Context. The transition from left-hand to right-hand polarized Alfvén waves depends on the wavenumber, the ratio of kinetic to magnetic pressure $β$, temperature anisotropy, and ion composition of the plasma. Along with the temperature anisotropy, the electron-to-proton temperature ratio $T_e/T_p$ is of great relevance for the characterization of the thermal properties of a plasma. This ratio varies significantly between different space plasma environments. Thus, studying how variations on this ratio affect the polarisation properties of electromagnetic waves becomes highly relevant for our understanding of the dynamics of space plasmas. Aim. We present an extensive study on the effect of the thermal properties of electrons on the behaviour and characteristics of Alfvénic waves in fully kinetic linear theory, as well as on the transition from electromagnetic ion-cyclotron (EMIC) to kinetic Alfvén waves (KAW). Method. We solve the fully kinetic dispersion relation for oblique electromagnetic waves of the Alfvén branch in a homogenous Maxwellian electron-proton plasma. We quantify the effect of the thermal properties of electrons by varying the electron-to-proton temperature ratio for different configurations of the propagation angle, $β_p=8πnkT_p/B^2$, and wavenumber. Results. We show that the temperature ratio $T_e/T_p$ has strong and non-trivial effects on the polarisation of the Alfvénic modes, especially at kinetic scales and $β_e+β_p>0.5$. We conclude that electron inertia plays an important role in the kinetic scale physics of the KAW in the warm plasma regime, and thus cannot be excluded in hybrid models for computer simulations.
Runaway particles can be produced in plasmas with large electric fields. Here we address the possibility that such runaway ions and electrons excite Alfvénic instabilities. The magnetic perturbation induced by these modes can enhance the loss of runaways. This may have important implications for the runaway electron beam formation in tokamak disruptions.
In the solar atmosphere, the chromospheric and coronal plasmas are much hotter than the visible photosphere. The heating of the solar atmosphere, including the partially ionized chromosphere and corona, remains largely unknown. In this paper we demonstrate that the ions can be substantially heated by Alfvén waves with very low frequencies in partially ionized low beta plasmas. This differs from other Alfvén wave related heating mechanisms such as ion-neutral collisional damping of Alfvén waves and heating described by previous work on resonant Alfvén wave heating. In this paper, we find that t…
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.
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 Alfven wave is analyzed in case of one quasineutral plasma propagating with some constant speed $v_0$ through another static quasineutral plasma. A dispersion equation is derived describing the Alfven wave coupled with the flow driven mode $ω= k v_0$ and solutions are discussed analytically and numerically. The usual solutions for two oppositely propagating Alfvén waves are substantially modified due to the flowing plasma. More profound is modification of the solution propagating in the negative direction with respect to the magnetic field and the plasma flow. For a large enough flow speed…
Large amplitude kinetic Alfvénon (exact Alfvén soliton) matching condition is investigated in quasineutral electron-ion and electron-positron-ion plasmas immersed in a uniform magnetic field. Using the standard pseudopotential method, the magnetohydrodynamics (MHD) equations are exactly solved and a global allowed matching condition for propagation of kinetic solitary waves is derived. It is remarked that, depending on the plasma parameters, the kinetic solitons can be sub- or super-Alfvénic, in general. It is further revealed that, either upper or lower soliton speed-limit is independent of f…
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 …
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…
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.
The dispersion relation of kinetic Alfvén wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum co…
A 1-D linear gyrokinetic code called AWECS is developed to study the kinetic excitation of Alfvenic instabilities in a high-beta tokamak plasma, with beta being the ratio of thermal to magnetic pressure. It is designed to describe physics associated with a broad range of frequencies and wavelengths. For example, AWECS is capable of simulating kinetic ballooning modes, Alfvenic ion-temperature-gradient-driven modes, as well as Alfven instabilities due to energetic particles. In addition, AWECS may be used to study drift-Alfven instabilities in the low-beta regime. Here, the layout of the code a…
A fast Alfvén wave with finite amplitude is shown to grow by a stimulated emission process that we propose for exploitation in toroidal magnetically confined fusion plasmas. Stimulated emission occurs while the wave propagates inward through the outer mid-plane plasma, where a population inversion of the energy distribution of fusion-born ions is observed to arise naturally. Fully nonlinear first principles simulations, which self-consistently evolve particles and fields under the Maxwell-Lorentz system, demonstrate this novel "alpha-particle channelling" scenario for the first time.
Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, the nonlinear decay process depends on thermal ion βvalue. Here, βis the plasma thermal to magnetic pressure ratio. In the low-βlimit, TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfvén wave continuous spectrum gap; while in the high-βlimit, TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear sa…
We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low $β$ plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter $κ$, plasma $β$ and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compr…
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…
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…
The Alfvenic waves and fast magneto-sound in the relativistically hot plasmas are considered. This study is based on the novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields: the concentration and the velocity field \emph{and} the average reverse relativistic $γ$ functor and the flux of the reverse relativistic $γ$ functor. Three temperature regimes giving considerably different behavior of the spectrum of Alfvenic waves are found. Four temperature regimes are obtained for the fast magneto-sound. All these regimes show consi…
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfvén wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one electromagnetic wave, with a low frequency cutoff at $\sqrt{1+2ω_p^2/Ω_p^2}$ (where $ω_p=(4πn e^2/m)^{1/2}$ is the electron/positron plasma frequency), and an Alfvén wave, with high frequency cutoff at the positron gyrofrequency $Ω_p$. There is only one forward propagating mode for a given frequency. However, due to relativistic effects, there is no low frequency cutof…
The resonant and non-resonant effects of core plasma on the excitation of low frequency modes with $ω< ω_{BAE}$, such as Beta-induced Alfvén Acoustic Eigenmodes (BAAEs) and Kinetic Ballooning Modes (KBMs) are examined in the framework of the generalized fishbone-like dispersion relation. The formalism of the fishbone-like equation contains all the necessary ingredients to describe the features of these low frequency fluctuations, and explain experimental findings. Core plasma properties (diamagnetic frequency and precession resonance with trapped ions) strongly affect the excitation of the mod…
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. …
Toroidal Alfven eigenmodes (TAEs) excited in purely ohmically heated plasmas without any auxiliary heating have been identified for the first time in the SUNIST spherical tokamak. The TAE modes are observed during minor disruptions and have a frequency range of 150-500 kHz. The mode structure analysis indicates the existence of both m/n=-3/-1 and -4/-1 harmonics, propagating in the electron diamagnetic direction in the laboratory frame of reference. These TAEs appear simultaneously with the generation of runaway electrons in the current quench phase, accompanying with the density sweeping duri…
It is shown that a three-dimensional (3D) modified-kinetic Alfvén waves (m-KAWs) can propagate in the form of Alfvénic tornadoes characterized by plasma density whirls or magnetic flux ropes carrying orbital angular momentum (OAM). By using the two fluid model, together with Ampère's law, we derive the wave equation for a 3D m-KAWs in a magnetoplasma with $m_e/m_i \ll β\ll 1$, where $m_e$ $(m_i)$ is the electron (ion) mass, $β=4 πn_0 k_B (T_e + T_i)/B_0^2$, $n_0$ the unperturbed plasma number density, $k_B$ the Boltzmann constant, $T_e (T_e)$ the electron (ion) temperature, and $B_0$ the stren…
We demonstrate analytically that, in toroidal plasmas, scattering by drift wave turbulence could lead to appreciable damping of toroidal Alfven eigenmodes via generation of short-wavelength electron Landau damped kinetic Alfven waves. A corresponding analytic expression of the damping rate is derived, and found to be, typically, comparable to the linear drive by energetic particles. The implications of this novel mechanism on the transport and heating processes in burning plasmas are also discussed.
We analyze plasma heating in weakly collisional kinetic Alfvén wave (KAW) turbulence using high resolution gyrokinetic simulations spanning the range of scales between the ion and the electron gyroradii. Real space structures that have a higher than average heating rate are shown not to be confined to current sheets. This novel result is at odds with previous studies, which use the electromagnetic work in the local electron fluid frame, i.e. $\mathbf{J} \!\cdot\! (\mathbf{E} + \mathbf{v}_e\times\mathbf{B})$, as a proxy for turbulent dissipation to argue that heating follows the intermittent sp…
This work presents a magnetic reconnection experiment in which the kinetic, magnetic and thermal properties of the plasma each play an important role in the overall energy balance and structure of the generated reconnection layer. Magnetic reconnection occurs during the interaction of continuous and steady flows of super-Alfvenic, magnetized, aluminum plasma, which collide in a geometry with two-dimensional symmetry, producing a stable and long-lasting reconnection layer. Optical Thomson scattering measurements show that when the layer forms, ions inside the layer are more strongly heated than…
In a magnetized plasma, both the transverse and longitudinal Alfvén waves carry an average energy density that, for each mode of oscillation, resembles the classical energy of a harmonic oscillator with unit mass and angular frequency that depends on the background magnetic field and plasma density. We employ this fact to introduce a pair of canonical variables for the underlying classical system, and then use the canonical quantization procedure to express the Alfvén wave velocity (or the corresponding plasma displacement vector) in terms of creation and annihilation operators. We thus introd…
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…
Turbulence in space and astrophysical plasmas is governed by the nonlinear interactions between counterpropagating Alfven waves. Here we present the theoretical considerations behind the design of the first laboratory measurement of an Alfven wave collision, the fundamental interaction underlying Alfvenic turbulence. By interacting a relatively large-amplitude, low-frequency Alfven wave with a counterpropagating, smaller-amplitude, higher-frequency Alfven wave, the experiment accomplishes the secular nonlinear transfer of energy to a propagating daughter Alfven wave. The predicted properties o…
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…
To guide the experimental design of a linear plasma device for studying the interaction between energetic ions and Alfvénic gap eigenmode (AGE), this work computes AGE referring to fusion conditions in a ultra-long large plasma cylinder ended with strong magnetic throats for axial confinement of charged particles. It is shown that: (i) for uniform equilibrium field between the ending throats, the dispersion relation of computed wave field agrees well with a simple analytical model for shear Alfvénic mode; (ii) for periodic equilibrium field with local defect, clear AGE is formed inside spectra…
A nonlocal coupling mechanism to directly transfer the energy from large-scale Magnetohydrodynamic(MHD) Alfven waves to small-scale kinetic Alfven waves is presented. It is shown that the interaction between a MHD Alfven wave and a reversely propagating kinetic Alfven wave can generate another kinetic Alfven wave, and this interaction exists in the plasmas where the thermal to magnetic pressure ratio is larger than the electron to ion mass ratio. The proposed nonlocal interaction may have a potential application to account for the observed electron scale kinetic Alfven waves in the solar wind …
In this paper, we consider the generation of magnetic island for the linearized MHD equations around the steady flowing plasma with velocity field $U_s=(u(y),0)$ and magnetic field $H_s=(b(y),0)$ in the finite channel.
This paper presents the numerical verification of an asymptotic analytical solution for the nonlinear interaction between counterpropagating Alfven waves, the fundamental building block of astrophysical plasma turbulence. The analytical solution, derived in the weak turbulence limit using the equations of incompressible MHD, is compared to a nonlinear gyrokinetic simulation of an Alfven wave collision. The agreement between these methods signifies that the incompressible solution satisfactorily describes the essential dynamics of the nonlinear energy transfer, even under the weakly collisional…
Global electromagnetic gyrokinetic simulations are performed with the Particle-in-Cell code ORB5 for an ITER Pre-Fusion-Power-Operation (PFPO) plasma scenario, with half-field (2.65 T) and half-current (7.5 MA). We report on a 'multi-scale' analysis of the discharge, considering eigenmodes and instabilies across three scale-lengths. Although the scenario will nominally have neutral beam heating with particles injected with 1 MeV, Alfvén eigenmodes are investigated in the absence of such source, and Reversed Shear (RSAE), Toroidal (TAE) and Elliptical (EAE) Alfvén eigenmodes are found with weak…
Magnetic energy around astrophysical compact objects can strongly dominate over plasma rest mass. Emission observed from these systems may be fed by dissipation of Alfvén wave turbulence, which cascades to small damping scales, energizing the plasma. We use 3D kinetic simulations to investigate this process. When the cascade is excited naturally, by colliding large-scale Alfvén waves, we observe quasithermal heating with no nonthermal particle acceleration. We also find that the particles are energized along the magnetic field lines and so are poor producers of synchrotron radiation. At low pl…
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 moder…
The aim of the present study is to shed light on the effects connected with thermal misbalance due to non-equal cooling and heating rates induced by density and temperature perturbations in solar active regions hosting either propagating torsional or shear Alfvén waves. A description for the nonlinear forces connected with Alfvén waves in non-ideal conditions is provided based on the second order thin flux tube approximation. This provides insight on the effects of Alfvén-induced motions on the boundary of thin magnetic structures in thermally active plasmas. The equations describing the proce…
Turbulence is a phenomenon found throughout space and astrophysical plasmas. It plays an important role in solar coronal heating, acceleration of the solar wind, and heating of the interstellar medium. Turbulence in these regimes is dominated by Alfven waves. Most turbulence theories have been established using ideal plasma models, such as incompressible MHD. However, there has been no experimental evidence to support the use of such models for weakly to moderately collisional plasmas which are relevant to various space and astrophysical plasma environments. We present the first experiment to …
The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs is solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also sh…
The interaction of laser with plasmas leads to many interesting phenomena which includes laser energy absorption, mode conversion, energetic particle generation etc. In this work, the excitation of Korteweg - de Vries (KdV) Alfven solitons in plasma is demonstrated with the help of 2-D Particle - In - Cell (PIC) simulations. For this purpose, the propagation of a pulsed $CO_2$ (with a wavelength of $10 μm$) laser normally incident on an overdense plasma target is considered in the presence of an external magnetic field. The magnitude of the external magnetic field is chosen so as to have the e…
We report on a theoretical discovery of new regimes of Alfvén eigenmode (AE) induced fast ion transport in tokamak plasmas, where microturbulence plays the role of a mediator of fast ion relaxation. Coulomb collisional scattering alone leads to small AE amplitudes and does not reproduce the steady state regimes observed in experiments. We show that in nonlinear regimes the effective pitch angle scattering due to microturbulence can lead to steady state AE amplitude evolution. This indicates a new route for fast ion losses, which is beyond the scenarios described in "Energetic ion transport by …
Evolution of ion distribution functions in ionospheric plasmas perturbed by Alfvén waves
University of Trento（特伦托大学）；National Institute of Astrophysics-IAPS（国家天体物理研究所-IAPS）；Northumbria University（诺森比亚大学）；Imperial College London（伦敦帝国理工学院）；University of L’Aquila（拉奎拉大学）
Whistler-Alfvén turbulence in a non-neutral ultrarelativistic pair plasma
University of Wisconsin at Madison（威斯康星大学麦迪逊分校）；Space Science Institute（空间科学研究所）；University of Kansas（堪萨斯大学）；Massachusetts Institute of Technology（麻省理工学院）
Fusion-born alpha particles in ITER disruption simulations are investigated as a possible drive of Alfvénic instabilities. The ability of these waves to expel runaway electron (RE) seed particles is explored in the pursuit of a passive, inherent RE mitigation scenario. The spatiotemporal evolution of the alpha particle distribution during the disruption is calculated using the linearized Fokker-Planck solver CODION coupled to a fluid disruption simulation. These simulations are done in the limit of no alpha particle transport during the thermal quench, which can be seen as a most pessimistic s…
Large-amplitude Alfvén waves are subject to parametric decays which can have important consequences in space, astrophysical, and fusion plasmas. Though the Alfvén wave parametric decay instability was predicted decades ago, observational evidence is limited, stimulating considerable interest in laboratory demonstration of the instability and associated numerical modeling. Here, we report novel hybrid simulation of the Alfvén wave parametric decay instability in a laboratory relevant plasma (based on the Large Plasma Device), using realistic wave injection and wave-plasma parameters. Considerin…
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…
We examine with particle-in-cell (PIC) simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the…
We report on first evidence of wave activity during neutral beam heating in KSTAR plasmas: 40 kHz magnetic fluctuations with a toroidal mode number of n=1. Our analysis suggests this a beta-induced Alfven eigenmode resonant with the q=1 surface. A kinetic analysis, when coupled with electron temperature measurements from electron cyclotron emission and ion/electron temperature ratios from crystallography, enables calculation of the frequency evolution, which is in agreement with observations. Complementary detailed MHD modelling of the magnetic configuration and wave modes supports the BAE mod…
The nonlinear interaction between counterpropagating Alfven waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfven wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfven waves interact to generate an inherently nonlinear, purely magnetic secondary fluctu…
On nonlinear saturation of toroidal Alfvén eigenmode due to thermal plasma nonlinearities
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Center for Nonlinear Plasma Science and C.R. ENEA Frascati（非线性等离子体科学中心及恩瑞亚弗拉斯卡蒂研究中心）；Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University（浙江大学物理学院聚变理论与模拟研究所）；Key Laboratory of Frontier Physics in Controlled Nuclear Fusion and Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所及受控核聚变前沿物理重点实验室）；De Vinci Higher Education, De Vinci Research Center（德文奇高等教育机构及德文奇研究中心）
