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.     

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.     

Measurements of collisional rate coefficients in laboratory plasmas

Line radiation emitted by highly ionized atoms embedded in hot laboratory plasmas can be utilized to obtain collisional rate coefficients for excitation and ionization. After a discussion of the principles underlying these measurements, the plasma device mostly used is explained briefly as are the various experimental techniques. All experimental results obtained so far are finally discussed and compared with theoretical calculations where possible.     

Stability and waves of transonic laboratory and space plasmas

The properties of magnetohydrodynamic waves and instabilities of laboratory and space plasmas are determined by the overall magnetic confinement geometry and by the detailed distributions of the density, pressure, magnetic field, and background velocity of the plasma. Consequently, measurement of the spectrum of MHD waves (MHD spectroscopy) gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward as well as the inverse spectral problems. This terminology entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in space. Here, helioseismology (which could be considered as one of the forms of MHD spectroscopy) may serve as a luminous example. The required study of magnetohydrodynamic waves and instabilities of both laboratory and space plasmas has been conducted for many years starting from the assumption of static equilibrium. Recently, there is a outburst of interest for plasma states where this assumption is violated. In fusion research, this interest is due to the importance of neutral beam heating and pumped divertor action for the extraction of heat and exhaust needed in future tokamak reactors. Both result in rotation of the plasma with speeds that do not permit the assumption of static equilibrium anymore. In astrophysics, observations in the full range of electromagnetic radiation has revealed the primary importance of plasma flows in such diverse situations as coronal flux tubes, stellar winds, rotating accretion disks, and jets emitted from radio galaxies. These flows have speeds which substantially influence the background stationary equilibrium state, if such a state exists at all. Consequently, it is important to study both the stationary states of magnetized plasmas with flow and the waves and instabilities they exhibit. We will present new results along these lines, extending from the discovery of gaps in the continuous spectrum and low-frequency Alfvén waves driven by rotation to the nonlinear flow patterns that occur when the background speed traverses the full range from sub-slow to super-fast. This revised version was published online in August 2006 with corrections to the Cover Date.     

Topics in Microphysics of Relativistic Plasmas

Astrophysical plasmas can have parameters vastly different from the more studied laboratory and space plasmas. In particular, the magnetic fields can be the dominant component of the plasma, with energy-density exceeding the particle rest-mass energy density. Magnetic fields then determine the plasma dynamical evolution, energy dissipation and acceleration of non-thermal particles. Recent data coming from astrophysical high energy missions, like magnetar bursts and Crab nebula flares, point to the importance of magnetic reconnection in these objects. In this review we outline a broad spectrum of problems related to the astrophysical relevant processes in magnetically dominated relativistic plasmas. We discuss the problems of large scale dynamics of relativistic plasmas, relativistic reconnection and particle acceleration at reconnecting layers, turbulent cascade in force-fee plasmas. A number of astrophysical applications are also 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.     

Expected charge states of energetic ions in the magnetosphere

This paper reviews major developments in our understanding of the physics of energetic heavy ions in the Earth's plasma environment during the past four years (1974–1977). Emphasis is placed on processes that influence or are influenced by the ion charge states. This has been a period of growing awareness of the important role heavy ions play in space plasmas. Large fluxes of helium ions and even heavier ions have been observed at the geostationary altitude and in the heart of the radiation belts. Such ions have also been observed on low latitude rockets and satellites, and oxygen ion precipitation exceeding that of protons has been reported. In the outer parts of the Earth's plasma envelope there is mounting evidence for significant fluxes of heavy ions: in the magnetotail, the magnetosheath and in the polar cusp regions. In the inner magnetosphere there is a limited theoretical understanding of equatorially mirroring ions, but generally only radial diffusion at one pitch angle and pitch angle diffusion at one L- shell have been studied; for ions the coupled equations are yet unsolved even for the simplest case of only one charge state (protons). Theoretical modeling of the charge state structures of geophysical heavy ion populations is in part frustrated by the lack of adequate laboratory measurements of the pertinent charge exchange cross sections. A first attempt has, however, been made to treat the charge state transformation processes in the radiation belts for equatorially mirroring atomic oxygen ions. Wave-particle interactions in the magnetosphere become much more complex in multi component and multi charge state plasmas where hybrid resonances and wave-particle interaction induced non-linear species-species coupling could be important. Heavy ion plasma physics in the Earth's magnetosphere and in the magnetospheres of other planets should be a field of fruitful study for both experimentalists and theoreticians in the years ahead.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Wave-particle diagnostics for plasma simulation

One important type of problem for particle simulation of plasmas, is one which is bounded and has external sources and sinks. For example, there are problems with antennas for studying RF heating or current drive in fusion plasmas, or problems in space simulation where particles are injected at one boundary with some specified energy or momentum distribution. In understanding such simulation results, it is useful to know how energy and momentum are flowing inside the plasma. This can be accomplished in electrostatic particle simulations on the basis of some theorems for energy and momentum flow. An important application of these theorems occurs when many waves are involved in producing some effect, e.g., generating a current by RF. One can then extract the contribution of each wave to the effect to identify which are most important. Examples of such wave-particle diagnostics will be given.     

Hybrid simulation codes with application to shocks and upstream waves

Hybrid codes in which part of the plasma is represented as particles and the rest as a fluid are discussed. In the past few years such codes with particle ions and massless, fluid electrons have been applied to space plasmas, especially to collisionless shocks. All of these simulation codes are one-dimensional and similar in structure, except for how the field equations are solved. We describe in detail the various approaches that are used (resistive Ohm's law, predictor-corrector, Hamiltonian) and compare results from the various codes with examples taken from collisionless shocks and low frequency wave phenomena upstream of shocks.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

Microphysics of Cosmic Plasmas: Background, Motivation and Objectives

With the maturing of space plasma research in the solar system, a more general approach to plasma physics in general, applied to cosmic plasmas, has become appropriate. There are both similarities and important differences in describing the phenomenology of space plasmas on scales from the Earth’s magnetosphere to galactic and inter-galactic scales. However, there are important aspects in common, related to the microphysics of plasma processes. This introduction to a coordinated collection of papers that address the several aspects of the microphysics of cosmic plasmas that have unifying themes sets out the scope and ambition of the broad sweep of topics covered in the volume, together with an enumeration of the detailed objectives of the coverage.     

Quantum Field Theoretic Description of Matter in the Universe

Quantum field theory at finite temperature and density can be used for describing the physics of relativistic plasmas. Such systems are frequently encountered in astrophysical situations, such as the early universe, supernova explosions, and the interior of neutron stars. After a brief introduction to thermal field theory the usefulness of this approach in astrophysics will be exemplified in three different cases. First the interaction of neutrinos within a supernova plasma will be discussed. Then the possible presence of quark matter in a neutron star core and finally the interaction of light with the Cosmic Microwave Background will be considered.     

Methods for Characterising Microphysical Processes in Plasmas

Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.     

Dielectronic satellite spectra in the soft X-ray region

Satellite lines, situated on the long wavelength side of the helium-like ion resonance line, can be observed in highly-ionized ions both in laboratory sources and from the Sun. Although seen for more than 30 years, these lines have only recently been classified in detail as inner-shell transitions in lithium-like ions. Laboratory experiments have shown that under steady-state conditions these satellites are produced by dielectronic recombination, although in transient ionizing plasmas direct inner-shell excitation can be important. Detailed calculations have been carried out for high Z ions up to copper, and the results can be compared with solar flare spectra in iron. Such comparisons allow both the electron temperature and the transient state of the plasma to be determined. Laboratory spectra from such high-Z ions are different in appearance, and may be dominated by processes resulting from the transient ionizing state of the plasma.     

The Earth's Dynamic Magnetotail

Geomagnetic field lines that are stretched on the nightside of the Earth due to reconnection with the interplanetary magnetic field constitute the Earth's magnetotail. The magnetotail is a dynamic entity where energy imparted from the solar wind is stored and then released to generate disturbance phenomena such as substorms. This paper gives an updated overview on the physics of the magnetotail by drawing heavily from recent research conducted with the GEOTAIL satellite. It summarizes firstly the basic properties of the magnetotail such as shape, size and magnetic flux content, internal motion and plasma regimes. Then it describes characteristics of tail plasmas of the solar-wind and the ionosphere origins. Thirdly it addresses acceleration and heating of plasmas in the magnetotail, where reconnection between the stretched field lines is the main driver but the site of the acceleration is not limited to the immediate vicinity of the neutral line. In the collisionless regime of the plasma sheet kinetic behaviors of ions and electrons control the acceleration process. The paper closes by enumerating the problems posed for future studies.     

Magnetic field reconnection theory and the solar wind — Magnetosphere interaction: A review

This review considers the theory of the magnetic field line reconnection and its application to the problem of the interaction between the solar wind and the Earth's magnetosphere. In particular, we discuss the reconnection models by Sonnerup and by Petschek (for both incompressible and compressible plasmas, for the asymmetric and nonsteady-state cases), the magnetic field annihilation model by Parker; Syrovatsky's model of the current sheet; and Birn's and Schindler's solution for the plasma sheet structure. A review of laboratory and numerical modelling experiments is given.Results concerning the field line reconnection, combined with the peculiarities of the MHD flow, were used in investigating the solar wind flow around the magnetosphere. We found that in the presence of a frozen-in magnetic field, the flow differs significantly from that in a pure gas dynamic case; in particular, at the subsolar. part of the magnetopause a stagnation line appears (i.e., a line along which the stream lines are branching) instead of a stagnation point. The length and location of the stagnation line determine the character of the interaction of the solar wind with the Earth's magnetosphere. We have developed the theory of that interaction for a steady-state case, and compare the results of the calculations with the experimental data.In the last section of the review, we propose a qualitative model of the solar wind — the Earth's magnetosphere interaction in the nonsteady-state case on the basis of the solution of the problem of the spontaneous magnetic field line reconnection.     

Ring Currents and Internal Plasma Sources

The discovery of terrestrial O⁺ and other heavy ions in magnetospheric hot plasmas, combined with the association of energetic ionospheric outflows with geomagnetic activity, led to the conclusion that increasing geomagnetic activity is responsible for filling the magnetosphere with ionospheric plasma. Recently it has been discovered that a major source of ionospheric heavy ion plasma outflow is responsive to the earliest impact of coronal mass ejecta upon the dayside ionosphere. Thus a large increase in ionospheric outflows begins promptly during the initial phase of geomagnetic storms, and is already present during the main phase development of such storms. We hypothesize that enhancement of the internal source of plasma actually supports the transition from substorm enhancements of aurora to storm-time ring current development in the inner magnetosphere. Other planets known to have ring current-like plasmas also have substantial internal sources of plasma, notably Jupiter and Saturn. One planet having a small magnetosphere, but very little internal source of plasma, is Mercury. Observations suggest that Mercury has substorms, but are ambiguous with regard to the possibility of magnetic storms of the planet. The Messenger mission to Mercury should provide an interesting test of our hypothesis. Mercury should support at most a modest ring current if its internal plasma source is as small as is currently believed. If substantiated, this hypothesis would support a general conclusion that the magnetospheric inflationary response is a characteristic of magnetospheres with substantial internal plasma sources. We quantitatively define this hypothesis and pose it as a problem in comparative magnetospheres.     

Fundamentals of plasma simulation

With the increasing size and speed of modern supercomputers, the incredibly complex nonlinear properties of plasmas in the laboratory and in space are being successfully explored in increasing depth. Of particular importance have been numerical simulation techniques involving finite size particles on a discrete mesh. After discussing the importance of this means of understanding a variety of nonlinear plasma phenomena, we describe the basic elements of particle-in-cell simulation and their limitations and advantages. The differencing techniques, stability and accuracy issues, data management and optimization issues are discussed by a simple example of a particle-in-cell code. Recent advances in simulation methods allowing large space and time scales to be treated with minimal sacrifice in physics are reviewed. Various examples of nonlinear processes successfully studied by plasma simulation are given.     

Energy Deposition in Planetary Atmospheres by Charged Particles and Solar Photons

We discuss here the energy deposition of solar FUV, EUV and X-ray photons, energetic auroral particles, and pickup ions. Photons and the photoelectrons that they produce may interact with thermospheric neutral species producing dissociation, ionization, excitation, and heating. The interaction of X-rays or keV electrons with atmospheric neutrals may produce core-ionized species, which may decay by the production of characteristic X-rays or Auger electrons. Energetic particles may precipitate into the atmosphere, and their collisions with atmospheric particles also produce ionization, excitation, and heating, and auroral emissions. Auroral energetic particles, like photoelectrons, interact with the atmospheric species through discrete collisions that produce ionization, excitation, and heating of the ambient electron population. Auroral particles are, however, not restricted to the sunlit regions. They originate outside the atmosphere and are more energetic than photoelectrons, especially at magnetized planets. The spectroscopic analysis of auroral emissions is discussed here, along with its relevance to precipitating particle diagnostics. Atmospheres can also be modified by the energy deposited by the incident pickup ions with energies of eV’s to MeV’s; these particles may be of solar wind origin, or from a magnetospheric plasma. When the modeling of the energy deposition of the plasma is calculated, the subsequent modeling of the atmospheric processes, such as chemistry, emission, and the fate of hot recoil particles produced is roughly independent of the exciting radiation. However, calculating the spatial distribution of the energy deposition versus depth into the atmosphere produced by an incident plasma is much more complex than is the calculation of the solar excitation profile. Here, the nature of the energy deposition processes by the incident plasma are described as is the fate of the hot recoil particles produced by exothermic chemistry and by knock-on collisions by the incident ions.     

Modelling Electrostatic Sheath Effects on Swarm Electric Field Instrument Measurements

The Electric Field Instrument (EFI) was designed to measure ionospheric ion flow velocities, temperatures and distribution functions at the ram face of the European Space Agency’s Swarm spacecraft. These flow velocities, combined with the known orbital velocity of the satellite and local magnetic field, will be used to infer local electric fields from the relation E=?v×B. EFI is among a class of many particle sensors and flow meters mounted on satellites to monitor in situ plasma conditions. The interpretation of the measurements made with EFI and similar sensors relies on a spacecraft sheath model. A common approach, valid in the relatively cold and dense ionospheric plasma, is to assume a potential drop in a thin sheath through which particle deflection and energisation can be calculated analytically. In such models, sheath effects only depend on the spacecraft floating potential, and on the angle of incidence of particles with respect to the normal to the surface. Corrections to measurements are therefore local as they do not depend on the geometry of nearby objects. In an actual plasma, satellites are surrounded by electrostatic sheaths with a finite thickness. As a result, local corrections to particle distribution functions can only be seen as an approximation. A correct interpretation of measured particle fluxes or particle distribution functions must, at least in principle, account for the extent and shape of the sheath in the vicinity of the measuring instrument. This in turn requires a careful analysis of the interaction of the satellite with the surrounding plasma, while accounting for detailed aspects of the geometry, as well as for several physical effects. In this paper, the validity of the thin sheath model is tested by comparing its predictions with detailed PIC (Particle In Cell) calculations of satellite-plasma interaction. Deviations attributed to sheath finite thickness effects are calculated for EFI measurements, with representative plasma parameters encountered along the planned Swarm orbit. Finite thickness effects of the plasma sheaths are found to induce EFI velocity measurement errors not exceeding 37 m/s, with larger errors occurring in plasmas that are simultaneously tenuous (10⁹ m^?3 or lower) and warm (0.5 eV or higher).