arXiv subjects

R. A. Treumann

Publications and source records attributed to R. A. Treumann.

85 records · Page 5Linked to original sources

arXiv2008

Fundamentals of Non-relativistic Collisionless Shock Physics: IV. Quasi-Parallel Supercritical Shocks

1. Introduction, 2. The (quasi-parallel) foreshock; Ion foreshock, Ion foreshock boundary region; Diffuse ions;Low-frequency upstream waves; Ion beam waves; The expected wave modes; Observations; Diffuse ion waves; Electron foreshock; Electron beams; Langmuir waves; stability of the electron beam; Electron foreshock boundary waves; Nature of electron foreshock waves; Radiation; Observations; Interpretation; 3. Quasi-parallel shock reformation; Low-Mach number quasi-parallel shocks; Turbulent reformation; Observations; Simulations of quasi-parallel shock reformation; Hybrid simulations in 1D; Hybrid simulations in 2D; Full particle PIC simulations; Conclusions; 4. Hot flow anomalies; Observations; Models and simulations; Solitary shock; 5. Downstream region; 6. Summary and conclusions.

astro-ph↗

arXiv2008

Fundamentals of Non-relativistic Collisionless Shock Physics: I. The Shock Problem

The problem of collisionless shocks is posed as the problem of understanding how in a completely collisionless streaming high-temperature plasma shocks can develop at all, forming discontinuous transition layers of thickness much less than any collisional mean free path length. The history of shock research is briefly reviewed. It is expressed that collisionless shocks as a realistic possibility of a state of matter have been realized not earlier than roughly half a centruy ago. The basic properties of collisionless shocks are noted in preparing the theory of collisionless shocks and a classification of shocks is given in terms of their physical properties, which is developed in the following chapters. The structure of this chapter is as follows: 1. A cursory historical overview, describing the early history, gasdynamic shocks, the realisation of the existence of collisionless shocks and their investigation over three decades in theory and observation until the numerical simulation age, 2. Posing the shock problem as the question: When are shocks? 3. Types of collisionless shocks, describing electrostatic shocks, magnetized shocks, MHD shocks, shock evolutionarity and coplanarity, switch-on and switch-off shocks, 4. Criticality, describing the transition from subcritical dissipative to supercritical viscose shocks, 5. Remarks.

astro-ph↗

arXiv2008

Fundamentals of Non-relativistic Collisionless Shock Physics: II. Basic Equations and Models

This paper develops the basic sets of equations which lead to the conservation laws describing collisionless plasma shock waves. We discuss the evolution of shock waves by wave steepening, derive the Rankine-Hugoniot conditions for magnetogasdynamic shocks, discuss various analytical models of shock formation, and discuss the basic instabilities which may become important in collisionless shock physics. We then present a survey of the theory of anomalous resistivity in the quasilinear limit and beyond and discuss mechanisms of shock particle reflection as far as they have been investigated in the published literature. The content of the chapter is the following: 1. Wave steepening, describing simple waves and steepening due to nonlinearity, balnced by dissipation in Burgers' shocks, by dispersive effects in the Korteweg-de Vries equation, the Sagdeev-Potential method, 2. Basic equations, presenting kinetic theory and the transition to moment equations in the fluid description, 3. Rankine-Hugoniot relations, giving the jump conditions across shocks, explicit MHD solution for perpendicular shocks and parallel shocks, and high Mach number conditions, 4. Waves and instabilities, giving the general dispersion relation, describing low-$β$-shocks, whistler and Alfvén shocks, the various shock-relevant instabilities, 5. Anomalous transport for the various electrostatic wave-particle interactions, general description of anomalous resistivity, shock particle reflection from potential and specularly, hole formation, 6. Briefing on numerical simulation techniques, giving a short idea on this important field and its methods.

astro-ph↗

arXiv2008

Fundamentals of Non-relativistic Collisionless Shock Physics: III. Quasi-Perpendicular Supercritical Shocks

The theory and simulations of quasi-perpendicular and strictly perpendicular collisionless shocks are reviewed. The text is structured into the following sections and subsections: 1. Setting the frame, where the quasi-perpendicular shock problem is formulated, reflected particle dynamics is described in theoretical terms, foot formation and foot ion acceleration discussed, and the shock potential explained. 2. Shock structure, 3. Ion dynamics, describing its role in shock reformation and the various ion-excited instabilities. 4. Electron dynamics, describing electron instabilities in the foot; 5. The problem of stationarity, posing the theoretical reasons for shocks being non-stationary, discussing nonlinear whistler mediated variability, two-stream and modified two-stream variability, formation of ripples in two-dimensions, 6. Summary and conclusions: The possibility of shock breaking.

astro-ph↗

arXiv2008

Physics of Atmospheric Electric Discharges in Gases: An Informal Introduction

A short account of the physics of electrical discharges in gases is given in view of its historical evolution and application to planetary atmospheres. As such it serves as an introduction to the articles on particular aspects of electric discharges contained in this book, in particular in the chapters on lightning and the violent discharges which in the recent two decades have been observed to take place in Earth's upper atmosphere. In addition of briefly reviewing the early history of gas discharge physics we discuss the main parameters affecting violent atmospheric discharges like collision frequency, mean free path and critical electric field strength. Any discharge current in the atmosphere is clearly carried only by electrons. Above the lower bound of the mesosphere the electrons must be considered magnetized with the conductivity becoming a tensor. Moreover, the collisional mean free path in the upper atmosphere becomes relatively large which lowers the critical electric field there and more easily enables discharges than at lower altitudes. Finally we briefly mention the relation of such discharges as sources for wave emission.

physics.space-ph↗

arXiv2008

Gibbsian theory of power law distributions

It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence. Gibbsian theory is extended on the fundamental level to statistically dependent subsystems introducing an `ordering parameter' $κ$. Particular forms for the entropy and partition functions are derived with super-additive (non-extensive) entropy, and a redefinition of temperature in such systems is given.

physics.plasm-ph↗

arXiv2005

Kinetic description of avalanching systems

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.

cond-mat.stat-mech↗

arXiv2000

Average observed properties of the Earth's quasi-perpendicular and quasi-parallel bow shock

We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of plasma and magnetic field parameters as well as of low frequency magnetic power spectra some minutes upstream and downstream of the bow shock by dividing the events into categories depending on the angle between bow shock normal and interplanetary magnetic field and on the plasma-beta, i.e., the ratio of plasma to magnetic pressure. Downstream of the quasi-perpendicular low-beta (beta < 0.5) bow shock we find a dominance of the left-hand polarized component at frequencies just below the ion cyclotron frequency with amplitudes of about 3 nT. These waves are identified as ion cyclotron waves which grow in a low-beta regime due to the proton temperature anisotropy. We find a strong correlation of this anisotropy with the intensity of the left-hand polarized component. Downstream of some nearly perpendicular high-beta (beta > 1.0) crossings mirror waves are identified. However, there are also cases where the conditions for mirror modes are met downstream of the nearly perpendicular shock, but no mirror waves are observed.

physics.space-ph↗

arXiv1999

On the Path Integral of the Relativistic Electron

We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is performed by means of a particular simple method different from both the combinatorial approach envisaged by Feynman and its Ising model correspondence.

quant-ph↗

arXiv1998

Generalised-Lorentzian Thermodynamics

We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All thermodynamic functions, including the definition of the temperature, are shown to be meaningful. The thermodynamic potential from which all relevant physical information in equilibrium can be extracted, is defined consistently. The most important findings are the following two: (1) The temperature is defined exactly in the same way as in classical statistical mechanics as the derivative of the energy with respect to the entropy at constant volume. (2) Observables are defined in the same way as in Boltzmannian statistics as the linear averages of the new equilibrium distribution function. This lets us conclude that the new state is a real thermodynamic equilibrium in systems capable of strong turbulence with the new distribution function replacing the Boltzmann distribution in such systems. We discuss the ideal gas, find the equation of state, and derive the specific heat and adiabatic exponent for such a gas. We also derive the new Gibbsian distribution of states. Finally we discuss the physical reasons for the development of such states and the observable properties of the new distribution function.

physics.space-ph↗

arXiv1998

Kinetic theoretical foundation of Lorentzian statistical mechanics

A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the so-called $κ$ distribution frequently found in collisionless turbulent systems like space plasmas. We show that this distribution function satisfies a generalised $H$-theorem, yields an expression for the entropy that is concave. Thus, the distribution is a `true' thermodynamic equilibrium distribution, presumably valid for turbulent systems. In equilibrium it is possible to construct the fundamental thermodynamic quantities. This is done for an ideal gas only. The new kinetic equation can form the basis for obtaining a set of hydrodynamic conservation laws and construction of a generalised transport theory for strongly correlated states of a system.

physics.plasm-ph↗

arXiv1997

A Note on the Statistical Mechanics of Violent Relaxation of Phase Space Elements of Different Densities

The statistical mechanical investigation of Violent Relaxation of phase space elements of different densities first derived by Lynden-Bell (1967) is re-examined. It is found that the mass independence of the equations of motion of Violent Relaxation calls for a constraint on the volume of the phase space elements used to formulate the statistical mechanical description of Violent Relaxation. In agreement with observations of astrophysical objects believed to have been subject to Violent Relaxation (e.g. clusters of galaxies), the coarse grained phase space distribution $\bar{f}$ of the final state in the non-degenerate limit turns into a superposition of Maxwellians of a common velocity dispersion. Thus, the velocity dispersion problem present in the investigation of Lynden-Bell (1967) is removed.

astro-ph↗

arXiv1996

Violent Relaxation of Indistinguishable Objects and Neutrino Hot Dark Matter in Clusters of Galaxies

The statistical mechanical investigation of violent relaxation (Lynden-Bell 1967) is extended to indistinguishable objects. It is found that, coincidentally, the equilibrium distribution is the same as that obtained for classical objects. For massive neutrinos, the Tremaine \& Gunn (1979) phase space bound is revisited and reinterpretated as the limit indicating the onset of degeneracy related to the coarse-grained phase space distribution. In the context of one of the currently most popular cosmological models, the Cold and Hot Dark Matter (CHDM) model (Primack et al. 1995), the onset of degeneracy may be of importance in the core region of clusters of galaxies. Degeneracy allows the neutrino HDM density to exceed the limit imposed by the Tremaine \& Gunn (1979) bound while accounting for the phase space bound.

astro-ph↗