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Plasma accelerator compressible turbulent boundary layers numerical calculation taking into account MHD effects, electron thermal nonequilibrium and finite rate ionization
The effect of the fluctuating buoyancy force on wave generation in a weakly magnetized plasma is considered. As expected, the efficiency of MHD wave generation is enhanced by including this force. However, it remains true that the observed variation of coronal emission at fixed spectral type cannot be accounted for by a wave generation process of the type discussed here.
We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.
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The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, β $\gg$ 1, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-β, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (~5%) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.
When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.
The electron cyclotron emission imaging (ECEI) diagnostic is a powerful tool to study the MHD and turbulent transport in magnetically confined fusion plasmas. In this work, the optical system including the local oscillator (LO) coupling and radio frequency (RF) receiving optics, has been designed and analyzed for the HL-2M ECEI diagnostic. The LO optics can illuminate the antenna array and drive the mixer diode to work efficiently, with more than 36% of the beam intensity for the channels which probe the plasma edge relative to those of channels which probe the plasma core. The RF optics aims at guiding the plasma emission signal to the antenna array. To meet different physical requirements, three types of field of view have been achieved for the plasma imaging, with zoom factors of around 1, 1.5 and 2, respectively. The focal surfaces are almost flat, with a maximum off-mapping (defined as the radial distance between the beam waists of the lower-/uppermost antennas and electron cyclotron emission layer) less than 2.5 cm, which can match the electron cyclotron emission layer quite well and suppress the image distortion in the plasma edge region. Furthermore, the impact of possible vibrations and installation error on the focal plane has been evaluated. In addition, the predefined MHD and turbulence perturbations are well reproduced by combining the optical simulation results and synthetic ECEI modeling, which further verifies the good performance of the RF optics.
The intracluster medium of galaxy clusters is an extremely hot and diffuse, nearly collisionless plasma, which hosts dynamically important magnetic fields of ~μG strength. Seed magnetic fields of much weaker strength of astrophysical or primordial origin can be present in the intracluster medium. In collisional plasmas, which can be approximated in the magnetohydrodynamical (MHD) limit, the turbulent dynamo mechanism can amplify weak seed fields to strong dynamical levels efficiently by converting turbulent kinetic energy into magnetic energy. However, the viability of this mechanism in weakly collisional or completely collisionless plasma is much less understood. In this study, we explore the properties of the collisionless turbulent dynamo using three-dimensional hybrid-kinetic particle-in-cell simulations. We explore the properties of the collisionless turbulent dynamo in the kinematic regime for different values of the magnetic Reynolds number, Rm, initial magnetic-to-kinetic energy ratio, (E mag /E kin ) i , and initial Larmor ratio, (r Larmor /L box ) i , i.e. the ratio of the Larmor radius to the size of the turbulent system. We find that in the ‘un-magnetized’ regime, (r Larmor /L box ) i > 1, the critical magnetic Reynolds number for the dynamo action Rm crit ≈ 107 ± 3. In the ‘magnetized’ regime, (r Larmor /L box ) i ≲ 1, we find a marginally higher Rm crit = 124 ± 8. We find that the growth rate of the magnetic energy does not depend on the strength of the seed magnetic field when the initial magnetization is fixed. We also study the distribution and evolution of the pressure anisotropy in the collisionless plasma and compare our results with the MHD turbulent dynamo.
A two-dimensional incompressible MHD spectral code is used to show that shear-driven turbulence is a possible means for producing many observed properties of the evolution of the magnetic and velocity fluctuations in the solar wind and, in particular, the evolution of the cross helicity ('Alfvenicity') at small scales. It is shown that large-scale shear can nonlinearly produce a cascade to smaller scale fluctuations even when the linear Kelvin-Helmholtz mode is stable, and that a roughly power law inertial range is established by this process. The evolution found is similar to that seen in some other simulations of MHD turbulence.
The results of two-dimensional spectral-method MHD simulations of the effect of turbulence on magnetic-reconnection processes are presented in extensive graphs and tables and characterized in detail. In a periodic sheet-pinch configuration, early-onset, persistent turbulence is found to occur when a low level of broadband fluctuations is introduced into the initial data. Features observed include small-scale unsteady coherent electric-current and vorticity structures, enhanced viscous and resistive dissipation, unsteady and spatially asymmetric fluid flow, large-scale and small-scale magnetic islands, multiple X points, large-amplitude electric-field fluctuations, and spectral characteristics indicating that the turbulence is broadband in both spatial directions and similar to homogeneous MHD turbulence. The importance of reconnection for studies of solar, magnetospheric, and laboratory plasmas in inhomogeneous magnetic fields is indicated.
When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.
The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega < omega(sub ci), other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., omega > omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) ∼ 1 and for high oblique angles of propagation 80 deg <= Theta (sub kB) < 90 deg as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation (Theta (sub kB) < 80 deg). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales kappa rho (sub i) approx. > 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW.
The effect of turbulence on particle acceleration in a MHD field was investigated by computing test particle trajectories in turbulent MHD reconnecting fields, including reconnection simulations at different magnetic Reynolds numbers. The dynamics of individual particles were investigated making it possible to examine the acceleration mechanism in great detail. It was found that turbulence influences the acceleration in two ways. It enhances the reconnection electric field while producing a stochastic electric field that gives rise to momentum diffusion; and it produces magnetic 'bubbles' and other irregularities that can temporarily trap test particles in the strong reconnection electric field for times comparable to the magnetofluid characteristic time.
Here, electron cyclotron emission imaging (ECEI) is employed to characterize the magneto hydraulics dynamics (MHD) fluctuations at the quiescent H-mode pedestals in DIII-D. Pedestal MHD fluctuations cause ECE radiation temperature fluctuations $\delta {T_{e{\text{,rad}}}}$ in both the pedestal and scrape-off-layer (SOL). A synthetic ECE platform is utilized for detailed interpretation of the ECEI signals in the SOL and pedestal regions. It is observed that the ECE radiation $\delta {T_{e{\text{,rad}}}}$, which is located in the SOL region according to the cold and optically thick plasma resonance assumption, is extremely sensitive to MHD radial displacements near the separatrix, exhibiting radiation inversion to $\delta {T_{e{\text{,rad}}}}$ at the pedestal. Here, the radiation inversion refers to the opposite phase between the radiation fluctuation at the pedestal and the radiation fluctuation at the SOL. Consequently, the quasi-coherent MHD (QCM), which displays a radiation inversion, is found to be consistent with an MHD radial structure that has a strong displacement near the separatrix. In contrast, the edge harmonic oscillation (EHO), which displays weak or no inversion, is found to be consistent with an MHD radial displacement structure peaking at the pedestal top. The ECEI data, interpreted with synthetic ECE, are in qualitative agreement with beam emission spectroscopy measurements on DIII-D for the relative radial extent and localization of the EHO and QCM. The high sensitivity of ECE radiation to separatrix displacements can be used to detect turbulence or MHD fluctuations near the separatrix, which may affect the transport across the separatrix and the wetted area in the divertor. The $\delta {T_{e{\text{,rad}}}}$ inversion measured with an ECE or ECEI system potentially provides important information on the magnetic field $\left| {{B_{{\text{sep}}}}} \right|$ at the separatrix, which helps constrain the pedestal equilibrium reconstruction and achieve an unambiguous mapping of the ECE/ECEI system with respect to the separatrix.
Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.
In the last two years, three major technical improvements have been made on J-TEXT in supporting of the expanded operation regions and diagnostic capabilities. (1) The successful commission of the 105 GHz/500 kW/1 s electron cyclotron resonance heating (ECRH) system increasing the core electron temperature from 0.9 keV up to around 1.5 keV. (2) The poloidal divertor configuration with an X-point in the high-field side has been achieved. In particular, the 400 kW electron cyclotron wave has also been successfully injected into the diverted plasma. (3) A 256-channel electron cyclotron emission imaging diagnostic system and two sets of four-channel Doppler backscattering diagnostics have been successfully developed on J-TEXT, allowing detailed measurement of the electron temperature and density fluctuations for turbulence and MHD research. The locked mode (LM), especially the 2/1 LM, is one of the biggest threats to the plasma operation. Both the thresholds of 2/1 and 3/1 LM are observed to vary non-monotonically on electron density. The electrode biasing was applied successfully to unlock the LM from either a rotating or static resonant magnetic perturbation (RMP) field. In the presence of 2/1 LM, three kinds of standing wave (SW) structures have been observed to share a similar connection to the island structure, i.e. the nodes of the SWs locate around the O- or X-points of the 2/1 island. The control and mitigation of disruption is essential to the safe operation of ITER, and it has been systematically studied by applying a RMP field, massive gas injection (MGI) and shattered pellet injection on J-TEXT. When the RMP-induced 2/1 LM is larger than a critical width, the MGI shutdown process can be significantly influenced. If the phase difference between the O-point of LM and the MGI valve is +90° (or –90°), the penetration depth and the assimilation of impurities can be enhanced (or suppressed) during the pre-thermal quench (TQ) phase and result in a faster (or slower) TQ. A secondary MGI can also suppress the runaway electron (RE) generation, if the additional high-Z impurity gas arrives at the plasma edge before TQ. When the secondary MGI has been applied after the formation of the RE current plateau, the RE current can be dissipated, and the dissipation rate increases with the injected impurity quantity but saturates with a maximum of 28 MA s –1 . The non-local transport is experimentally observed in the ion transport channel. The electron thermal diffusivity significantly increases with the ECRH power. Theoretical work shows that significant intrinsic current can be driven by electromagnetic turbulence, and the robust formation mechanism of the E × B staircase is identified from the Hasegawa–Wakatani system.
Recently, the numerical scheme presented by Mishchenko et al. enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.
An upgrade to the Phase Contrast Imaging (PCI) diagnostic on the DIII-D tokamak has successfully combined PCI with density interferometry to provide electron density fluctuation measurements across an unprecedented range in wavenumber. The combined diagnostic uses a single laser and a single beam path through the tokamak, minimizing machine resources in anticipation of future reactor-scale devices where port access will be at a premium. The PCI multichannel detector provides low-noise, wavenumber-resolved detection of moderate-wavenumber turbulence, while the interferometer channel is sensitive to long-wavelength turbulence, including the peak of ion-scale turbulence and MHD. The overlap in wavenumber range between the two schemes allows for an in situ absolute calibration of the PCI.