Alfv\'en waves (KAWs). Specifically, it is found that scatterings to upper-sideband KAW lead to stimulated absorption of eDW. Scatterings to the lower-sideband KAW, on the contrary, lead to its spontaneous emission. As a consequence, for typical parameters and fluctuation intensity, nonlinear scatterings by TAE have negligible net effects on the eDW stability; in contrast to the ``reverse" process investigated in Ref. [Nuclear Fusion {\bf 62}, 094001 (2022)], where it is shown that nonlinear scattering by ambient eDW may lead to significant damping of TAE., Comment: Submitted to Nuclear Fusion on March 19th, 2023

The energetic electrons (EEs) generated through auxiliary heating have been found to destabilize various Alfven eigenmodes (AEs) in recent experiments, which in turn lead to the EE transport and degrade the plasma energy confinement. In this work, we propose a global fluid-kinetic hybrid model for studying corresponding kinetic-magnetohydrodynamic (MHD) processes by coupling the drift-kinetic EEs to the Landau-fluid model of bulk plasmas in a non-perturbative manner. The numerical capability of Landau-fluid bulk plasmas is obtained based on a well-benchmarked eigenvalue code MAS [Multiscale Analysis of plasma Stabilities, J. Bao et al. Nucl. Fusion accepted 2023], and the EE responses to the electromagnetic fluctuations are analytically derived, which not only contribute to the MHD interchange drive and parallel current but also lead to the newly kinetic particle compression with the precessional drift resonance in the leading order. The hybrid model is casted into a nonlinear eigenvalue matrix equation and solved iteratively using Newton's method. By calibrating the EE precession frequency against the particle equation of motion in general geometry and applying more realistic trapped particle distribution in the poloidal plane, MAS simulations of EE-driven beta-induced Alfven eigenmodes (e-BAE) show excellent agreements with gyrokinetic particle-in-cell simulations, and the non-perturbative effects of EEs on e-BAE mode structure, growth rate and damping rate are demonstrated. With these efforts, the upgraded MAS greatly improves the computation efficiency for plasma problems related to deeply-trapped EEs, which is superior than initial-value simulations restricted by the stringent electron Courant condition regarding to the practical application of fast linear analysis., Comment: 24 pages, 11 figures

Nonlinear wave-wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry breaking shear Alfvén wave (SAW) instabilities are expected to be excited by energetic fusion alpha particles, and self-consistently determine the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave-wave coupling processes. More specifically, one needs to employ the gyrokinetic approach in order to account for the breaking of the ``pure Alfvénic state" in the short wavelength kinetic regime, due to the short wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfvén eigenmode (TAE) as a paradigm case, three nonlinear wave-wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1. the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion induced scattering and the resulting saturated TAE spectrum; and 3. the cross-scale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating., submitted to Reviews of Modern Plasma Physics

We have investigated hybridized magnon-phonon excitation (magnon polarons) in spin Seebeck effects (SSEs) in Bi$_x$Y$_{3-x}$Fe$_{5}$O$_{12}$ (Bi$_x$Y$_{3-x}$IG; $x=0$, $0.5$, and $0.9$) films with Pt contact. We observed sharp peak structures in the magnetic field $H$ dependence of the longitudinal SSE (LSSE) voltages, which appear when the phonon dispersions are tangential to the magnon dispersion curve in Bi$_x$Y$_{3-x}$IG. By increasing the Bi amount $x$, the peak fields in the LSSE shift toward lower $H$ values due to the reduction of the sound velocities in Bi$_x$Y$_{3-x}$IG. We also measured the SSE in a nonlocal configuration and found that magnon-polaron anomalies appear with different signs and intensities. Our result shows composition-tunability of magnon-polaron anomalies and provides a clue to further unravel the physics of magnon-polaron SSEs., Comment: Editors' Suggestion, 14 pages, 11 figures

Hybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfv��n 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 maximizing wave-EP power transfer. In linear stage, EPs induce evident mode structure and frequency shifts; meanwhile, RSAE saturates by radial decoupling with resonant EPs due to weak magnetic shear, and gives rise to global EP convective transport and non-adiabatic frequency chirping. The spatiotemporal scales of phase space wave-EP interactions are characterized by the perpendicular wavelength and wave-particle trapping time. The simulations provide insights into general as well as specific features of RSAE spectra and EP transport from experimental observations, and illustrate the fundamental physics of wave-EP resonant interaction with the interplay of magnetic geometry, plasma non-uniformity and non-perturbative EPs., 36 pages, 21 figures

There is a fundamental difference between loss of excitation protection of synchronous condenser and generator. The low excitation limit of synchronous condenser is very low, which is close to leading reactive power when full loss of excitation occurs. Loss of excitation protection may maloperate when synchronous condenser operating under low excitation limit. Moreover, the power angle cannot be applied to constitute protection criterion. The stepped characteristic curve is adopted by the existing loss of excitation protection of synchronous condenser which resulting in protection dead zone. Under high system voltage condition, the existing protection may refuse to operate when partial loss of excitation occurs. A novel loss of excitation protection principle for synchronous condenser based on leading rate is proposed in this paper. The stator side plane and the rotor side plane are constructed respectively by using stator internal potential and excitation voltage. The characteristic curve based on hyperbolic function is proposed to avoid the dead zone. The leading rate detector is proposed to distinguish partial loss of excitation and normal regulation under high system voltage condition. In addition, blocking criterion is introduced in this paper to prevent the maloperation of leading rate detector when sudden increase of system voltage occurs. The novel loss of excitation protection reliably operates when partial loss of excitation occurs under high system voltage condition. The reliability and sensitivity of loss of excitation protection is substantially improved. The PSCAD simulation results verify the inadequacy of existing protection and the superior performance of novel protection principle .

Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfv��n eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, the nonlinear decay process depends on thermal ion ��value. Here, ��is the plasma thermal to magnetic pressure ratio. In the low-��limit, TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfv��n wave continuous spectrum gap; while in the high-��limit, TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear saturation levels of both GAM and daughter wave are derived. The corresponding power balance and wave particle power transfer to thermal plasma are computed. Implications on thermal plasma heating are also discussed., submitted to Nuclear Fusion

Gyrokinetic theory of nonlinear mode coupling as a mechanism for toroidal Alfven eigenmode (TAE) saturation in the fusion plasma related parameter regime is presented, including 1) para- metric decay of TAE into lower kinetic TAE (LKTAE) and geodesic acoustic mode (GAM), and 2) enhanced TAE coupling to shear Alfven wave (SAW) continuum via ion induced scattering. Our theory shows that, for TAE saturation in the parameter range of practical interest, several processes with comparable scattering cross sections can be equally important., Comment: Proceeding of 27th IAEA-Fusion Energy Conference

Following the analysis on linear spectra of shear Alfv��n 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 Alfv��n 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. Consistent with the wave-EP resonance structure, EP transport occurs in a similar scale to the mode width. On the other hand, passing EP transport is analyzed in detail for toroidal Alfv��n eigenmode in the outer core region, with mode drive from both passing and trapped EPs. It is shown that passing EPs experience only weak redistributions in the weakly unstable case; and the transport extends to meso-scale diffusion in the strongly unstable case, due to orbit stochasticity induced by resonance overlap. Here, weakly/strongly unstable regime is determined by Chirikov condition for resonance overlap. This work then further illuminates rich and diverse nonlinear EP dynamics related to burning plasma studies, and the capability of DTT to address these key physics., 32 pages, 20 figures

Magnetic moments in an ultra-thin Pt film on a ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ (YIG) have been investigated at high magnetic fields and low temperatures by means of X-ray magnetic circular dichroism (XMCD). We observed an XMCD signal due to the magnetic moments in a Pt film at the Pt $L_{3}$- and $L_{2}$-edges. By means of the element-specific magnetometry, we found that the XMCD signal at the Pt $L_{3}$-edge gradually increases with increasing the magnetic field even when the field is much greater than the saturation field of YIG. Importantly, the observed XMCD intensity was found to be much greater than the intensity expected from the Pauli paramagnetism of Pt when the Pt film is attached to YIG. These results imply the emergence of induced paramagnetic moments in Pt on YIG and explain the characteristics of the unconventional Hall effect in Pt/YIG systems., Comment: 8 pages, 5 figures

We study the Landau resonance between geodesic acoustic mode (GAM) and trapped electrons as a GAM's collisionless damping. The assumption of de ωbe is adopted. The damping rate induced by trapped electrons is found to be an increasing function of q. In low q range, circulating-ion-induced damping rate is larger than that induced by trapped electrons. As q increases, the latter becomes larger than the former. The reason is that trapped electrons' resonant velocity is close to υte from the lower side, whiles circulating ions' resonant velocity gets bigger further from υti. So the number of resonant trapped electrons increases, whiles the number of resonant circulating ions decreases. The amplitude of damping rate induced by trapped electrons in the edge plasma can be comparable to that induced by circulating ions in the low q range. Another phenomenon we found is that in the chosen range of e, the damping caused by trapped electrons has a maximum value at point eq for different q. The reason is that as e is close to eq, trapped electorns' resonant velocity is close to υte.

Geodesic acoustic modes (GAMs) are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports. In this paper, three important aspects of GAM dynamics are investigated, namely (1) GAM continuous spectrum and its mode conversion to kinetic GAM (KGAM); (2) linear excitation of energetic particle induced GAM (EGAM) and its coupling to the GAM continuum, and (3) nonlinear saturation of EGAM via wave particle trapping. The analogy between the GAM-EGAM dynamics and the well known beam-plasma instability are also discussed.

In this paper, a solution to the Fokker–Planck equation is presented, which is extended to the field particles' high-energy-tail non-Maxwellian velocity distribution function in transport theory. Based on the correct physical concept of collision intensity, introduced by CHANG and LI, the electrical conductivities for like-particles collisions are obtained in different conditions. The modified Fokker–Planck coefficients for non-Maxwellian scattering are applied in the study. It is found that the parallel part of the collision operator plays an important role. The non-Maxwellian scattering will stimulate the transport processes in various degrees with mutative deviation parameters.