Transonic Flows in Two-Fluid Plasmas

Transonically rotating toroidal plasmas occur at all scales in the plasma universe and, recently, also in laboratory tokamak plasmas. This offers great opportunities for new insights of the effects of transonic transitions on the background equilibrium flows, and on the waves and instabilities excited. Transfer of knowledge and computational methods on MHD and two-fluid waves and instabilities in magnetically confined laboratory fusion plasmas to space and astrophysical plasmas is seriously hampered though by two related difficulties:

1. in contrast to laboratory plasmas, astrophysical plasmas always have sizeable plasma flows so that they can never be described as a static equilibrium;
2. these flows are usually ‘transonic’, i.e., surpass one of the critical speeds related to the different flow regimes with quite different physical characteristics.

Based on previously obtained MHD results on the stationary states and instabilities of transonically rotating accretion disks about compact objects, the extension to two-fluid plasmas is initiated: A variational principle for the computation of two-fluid stationary states is constructed which involves seven fields determining the different physical variables, and six arbitrary stream functions that should be determined by spatially resolved astrophysical observations. It exhibits all the intricacies due to the electron and ion flow excursions from the magnetic flux surfaces. New hyperbolic flow regimes are found with quite different properties than the MHD ones.     

Low-Frequency Waves and Instabilities in Collisionless Plasmas

We present a theoretical overview of low-frequency waves and instabilities in collisionless, multi-component plasmas with gyrotropic ( ) thermal pressure. We show that the complete dispersion relation can be obtained in the framework of a mixed magnetohydrodynamic (MHD)-kinetic formalism, which uses the MHD mass, momentum, and induction equations, together with the kinetically corrected version of the double-adiabatic equations of state. The complete dispersion relation contains not only the three standard modes (fast, slow, and Alfvén) from double-adiabatic MHD, but also the mirror mode from kinetic theory. We examine the stability properties of these four modes, firstly in the case of a uniform medium, and secondly in the case of a stratified and rotating medium. We also discuss the connections with the quasi-interchange modes (interchange and translation) often referred to in the context of magnetospheric physics.     

Why space physics needs to go beyond the MHD box

Magnetohydrodynamic (MHD) theory has been used in space physics for more than forty years, yet many important questions about space plasmas remain unanswered. We still do not understand how the solar wind is accelerated, how mass, momentum and energy are transported into the magnetosphere and what mechanisms initiate substorms. Questions have been raised from the beginning of the space era whether MHD theory can describe correctly space plasmas that are collisionless and rarely in thermal equilibrium. Ideal MHD fluids do not induce electromotive force, hence they lose the capability to interact electromagnetically. No currents and magnetic fields are generated, rendering ideal MHD theory not very useful for space plasmas. Observations from the plasma sheet are used as examples to show how collisionless plasmas behave. Interpreting these observations using MHD and ideal MHD concepts can lead to misleading conclusions. Notably, the bursty bulk flows (BBF) with large mean velocities left(〈 v 〉≥400 km s right) that have been interpreted previously as E×B flows are shown to involve much more complicated physics. The sources of these nonvanishing 〈 v 〉 events, while still not known, are intimately related to mechanisms that create large phase space gradients that include beams and acceleration of ions to MeV energies. The distributions of these nonvanishing 〈 v 〉 events are associated with large amplitude variations of the magnetic field at frequencies up to and exceeding the local Larmor frequency where MHD theory is not valid. Understanding collisionless plasma dynamics such as substorms in the plasma sheet requires the self-consistency that only kinetic theory can provide. Kinetic modeling is still undergoing continual development with many studies limited to one and two dimensions, but there is urgent need to improve these models as more and more data show kinetic physics is fundamentally important. Only then will we be able to make progress and obtain a correct picture of how collisionless plasmas work in space.     

Damping Mechanisms for Oscillations in Solar Prominences

Small amplitude oscillations are a commonly observed feature in prominences/filaments. These oscillations appear to be of local nature, are associated to the fine structure of prominence plasmas, and simultaneous flows and counterflows are also present. The existing observational evidence reveals that small amplitude oscillations, after excited, are damped in short spatial and temporal scales by some as yet not well determined physical mechanism(s). Commonly, these oscillations have been interpreted in terms of linear magnetohydrodynamic (MHD) waves, and this paper reviews the theoretical damping mechanisms that have been recently put forward in order to explain the observed attenuation scales. These mechanisms include thermal effects, through non-adiabatic processes, mass flows, resonant damping in non-uniform media, and partial ionization effects. The relevance of each mechanism is assessed by comparing the spatial and time scales produced by each of them with those obtained from observations. Also, the application of the latest theoretical results to perform prominence seismology is discussed, aiming to determine physical parameters in prominence plasmas that are difficult to measure by direct means.     

MHD Waves and Instabilities in Space Plasma Flows

Shear flow instabilities are an important aspect of hydrodynamic studies. The present review article discusses the role of an ambient magnetic field which both modifies the Kelvin-Helmholtz instability and may introduce new types of magnetohydrodynamic waves and instabilities. A brief overview of magnetospheric pulsations is presented with an emphasis on the long-period resonant Alfv??n waves associated with the high speed solar wind. The spatio-temporal evolution of magnetically modified shear flow instabilities in various space plasma structures is addressed. A distinction between convective and absolute instabilities is necessary for proper understanding of theory and correct interpretation of the observations. Finally, it is shown how incompressible Alfv??nic disturbances may become unstable in a compressible flow in the absence of any shear. An application to coronal loops is presented.     

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

Understanding transport of thermal and suprathermal particles is a fundamental issue in laboratory, solar-terrestrial, and astrophysical plasmas. For laboratory fusion experiments, confinement of particles and energy is essential for sustaining the plasma long enough to reach burning conditions. For solar wind and magnetospheric plasmas, transport properties determine the spatial and temporal distribution of energetic particles, which can be harmful for spacecraft functioning, as well as the entry of solar wind plasma into the magnetosphere. For astrophysical plasmas, transport properties determine the efficiency of particle acceleration processes and affect observable radiative signatures. In all cases, transport depends on the interaction of thermal and suprathermal particles with the electric and magnetic fluctuations in the plasma. Understanding transport therefore requires us to understand these interactions, which encompass a wide range of scales, from magnetohydrodynamic to kinetic scales, with larger scale structures also having a role. The wealth of transport studies during recent decades has shown the existence of a variety of regimes that differ from the classical quasilinear regime. In this paper we give an overview of nonclassical plasma transport regimes, discussing theoretical approaches to superdiffusive and subdiffusive transport, wave–particle interactions at microscopic kinetic scales, the influence of coherent structures and of avalanching transport, and the results of numerical simulations and experimental data analyses. Applications to laboratory plasmas and space plasmas are discussed.     

Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

Complexity,Forced and/or Self-Organized Criticality,and Topological Phase Transitions in Space Plasmas

The first definitive observation that provided convincing evidence indicating certain turbulent space plasma processes are in states of ‘complexity’ was the discovery of the apparent power-law probability distribution of solar flare intensities. Recent statistical studies of complexity in space plasmas came from the AE index, UVI auroral imagery, and in-situ measurements related to the dynamics of the plasma sheet in the Earth's magnetotail and the auroral zone. In this review, we describe a theory of dynamical ‘complexity’ for space plasma systems far from equilibrium. We demonstrate that the sporadic and localized interactions of magnetic coherent structures are the origin of ‘complexity’ in space plasmas. Such interactions generate the anomalous diffusion, transport, acceleration, and evolution of the macroscopic states of the overall dynamical systems. Several illustrative examples are considered. These include: the dynamical multi- and cross-scale interactions of the macro-and kinetic coherent structures in a sheared magnetic field geometry, the preferential acceleration of the bursty bulk flows in the plasma sheet, and the onset of ‘fluctuation induced nonlinear instabilities’ that can lead to magnetic reconfigurations. The technique of dynamical renormalization group is introduced and applied to the study of two-dimensional intermittent MHD fluctuations and an analogous modified forest-fire model exhibiting forced and/or self-organized criticality [FSOC] and other types of topological phase transitions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spectrum of global ideal-magnetohydrodynamic three-dimensional ballooning modes

The class of pressure-driven plasma instabilities known as ballooning modes may be responsible for such diverse phenomena as high-beta disruptions in tokamaks, solar flares and magnetospheric substorms. In this paper the theory of the spectrum of unstable eigenvalues of the linearized ideal magnetohydrodynamic (MHD) equations of motion in non-axisymmetric toroidal equilibria is sketched, comparing and contrasting systems with open field lines and systems with toroidally confined field lines. The need to regularize ideal MHD to keep the wavenumber finite, and the relevance of quantum chaos theory to understand the structure of the spectrum, is pointed out. This revised version was published online in August 2006 with corrections to the Cover Date.     

Grid-Adaptive Computations of Magnetized Jets

We present grid-adaptive numerical simulations of magnetized plasma jets, modeled by means of the compressible magnetohydrodynamic equations. The Adaptive Mesh Refinement strategy makes it possible to investigate long-term jet dynamics where both large-scale and small-scale effects are at play. We extend recent findings for uniformly magnetized, periodic shear layers to planar and fully 3D extended jet segments. The jet lengths cover multiple, typically 10, axial wavelengths of the fastest growing Kelvin–Helmholtz (KH) like modes. The dominant linear MHD instabilities of the jet flows are quantified by means of MHD spectroscopic analysis. In cases characterized by sonic Mach numbers about unity and large plasma beta values, both single and double shear layers (planar jets) manifest self-organizing trends to large scales, e.g. by continuous pairing/merging between co-rotating vortices, simultaneously with the introduction of small-scale features by magnetic reconnection events. The vortices form as a result of KH unstable shear-flow layers, and their coalescence arises from the growth of subharmonic modes at multiple wavelengths of the fastest growing KH instability. In extended two-dimensional jet segments, we investigate how varying jet width alters this coalescence process occurring at both edges, e.g. by introducing Batchelor-like coupling between counter-rotating vortices formed at opposing weakly magnetized, close shear layers. Finally, periodic segments of supersonic magnetized jets are simulated in two- and three-dimensional cases, which are characterized by violent shock-dominated transients.     

MHD Spectroscopy of Transonic Flows

In previous publications (Keppens et al.: 2002, Astrophys. J. 569, L121; Goedbloed et al.: 2004a, Phys. Plasmas 11, 28), we have demonstrated that stationary rotation of magnetized plasma about a compact central object permits an enormous number of different MHD instabilities, with the well-known magneto-rotational instability (Velikhov, E. P.: 1959, Soviet Phys.–JETP Lett. 36, 995; Chandrasekhar, S.: 1960, Proc. Natl. Acad. Sci. U.S.A. 46, 253; Balbus, S. A. and Hawley, J. F.: 1991, Astrophys. J. 376, 214) as just one of them. We here concentrate on the new instabilities found that are driven by transonic transitions of the poloidal flow. A particularly promising class of instabilities, from the point of view of MHD turbulence in accretion disks, is the class of trans-slow Alfv’en continuum modes, that occur when the poloidal flow exceeds a critical value of the slow magnetosonic speed. When this happens, virtually every magnetic/flow surface of the disk becomes unstable with respect to highly localized modes of the continuous spectrum. The mode structures rotate, in turn, about the rotating disk. These structures lock and become explosively unstable when the mass of the central object is increased beyond a certain critical value. Their growth rates then become huge, of the order of the Alfv’en transit time. These instabilities appear to have all requisite properties to facilitate accretion flows across magnetic surfaces and jet formation.     

Resonant MHD Waves in the Solar Atmosphere

The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.     

三维磁流体动力学管道流动加减速控制数值研究

阐述了磁流体动力学(MHD)控制流场作用机理.在小磁雷诺数条件下,运用数值模拟方法,对不同外加电磁场条件下三维MHD管道流动的流场情况进行研究,得出不同磁场、电场等MHD参数作用下MHD加速器的性能.对MHD加速器的应用前景进行了展望.计算结果显示,电场取6000V/m,磁场为0.92T 情况下,流场的加速性能可达13.46%,并且可以通过减小磁场或增大电场进一步提高加速性能;在仅添加0.92T磁场条件下,速度减速可达16.35%.     

Microphysics of Cosmic Ray Driven Plasma Instabilities

Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.     

Kinetic Excitation Mechanisms for ION-Cyclotron Kinetic Alfvén Waves in Sun-Earth ConnectionI

We study kinetic excitation mechanisms for high-frequency dispersive Alfvén waves in the solar corona, solar wind, and Earth's magnetosphere. The ion-cyclotron and Cherenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (ICKAWs). Ion beams, anisotropic particles distributions and currents provide free energy for the excitation of ICKAWs in space plasmas. As particular examples we consider ICKAW instabilities in the coronal magnetic reconnection events, in the fast solar wind, and in the Earth's magnetopause. Energy conversion and transport initiated by ICKAW instabilities is significant for the whole dynamics of Sun-Earth connection chain, and observations of ICKAW activity could provide a diagnostic/predictive tool in the space environment research. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electromagnetic ion/ion instabilities and their consequences in space plasmas: A review

This paper reviews recent research on the theory and computer simulations of electromagnetic ion/ion instabilities and their consequences in space plasmas. Ion/ion instabilities are growing modes in a collisionless plasma driven unstable by the relative streaming velocity v ₀of two distinct ion components such that v ₀is parallel or antiparallel to the uniform background magnetic field B ₀0. The space physics regimes which display enhanced fluctuations due to these instabilities and which are reviewed in this paper include the solar wind, the terrestrial foreshock, the plasma sheet boundary layer, and distant cometary environments.     

Heating Diagnostics with MHD Waves

The heating of the solar atmosphere is a fundamental problem of modern solar and astrophysics. A review of the seismological aspects of magnetohydrodynamic (MHD) waves with an emphasis on standing longitudinal waves in the context of coronal heating is presented. Efforts made recently may be split into two categories: forward modelling and data inversion. Forward modelling can be applied to predict the observational footprints of various heating scenarios. A new diagnostic method based on the analysis of Doppler shift time series is outlined with specific application to solar coronal conditions. The power of the method is demonstrated and tested using synthetic data and comparing them with actual high-resolution (e.g. SoHO/SUMER) observations. Further, related recent examples of standing longitudinal oscillations in coronal loop structures observed with the new Hinode/EIS instrument are also presented. These latter observations provide an advanced ground for MHD seismology as a tool for plasma heating diagnostics in the atmosphere of the Sun.