Computational Simulation of Plasmas

This paper reviews the use of computational simulation in plasma physics. It describes a range of numerical models varying from particle models of low density collisionless plasmas to fluid models of high density collision-dominated plasmas. Some applications of these models, particularly to laser-produced and astrophysical plasmas, are described.     

Advances in numerical modeling of astrophysical and space plasmas

Plasma science is rich in distinguishable scales ranging from the atomic to the galactic to the meta-galactic, i.e., themesoscale. Thus plasma science has an important contribution to make in understanding the connection between microscopic and macroscopic phenomena. Plasma is a system composed of a large number of particles which interact primarily, but not exclusively, through the electromagnetic field. The problem of understanding the linkages and couplings in multi-scale processes is a frontier problem of modern science involving fields as diverse as plasma phenomena in the laboratory to galactic dynamics.Unlike the first three states of matter, plasma, often called the fourth state of matter, involves the mesoscale and its interdisciplinary founding have drawn upon various subfields of physics including engineering, astronomy, and chemistry. Basic plasma research is now posed to provide, with major developments in instrumentation and large-scale computational resources, fundamental insights into the properties of matter on scales ranging from the atomic to the galactic. In all cases, these are treated as mesoscale systems. Thus, basic plasma research, when applied to the study of astrophysical and space plasmas, recognizes that the behavior of the near-earth plasma environment may depend to some extent on the behavior of the stellar plasma, that may in turn be governed by galactic plasmas. However, unlike laboratory plasmas, astrophysical plasmas will forever be inaccessible to in situ observation. The inability to test concepts and theories of large-scale plasmas leaves only virtual testing as a means to understand the universe. Advances in in computer technology and the capability of performing physics first principles, fully three-dimensional, particle-in-cell simulations, are making virtual testing a viable alternative to verify our predictions about the far universe.The first part of this paper explores the dynamical and fluid properties of the plasma state, plasma kinetics, and the radiation emitted from plasmas. The second part of this paper outlines the formulation for the particle-in-cell simulation of astrophysical plasmas and advances in simulational techniques and algorithms, as-well-as the advances that may be expected as the computational resource grows to petaflop speed/memory capabilities.Dedicated to the memories of Hannes Alfvén and Oscar Buneman; Founders of the Subject.     

Nonlinear wave-wave interactions in astrophysical and space plasmas

We discuss nonlinear mode-mode coupling phenomena in cosmic plasmas. Four problems are considered: (1) nonlinear three-wave processes in the planetary magnetosphere involving the interaction of auroral Langmuir, Alfvén and whistler waves, (2) nonlinear three-wave processes in the solar wind involving the modulation of Langmuir and electromagnetic waves by ion-acoustic waves, (3) order and chaos in nonlinear four-wave processes in cosmic plasmas, and (4) regular and chaotic dynamics of the relativistic Langmuir turbulence and its application to pulsar and AGN emissions. The observational evidence in support of nonlinear wave-wave interactions in space and astrophysical plasmas is presented.     

Scalable Dynamics of High Energy Relativistic Electrons: Theory, Numerical Simulations and Experimental Results

Similarity theory, which is necessary in order to apply the results of laboratory astrophysics experiments to relativistic astrophysical plasmas, is presented. The analytical predictions of the similarity theory are compared with PIC numerical simulations and the most recent experimental data on monoenergetic electron acceleration in diluted plasmas and high harmonic generation at overdense plasma boundaries. We demonstrate that similarity theory is a reliable tool for explaining a surprisingly wide variety of laboratory plasma phenomena the predictions of which can be scaled up to astrophysical dimensions.     

Some Physical Processes in Dusty Plasmas

Ionized gases containing fine (μm to sub-μm sized) charged dust grains, referred to as dusty plasmas, occur in diverse cosmic and laboratory environments. Dust occurs in many space and astrophysical environments, including planetary rings, comets, the Earth's ionosphere, and interstellar molecular clouds. Dust also occurs in laboratory plasmas, including processing plasmas, and crystallized dusty plasmas. Charged dust can lead to various effects in a plasma. In this review, some physical processes in dusty plasmas are discussed, with an emphasis on applications to dusty plasmas in space. This includes theoretical work on several wave instabilities, the role of dust as an electron source, and Coulomb crystals of positively charged dust. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electron acoustic double layers in a plasma with a <Emphasis Type="Italic">q</Emphasis>-nonextensive electron velocity distribution

Electron-acoustic double-layers (EA-DLs) are addressed in a plasma with a q-nonextensive electron velocity distribution. The domain of their allowable Mach numbers depends drastically on the plasma parameters and, in particular, on the electron nonextensivity. As the electrons evolve far away from their thermodynamic equilibrium, the negative EA-DLs shrinks and may develop into compressive EA-DLs. Our results may be relevant to the double-layers observed both in the auroral region and the plasma sheet of Earth’s magnetosphere (during enhanced magnetic activity). These DLs associated parallel electric fields are thought to be responsible for particle (electrons and ions) acceleration. Furthermore, our theoretical analysis brings a possibility to develop more refined theories of nonlinear cosmic DLs that may occur in astrophysical plasmas.     

Transport phenomena and abundance anomalies in cosmic plasma

Hydrodynamical equations for a fully ionized hydrogen-helium plasma are derived by the Chapman-Enskog method. The electron and ion transport coefficients are found as the functions of electron and ion temperatures and number densities as well as of the magnetic field strength. The presented equations are needed for describing transport phenomena in laboratory and cosmic plasmas. It is shown that transport phenomena can produce abundance anomalies; e. g., a sound wave propagating through a homogeneous plasma may be accompanied by the oscillations of chemical composition. Various astrophysical consequences of the theory are discussed.     

Properties of dispersive Alfvén waves: 3. Hydrodynamics (Very Low,Intermediate, and Low Density Plasmas)

The behavior of dispersive Alfvén waves (DAWs), including inertial and kinetic Alfvén waves, in astrophysical plasmas of very low, intermediate, and low pressure is investigated in the hydrodynamic approximation. New full solutions are obtained. Our results are analyzed and compared with those from the kinetic approach. It is shown that one general solution for the DAWs in plasmas of very low, intermediate, and low pressure can be obtained in the framework of the hydrodynamic approach, as opposed to the kinetic one. In the very low damping region, the kinetic and hydrodynamic solutions agree very well; but there are parameter regions where the solutions are essentially different. The influence of the astrophysical medium parameters on the DAW behavior and properties is analyzed. All main wave characteristics—the dispersion, damping, polarization, density perturbations, and charge density perturbations—are obtained, whose the consideration is very important for the observation and detection of these waves, as well as for a more correct understanding of their behavior and role in various astrophysical processes taking place in the cosmic medium.     

Particle acceleration and nonthermal radiation in space plasmas

Acceleration processes for fast particles in astrophysical and space plasmas are reviewed with emphasis on stochastic acceleration by MHD turbulence and on acceleration by shock waves. Radiation processes in astrophysical and space plasmas are reviewed with emphasis on plasma emission from the solar corona and electron cyclotron maser emission from planets and stars.     

Properties of dispersive Alfven waves: 4. Hydrodynamics (finite and high-pressure plasmas)

The behavior of dispersive Alfven waves (DAWs) in astrophysical plasmas of finite and high pressure, which have not been considered thus far, is studied in the hydrodynamic approximation. The results are analyzed and compared with those obtained in the kinetic approach. It is shown that one general solution for DAWs in plasmas of finite and high pressure can be obtained using the hydrodynamic approach in contrast to the kinetic one. Kinetic and hydrodynamic solutions correspond to each other very well in a domain with weakly damped DAWs; however, solutions may differ appreciably in some parameter domains, especially in high-pressure plasma. The effect of parameters of the astrophysical medium on the DAW behavior and properties is analyzed. All the main wave characteristics were determined: dispersion, damping, polarization, density perturbations, and charge density perturbations. Since finite-pressure plasma is one of the most frequently encountered states of astrophysical plasma, it is very important to take into account specific features in behavior of these waves for their detecting and a more correct understanding of their behavior and the role they play in different astrophysical processes that occur in space environment.     

等离子天体物理学与现代等离子体宇宙观

现代科学表明宇宙中99%以上的可观测物质都处于等离子体状态,从小尺度的微观粒子动力学集体过程与能量转换机制到大尺度的宇宙等离子天体结构状态与爆发活动现象,都是等离子天体物理学的研究课题.从宇宙演化历史、大尺度结构形成以及爆发活动现象等方面,系统地论述了等离子天体物理学在现代天文学发展以及现代等离子体宇宙观形成中的重要作用.同时,结合空间卫星科学探测研究及其对现代天文学的巨大影响,进一步阐述了地球磁层和日球层等空间等离子体实地探测研究在等离子天体物理学研究中所扮演的“天然实验室”的独特作用.     

Plasma and the universe: large scale dynamics,filamentation, and radiation

One of the earliest predictions about the morphology of the universe is that it be filamentary (Alfvén, 1950). This prediction followed from the fact that volumewise, the universe is 99.999% matter in the plasma state. When the plasma is energetic, it is generally inhomogeneous with constituent parts in motion. Plasmas in relative motion are coupled by the currents they drive in each other and nonequilibrium plasma often consists of current-conducting filaments.In the laboratory and in the Solar System, filamentary and cellular morphology is a well-known property of plasma. As the properties of the plasma state of matter is believed not to change beyond the range of our space probes, plasma at astrophysical dimensions must also be filamentary.During the 1980s a series of unexpected observations showed filamentary structure on the Galactic, intergalactic, and supergalactic scale. By this time, the analytical intractibility of complex filamentary geometries, intense self-fields, nonlinearities, and explicit time dependence had fostered the development of fully three-dimensional, fully electromagnetic, particle-in-cell simulations of plasmas having the dimensions of galaxies or systems of galaxies. It had been realized that the importance of applying electromagnetism and plasma physics to the problem of radiogalaxy and galaxy formation derived from the fact that the universe is largely aplasma universe. In plasma, electromagnetic forces exceed gravitational forces by a factor of 10³⁶, and electromagnetism is 10⁷ times stronger than gravity even in neutral hydrogen regions, where the degree of ionization is a miniscule 10^–4.The observational evidence for galactic-dimensioned Birkeland currents is given based on the direct comparison of the synchrotron radiation properties of simulated currents to those of extra-galactic sources including quasars and double radio galaxies.     

Self-Generation of Magnetic Fields in Weakly Ionized Astrophysical Plasmas

In weakly ionized astrophysical plasmas, shear flow induced plasma - neutral gas friction yields self-generated magnetic fields of seed-field order. This process is of cosmological importance and relevant for protogalactic systems like Lyα-clouds. In our contribution we illustrate this mechanism by the help of 3-dimensional 2-fluid simulations of primordial rotating gas clumps in Lyα-clouds showing that plasma - neutral gas interactions cause large scale magnetic fields of the order of 10⁻¹⁵G on time scales of the order of 10⁶yrs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Relativistic anisotropic pair plasmas

The properties of waves able to propagate in a relativistic pair plasma are at the basis of the interpretation of several astrophysical observations. For instance, they are invoked in relation to radio emission processes in pulsar magnetospheres and to radiation mechanisms for relativistic radio jets. In such physical environments, pair plasma particles probably have relativistic, or even ultrarelativistic, temperatures. Besides, the presence of an extremely strong magnetic field in the emission region constrains the particles to one-dimensional motion: all the charged particles strictly move along magnetic field lines.
We take anisotropic effects and relativistic effects into account by choosing one-dimensional relativistic Jűttner–Synge distribution functions to characterize the distribution of electrons and/or positrons in a relativistic, anisotropic pair plasma. The dielectric tensor, from which the dispersion relation associated with plane wave perturbations of such a pair plasma is derived, involves specific coefficients that depend on the distribution function of particles. A precise determination of these coefficients, using the relativistic one-dimensional Jűttner–Synge distribution function, allows us to obtain the appropriate dispersion relation. The properties of waves able to propagate in anisotropic relativistic pair plasmas are deduced from this dispersion relation. The conditions in which a beam and a plasma, both ultrarelativistic, may interact and trigger off a two-stream instability are obtained from this same dispersion relation. Two astrophysical applications are discussed.     

X‐ray luminosity functions of different morphological and X‐ray type AGN populations

Luminosity functions are one of the most important observational clues when studying galaxy evolution over cosmic time. In this paper we present the X‐ray luminosity functions for X‐ray detected AGN in the SXDS and GWS fields. The limiting fluxes of our samples are 9.0 ×10^–15 and 4.8 ×10^–16 erg cm^–2 s^–1 in the 0.5–7.0 keV band in the two fields, respectively. We carried out analysis in three X‐ray bands and in two redshift intervals up to z ≤ 1.4. Moreover, we derive the luminosity functions for different optical morphologies and X‐ray types. We confirm strong luminosity evolution in all three bands, finding the most luminous objects at higher redshift. However, no signs of density evolution are found in any tested X‐ray band. We obtain similar results for compact and early‐type objects. Finally, we observe the “Steffen effect”, where X‐ray type‐1 sources are more numerous at higher luminosities in comparison with type‐2 sources. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

GRBs on probation: Testing the UHE CR paradigm with IceCube

Gamma ray burst (GRB) fireballs provide one of very few astrophysical environments where one can contemplate the acceleration of cosmic rays to energies that exceed 10²⁰ eV. The assumption that GRBs are the sources of the observed cosmic rays generates a calculable flux of neutrinos produced when the protons interact with fireball photons. With data taken during construction IceCube has already reached a sensitivity to observe neutrinos produced in temporal coincidence with individual GRBs provided that they are the sources of the observed extra-galactic cosmic rays. We here point out that the GRB origin of cosmic rays is also challenged by the IceCube upper limit on a possible diffuse flux of cosmic neutrinos which should not be exceeded by the flux produced by all GRB over Hubble time. Our alternative approach has the advantage of directly relating the diffuse flux produced by all GRBs to measurements of the cosmic ray flux. It also generates both the neutrino flux produced by the sources and the associated cosmogenic neutrino flux in a synergetic way.     

Astrophysical naturally moderated classical positron beam interaction with nonlinear waves in nonextensive astrophysical plasmas

The positron acoustic shock and solitary wave are explored in nonextensive electron-positron-ion plasma. The plasma system under-consideration, consists of a classical positron beam, q distributed electrons and positively charged bulky ions constitute a neutralizing background. The nonlinear Korteweg-de Vries and Burger equations are derived by employing the standard reductive perturbation method. The positron acoustic wave in linear limit is also discussed for dissipative as well as nondissipative cases of nonextensive plasmas. The plasma parameters such as, the concentration of neutralizing ions background, beam velocity, temperature and q parameter of the nonextensive electrons are noticed to significantly affect the positron acoustic shock and solitary waves. Our findings may be helpful in the understanding of laboratory beam plasma interaction experiments as well as the astrophysical nonextensive plasmas interacting with positron beam.     

Statistics of faint gamma-ray bursts from the GRIF experiment on the Mir orbiting station

During the GRIF experiment onboard the Mir orbiting station, cosmic gamma-ray bursts (GRBs) were observed in the photon energy range 10–300 keV. We developed a technique for selecting events, cosmic GRB candidates, based on output readings from the PX-2 scintillation spectrometer, the main astrophysical instrument. Six events interpreted as cosmic GRBs were identified at a threshold sensitivity level of ≥10^?7 erg cm^?2. The GRIF burst detection rate recalculated to all the sky is ～10³ yr^?1 (fluence ≥10^?7 erg cm^?2). This rate matches the BATSE/CGRO estimate and significantly differs from the value predicted by the S^?3/2 dependence, which holds for a spatially uniform source distribution. The GRB detection rate at low peak fluxes is compared with the results of analysis for BATSE/CGRO “nontriggered” events and with predictions of major cosmological models. We conclude that the PX-2 observational data on faint cosmic GRBs are consistent with predictions of models with the highest frequency of GRB occurrence at z ≥1.5–2.     

Universal characteristics of ion-acoustic wave dynamics in magnetized plasmas with emphasis on Tsallis distribution

Using the extended Poincaré-Lighthill-Kuo (PLK) reductive perturbation method, which incorporates the phase-shift variations, it is shown that common features on propagation and head-on collisions of ion-acoustic waves exist for a magnetized plasmas of different inertial-less particle distributions. For instance it is remarked that, the soliton amplitude is always independent of magnetic field strength while strictly depends on its angle regarding the propagation direction. Both types of solitons (compressive or rarefactive) are shown to exist which are defined through the critical angle γ=π/2 or other critical values depending on plasma fractional parameters. These critical plasma parameter values also define the sign of head-on collision phase shift. Furthermore, it is proved that for a given set of plasma parameters there is always a relative angle of propagation regarding to that of the magnetic-field for which the soliton width is maximum. Current findings apply to a wide range of magnetized plasmas including those containing background dust ingredients or two-temperature inertial-less particles and may be used to study laboratory or astrophysical magnetoplasmas.     

The size of antimatter bodies and the primary very high energy cosmic ray flux

The consequences of antimatter bodies on the very high energy primary cosmic ray flux are considered. The effects of various models of cosmic ray origin and properties of astrophysical parameters are discussed. A simple expression for the production of antiprotons inN–N collisions as a function of energy of the incident proton is obtained by utilizing characteristics of particles produced in high energy collisions. It is assumed that sufficient time will have elapsed for all antibaryons to decay to antiprotons. It is shown that the measurement of antinuclei in the primary cosmic ray spectrum above 10¹⁷ eV could help to establish the size of antimatter bodies.This research was supported by A.F.O.S.R. Grant No. F-44620-69-C-0019.