Plasma Modes Research Articles

Nonlinear simulations of energetic particle modes in tokamak plasmas with reversed magnetic shear

Nonlinear simulations of energetic particle modes in tokamak plasmas with reversed magnetic shear

Measurement of the scaling slope of compressible magnetohydrodynamic turbulence by synchrotron radiation statistics

ABSTRACT Based on magnetohydrodynamic (MHD) turbulence simulations, we generate synthetic synchrotron observations to explore the scaling slope of the underlying MHD turbulence. We propose the new Q-U cross-intensity X and cross-correlation intensity Y to measure the spectral properties of magnetic turbulence, together with statistics of the traditional synchrotron I and polarization PI intensities. By exploring the statistical behaviour of these diagnostics, we find that the new statistics X and Y can extend the inertial range of turbulence to improve measurement reliability. When focusing on different Alfvénic and sonic turbulence regimes, our results show that the diagnostics proposed in this paper not only reveal the spectral properties of the magnetic turbulence but also gain insight into the individual plasma modes of compressible MHD turbulence. The synergy of multiple statistical methods can extract more reliable turbulence information from the huge amount of observation data from the Low-Frequency Array for radio astronomy and the Square Kilometer Array.

Numerical study of impurity effects on ion temperature gradient modes in tokamak edge plasmas based on the Euler matrix eigenvalue method

Low-Z impurity injection is frequently used for divertor detachment operations in current tokamaks; however, the impurity effects on the main plasma are yet to be fully understood. In this paper, the impurity effects on the ion temperature gradient (ITG) modes in tokamak edge plasmas are investigated based on the Euler matrix eigenvalue method. The eigen-equations with multiple ion species are established from the fundamental gyrokinetic theory, in which each ion species is treated equally. A novel and efficient gyro-kinetic code is developed for this numerical study, and the code’s availability to examine quasi-linear ITG modes is demonstrated by its comparison with existing results. At the pedestal top parameters in Experimental Advanced Superconducting Tokamak high-β p H-mode plasmas, the ITG mode behavior is investigated in pure deuterium plasmas and with impurities. Impurities can induce destabilizing or stabilizing effects on ITG modes, which are determined by the impurity density scale length. The inwardly peaked impurity density profile tends to reduce the ITG growth rate. The effect strength also increases with the impurity charge concentration. The effects of impurity species, including boron, carbon, neon and argon, are also evaluated. Numerical results show that the strength of destabilizing or stabilizing effect inverses with impurity ion charge at the same effective charge.

Spin effects on the relativistic strong EM wave modes in magnetized plasma* *The project supported by the National Natural Science Foundation of China under Grant No. 12065011, and the PhD Starting Fund program of TongRen University under Grant No. trxyDH2223.

Based on the relativistic hydrodynamic model of EM wave–spin plasmas interaction, the spin effects on the relativistic strong EM modes in magnetized plasma are investigated. The dispersion relations of the EM wave propagating parallel and perpendicular to the external magnetic field are obtained. Results show that the strong EM wave modes are affected by the time component of four-spin as well as the increase of electron effective mass. Especially in the case of EM wave propagating parallel to the external magnetic field, the time component of four-spin amplifies the influence of spin effects on the low-frequency modes obviously.

MHD mode tracking using high-speed cameras and deep learning

We present a new algorithm to track the amplitude and phase of rotating magnetohydrodynamic (MHD) modes in tokamak plasmas using high speed imaging cameras and deep learning. This algorithm uses a convolutional neural network (CNN) to predict the amplitudes of the n = 1 sine and cosine mode components using solely optical measurements from one or more cameras. The model was trained and tested on an experimental dataset consisting of camera frame images and magnetic-based mode measurements from the High Beta Tokamak - Extended Pulse (HBT-EP) device, and it outperformed other, more conventional, algorithms using identical image inputs. The effect of different input data streams on the accuracy of the model’s predictions is also explored, including using a temporal frame stack or images from two cameras viewing different toroidal regions.

Nonlinear dynamics of nonadiabatic chirping-frequency Alfvén modes in tokamak plasmas

Frequency chirping of Alfvén modes, a phenomenon observed in tokamak fusion plasmas driven by energetic particles (EPs), can result in significant losses of EPs. In this study, we use the global gyrokinetic code ORB5 (Lanti et al 2020 Comput. Phys. Commun. 251 107072) to investigate the nonlinear dynamics of non-adiabatic frequency chirping EP modes (EPMs). Our results illuminate non-perturbative features of EPMs caused by the presence of EPs. Additionally, we find that, with a fixed safety factor profile and a single toroidal mode number, the frequency chirping rate is linearly proportional to the mode saturation amplitude, as predicted by the theory (Chen and Zonca 2016 Rev. Mod. Phys. 88 015008).

Axisymmetric oscillatory modes in cylindrical magnetized plasma bounded by a conducting wall

A comparison between analytic theory and numerical simulations of axisymmetric modes in magnetically confined, cylindrical plasma with non-circular cross-section bounded by a conducting wall is presented. If the wall is close to the plasma, modes are oscillatory, with frequency scaling with the Alfvén frequency. The two frequencies differ when the plasma cross-section is elongated, but they become equal in the circular limit. The mechanism for oscillatory behavior is a consequence of the currents induced on the perfectly conducting wall when the plasma is displaced from its equilibrium positions. The induced currents exert a restoring force on the plasma, and the oscillation frequency is a combination of the strength of this force and the plasma mass density. An additional parameter, depending on the distance between the wall and the plasma boundary, also affects the oscillation frequency so that the frequency becomes large when the wall-plasma boundary distance approaches zero.

Second-harmonic electron-cyclotron resonance heating: A possible impact from mode coupling near the resonance.

The short-wavelength paraxial asymptotic technique, known as Gaussian beam tracing, is extended to the case of two linearly coupled modes in plasmas with resonant dissipation. The system of amplitude evolution equations is obtained. Apart from purely academic interest, this is exactly what happens near the second-harmonic electron-cyclotron resonance if the microwave beam propagates almost perpendicularly to the magnetic field. Because of non-Hermitian mode coupling, the strongly absorbed extraordinary mode may partly transform into the weakly absorbed ordinary mode near the resonant absorption layer. If this effect is significant, it could impair the well-localized power deposition profile. The analysis of parameter dependencies gives insight into what physical factors affect the power exchange between the coupled modes. The calculations show a rather small impact of non-Hermitian mode coupling on the overall heating quality in toroidal magnetic confinement devices at electron temperatures above 200 eV.

Ponderomotive forces due to electron modes in unmagnetized plasmas described by kappa distribution functions

The Washimi and Karpman ponderomotive interaction due to electron wave propagation is investigated for low-temperature unmagnetized plasmas described by an isotropic kappa distribution. We perform a brief analysis of the influence of the kappa distribution in the dispersion relations for a low-temperature plasma expansion at the lowest order in which the thermal effects are appreciable without considering the damping characteristics of the wave. The spatial and temporal factors of the ponderomotive force are obtained as a function of the wavenumber, the spectral index κ and the ratio between the plasma thermal velocity and the speed of light. Our results show that for unmagnetized plasmas non-thermal effects are negligible due to the spatial ponderomotive force when non-relativistic thermal velocities are considered. However, for unmagnetized plasmas, the temporal factor of the ponderomotive force appears only due to the presence of suprathermal particles, with a clear dependence on the κ index. We also analyze the role of the non-thermal effect in the induced Washimi and Karpman ponderomotive magnetization and the total power radiated associated with it. Furthermore, we show that the magnitude of the slowly varying induced ponderomotive magnetic field increases as the plasma moves away from thermal equilibrium.

Rayleigh–Taylor stability of quantum magnetohydrodynamic plasma with electron inertia and resistivity

Abstract The analytical observation of the simultaneous impacts of electrical resistivity, finite Larmor radius (FLR) correction, and electron inertia on the magnetohydrodynamic Rayleigh–Taylor unstable mode of incompressible rotating quantum plasma is carried out. The perturbation formulations of the problem are derived by applying the QMHD model to obtain the dispersion equation for the stratified quantum hydrodynamic fluid plasma. The dispersion equation is analyzed graphically and numerically for the various cases. It is obtained that the simultaneous impacts of rotation, resistivity, FLR correction, electron inertia, and quantum correction modify the Rayleigh–Taylor (RT) unstable mode of the stratified magnetized fluid plasma. The graphical studies show that the rotational effect destabilizes or stabilizes the Rayleigh–Taylor (RT) instability of the magnetized quantum plasma, with or without the impacts of electrical resistivity and electron inertia. This result may be useful for studying the magnetic reconnection process and its applications, viz., supernova explosions, neutron stars, white dwarfs, etc.

Destabilization mechanism of the collisional microtearing mode in magnetized slab plasmas

The destabilization mechanism of the collisional microtearing mode driven by an electron temperature gradient is studied using theoretical analyses and gyrokinetic simulations including a comprehensive collision model, in magnetized slab plasmas. The essential destabilization mechanism of the microtearing mode is the lag of the parallel inductive electric field behind the magnetic field owing to the time-dependent thermal force and inertia force induced by the velocity-dependent electron–ion collisions. Quantitative measurements of the collision effects enable us to identify the unstable regime against collisionality and reveal the relevance of the collisional microtearing mode with existing toroidal experiments. A nonlinear simulation demonstrates that the microtearing mode does not drive magnetic reconnection with the explosive release and conversion of the magnetic energy.

Terahertz third harmonic generation in c -axis La1.85Sr0.15CuO4

Terahertz nonlinear optics is a viable method to interrogate collective phenomena in quantum materials spanning ferroelectrics, charge-density waves, and superconductivity. In superconductors this includes the Higgs amplitude and Josephson phase modes. We have investigated the nonlinear $c$-axis response of optimally doped ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_{4}$ using high-field THz time domain spectroscopy at field strengths up to $\ensuremath{\sim}80$ kV/cm. With increasing field, we observe a distinct redshift of the Josephson plasma edge and enhanced reflectivity (above the plasma edge) arising from third harmonic generation. The nonmonotonic temperature-dependent response is consistent with nonlinear drive of the Josephson plasma mode (JPM) as verified with comparison to theoretical expectations. Our results add to the understanding that, using THz light, the JPM (in addition to the Higgs mode) provides a route to interrogate and control superconducting properties.

Formation and evolution of coherent structures in 3D strongly turbulent magnetized plasmas

We review the current literature on the formation of coherent structures (CoSs) in strongly turbulent 3D magnetized plasmas. CoSs [Current Sheets (CS), magnetic filaments, large amplitude magnetic disturbances, vortices, and shocklets] appear intermittently inside a turbulent plasma and are collectively the locus of magnetic energy transfer (dissipation) into particle kinetic energy, leading to heating and/or acceleration of the latter. CoSs and especially CSs are also evolving and fragmenting, becoming locally the source of new clusters of CoSs. Strong turbulence can be generated by the nonlinear coupling of large amplitude unstable plasma modes, by the explosive reorganization of large-scale magnetic fields, or by the fragmentation of CoSs. A small fraction of CSs inside a strongly turbulent plasma will end up reconnecting. Magnetic Reconnection (MR) is one of the potential forms of energy dissipation of a turbulent plasma. Analyzing the evolution of CSs and MR in isolation from the surrounding CoSs and plasma flows may be convenient for 2D numerical studies, but it is far from a realistic modeling of 3D astrophysical, space, and laboratory environments, where strong turbulence can be exited, such as in the solar wind, the solar atmosphere, solar flares and Coronal Mass Ejections, large-scale space and astrophysical shocks, the magnetosheath, the magnetotail, astrophysical jets, and Edge Localized Modes in confined laboratory plasmas (tokamaks).

TWO-STREAM NONLINEAR LANGMUIR OSCILLATIONS

Langmuir oscillations of a large amplitude in a cold collisionless plasma are considered in this work. We passed to the conclusion that multiple streams is an inevitable feature of the Langmuir oscillations in the cold collisionless inhomogeneous plasma with resonant point even in the low-signal limit. By extending the equation of the cold plasma oscillations on the multi-stream regimes, we find two-stream modes in the homogeneous plasma, which are stationary solutions of this equation.

Effects of Pulse Interval on Forming Process in Wire Arc Metal Additive Manufacturing Using Pulsed Arc Plasma.

To overcome the material processing challenges induced by high levels of heat input in wire arc additive manufacturing (WAAM), an innovative WAAM method using pulsed arc plasma (PAP-WAAM), was developed by the authors in the previous study. In this method, the PAP generated by the pulsed voltage was used as the heat source. The pulse interval can be defined as the time interval between adjacent pulse voltages, which determines the ignition time and frequency of the arc plasma, thus influencing the forming process. However, the effect of pulse interval on the forming process has not yet been revealed. Here, the effects of pulse interval on forming process during the PAP-WAAM of Ti6Al4V, including thermal behavior, arc plasma characteristics, and metal transfer process, were investigated by experiments and simulation. The results exhibited that the interpass temperature and maximum peak temperature decrease with increasing pulse interval at the same arc plasma power, indicating an alleviation of heat accumulation along the building direction. As the pulse interval increased, the ignition mode of the arc plasma changed from ignition between the tungsten electrode and the previously deposited layer to ignition between the tungsten electrode and filler wire, which increased the proportion of discharge energy allocated to the filler wire, thus reducing the overall heat input required for material deposition. When the pulse interval was 300 and 400 ms, only the uninterrupted bridging transfer mode was observed during the deposition process. The uninterrupted bridging transfer is considered to contribute to forming a smooth and consistent layer appearance. In addition, longer pulse intervals resulted in less surface oxidation, narrower wall thickness, and better macrostructure, attributed to reduced heat input and improved effective heat dissipation. This research reveals the effect of pulse interval on forming process during PAP-WAAM, which benefits the fabrication of desirable metal parts.

Global linear stability analysis of kinetic trapped ion mode (TIM) in tokamak plasma using the spectral method

Trapped ion modes (TIMs) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the magnetic flux ψ dependency of the equilibrium Hamiltonian in both the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function . Using this spectral method, linear growth rates of TIM instability in the presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact ψ dependent equilibrium Hamiltonian, are investigated. The growth rate depends on the logarithmic gradient of temperature κ T , density κ n and equilibrium Hamiltonian . With the exact ψ dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with an approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with good accuracy. This spectral method is very fast and requires much less computation resources compared to a linear version of the Vlasov-solver based on a semi-Lagrangian scheme.

Localization of electron modes in nonuniform helicon plasma

New guided electrostatic and electromagnetic modes propagating in a nonuniform magnetized plasma with plane geometry are presented. The modes may arise in a plasma with a region of strong inhomogeneity leading to a concentration of wave energy and, thus, a localization of the modes. These localized modes can only propagate if the density gradient is sufficiently strong, whereas they do not exist in weakly nonuniform plasma. The eigenfunctions and the spectrum of the modes are found. In detail, the properties of the modes are studied for particular profiles in the transitional layer between two uniform plane plasma regions.

Theory of magnetic turbulence and shock formation induced by a collisionless plasma instability

Magnetic fields are ubiquitous in universe, space, and laboratory plasmas. Especially, self-generated magnetic fields are important to know the mind of nature. The formation of Weibel-mediated collisionless shock is studied theoretically as a structure formation by the linear plasma wave growth, nonlinear saturation, and mode–mode coupling. Following a series of computer simulations and experimental studies of the physics, a simple model equation is proposed here to describe the time evolution of magnetic turbulence. Weibel instability is saturated by magnetic pressure, and thicker filaments continue to be generated by current coalescence (magnetic reconnection) mechanism. The model equation concludes the fact that the filament spacing increases linearly in time, and the magnetic energy power spectrum is given as Bk2 ∝ k−2. The time evolution of the turbulence is characterized with the cascade toward smaller k. Such inverse cascade is well-known in 2D hydrodynamic turbulence such as a typhoon or hurricane formation and is known to have Kolmogorov spectrum k−5/3. Although only a small difference in power, the physics of inverse cascades is very different as shown in the present paper. With use of Alfvén current limit condition, the criteria of collisionless shock formation are evaluated. The present theory is compared to corresponding experiments done with Omega and NIF lasers and a variety of PIC simulations. The theory is also applied to evaluate the strength of magnetic field near the shock front of the supernova remnant SN1006. The enhancement of magnetic field of about 25 μG is concluded in the present theory. Finally, a universality of the model equation is shown by applying the theory to the turbulent mixing due to Rayleigh–Taylor instability at the contact surface of two fluids in a gravitational or inertial force, which is very important in compressing plasma such as inertial confinement fusion by implosion. It is shown that the well-known evolution physics, mixing layer of the two fluids grows in proportion to (time)2, can be explained with the same model equation.

Effects of radial electric field on kinetic ballooning mode in toroidal plasma

Global gyrokinetic particle simulations show that the radial electric field (Er) shear can suppress the kinetic ballooning mode (KBM) in a toroidal plasma. The linear KBM growth rate reaches a maximum when the toroidal rotation induced by the ion diamagnetic shear is canceled by the E × B flow shear. High toroidal-mode-number (high-n) KBMs are more sensitive to the Er shear than low-n KBMs. Nonlinear simulations find that both the Er shear and a self-generated zonal flow can reduce the nonlinear KBM saturation level with smaller particle and ion heat transport. Meanwhile, the zonal flow can weaken the suppressing effects of the Er shear on KBM nonlinear saturation amplitude. The radial correlation length of the turbulence is reduced by the Er shear and the zonal flow.

Role of edge-localized neoclassical tearing modes in quiescent H-mode plasmas in the DIII-D tokamak

The edge-harmonic oscillations (EHOs) in standard quiescent H-mode (QH-mode) plasmas in DIII-D are consistent with edge-localized neoclassical tearing modes (NTMs) based on nonlinear two-fluid MHD simulations. Using kinetic equilibria constrained by edge profile measurements, the MHD simulations show that the n = 1 NTM and its harmonics can be destabilized at the pedestal top of QH-mode plasma by the edge bootstrap current. The simulations further show that the unstable NTMs can saturate either at small (<2% ψN) or large (>4% ψN) island width depending on the magnitude of the edge bootstrap current, where ψN is the normalized radius in poloidal flux. The onset of the EHO also results in a prompt decrease in the pedestal width and height, consistent with simulation results for the onset of the NTM at the top of the QH-mode pedestal. This suggests that the avoidance of edge-localized modes (ELMs) in QH-mode can be attributed to the enhanced local transport induced by the NTM that is sufficient to prevent the expansion of the pedestal to an unstable width, analogous to the mechanism explored for ELM suppression by resonant magnetic perturbations. Nonlinear MHD simulations scanning the E × B frequency and the ratio of parallel and perpendicular thermal diffusivity (χǁ/χ⊥) at the pedestal top show that edge-localized NTMs are destabilized for conditions of high E × B frequency, high pedestal temperature, and low pedestal density, qualitatively consistent with experimental conditions required for observing the EHO.