arXiv subjects

R. A. Treumann

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

At least 19 recordsLinked to original sources

arXiv2023

Entropic Force in MHD, MHD turbulence, and the Entropy-Kinetic Equation

Following earlier work, reference is made to the classical entropic force which results from spatially variable disorder, an exclusively repulsive force. In terms of macroscopic variables it is applied to magnetohydrodynamics, causing minor changes on the dispersion of magnetohydrodynamic waves. More important is its effect in magnetohydrodynamic turbulence. Here the entropic force affects the ion inertial-range scales on the electron-dominated perpendicular spectrum causing a steeper than Kolmogorov $κ_\perp=-8/3$ spectral slope in agreement with gyro-kinetic simulations. In kinetic theory, inclusion of the ensemble-averaged entropic force weakly modifies the Langmuir wave dispersion. It leads to re-formulation of kinetic theory in terms of Gibbs-Boltzmann-entropy. Liouville's equation in this case becomes an entropy-kinetic equation under Hamiltonian action, with the entropic force-density appearing as an additional force term. This entropy-kinetic equation governs the self-consistent kinetic evolution of the classical entropy including self-modulation.

physics.space-ph↗

arXiv2023

ECMI Resonance in AKR Revisited: Hyperbolic Resonance, Harmonics, Wave-Wave Interaction

Recapitulation of the resonance condition for the fundamental and higher electron cyclotron harmonics in the Electron Cyclotron Maser Instability (ECMI) enables radiation below and confirms the possibility of radiation in a narrow band above harmonics $n>1$. Near $n=1$ resonance on the confined lower X-mode branch, amplification is supported by the decrease of phase and group speeds. Confined slow large-amplitude quasi-electrostatic X-modes nonlinearly modulate the plasma to form cavitons until self-trapped inside them at further increasing wavenumber. They undergo wave-wave interaction, enabling escape to free space in the second harmonic band below $n=2$. At sufficiently large parallel wavenumber (oblique propagation), the fundamental resonance $n=1$ is hyperbolic, a possibility so far missed but vital for an effective ECMI in the upward current region. Here, the resonance hyperbola favourably fits the loss cone boundary, the presumably important ECMI upward-current source-electron distribution, to stimulate ECMI growth at available auroral electron energies.

physics.plasm-ph↗

arXiv2023

Auroral Kilometric Radiation -- the Electron Cyclotron Maser Paradigm

Auroral kilometric radiation (AKR) is the paradigm of intense radio emission from planetary magnetospheres. Being close to the electron gyro frequency and/or its lower harmonics, its observation indicates the non-thermal state of the source plasma. Emission is produced when the plasma enters a state of energetic excitation which results in deformation of the electron distribution function. Under certain conditions this leads to "quasi-coherent" emission. It is believed that the weakly-relativistic electron-cyclotron-maser instability is responsible for this kind of radiation. Since energetically radio radiation normally is not of {primary} importance in the large-scale magnetospheric phenomena, AKR as such has, for the purposes of large-scale magnetospheric physics, become considered a marginal problem. Here this notion is questioned. AKR while applying to the auroral region mainly during magnetospherically disturbed times {carries just a fraction of the total substorm energy. It is, however, of diagnostic power in the physics of the upper auroral ionosphere and Space Weather research}. As a fundamental physical problem of generation of radiation in non-thermal plasmas {it remains not resolved yet. Many questions have been left open even when dealing only with the electron-cyclotron-maser. These can advantageously be studied in the magnetosphere proper both by observation and theory, the only continuously accessible place in space. The most important are listet here with hint on how they should be attacked. Its value is to be sought in the role it should play in application to the other magnetized planets, extra-solar planets, and to strongly magnetized astronomical objects} as an important {tool to diagnose the matter state responsible for radiation in the radio frequency range beyond thermal, shock or synchrotron radiation.

physics.space-ph↗

arXiv2021

Diffuse Josephson Radiation in Turbulence

The possibility of generating diffuse radiation in extended astronomical media by plasma turbulence is investigated under the assumption that the turbulence can be understood as an ensemble of small-scale magnetic filaments (narrow current sheets) forming a texture around a large number of magnetic depletions (voids). On astronomically microscopic scales the dilute high temperature medium (plasma) is to be considered ideally conducting forming a collection of Josephson junctions between two such adjacent quasi-superconductors. The oscillation frequency of those junctions depends on the part of the spectrum that contributes to the oscillation causing weak {radio backgrounds}. Lowest Josephson frequencies/energies near zero may become sources of quasi-stationary magnetic fields.

physics.space-ph↗

arXiv2021

Condensate formation in collisionless plasma

Particle condensates in general magnetic mirror geometries in high temperature plasma may be caused by a discrete resonance with thermal ion-acoustic background noise near mirror points. The resonance breaks the bounce symmetry, temporally locking the particles to the resonant wavelength. The relevant correlation lengths are the Debye length in parallel direction and the ion gyroradius in perpendicular direction.

physics.plasm-ph↗

arXiv2021

Olbert's kappa Fermi and Bose distributions

The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play, dominate the microscopic scale but may have macroscopic consequences.

cond-mat.stat-mech↗

arXiv2021

Increased critical temperature $T_c$ in the ideal anisotropic boson gas

A finite thermal anisotropy, if maintained for times longer than thermal relaxation times, may have a positive effect on the critical temperature in Bose-Einstein condensation of a dilute boson gas not in thermal equilibrium or quasi-particle fermi fluid consisting of spin-compensated electron pairs. It raises the transition temperature while increasing the condensate density.

cond-mat.stat-mech↗

arXiv2021

Mirror mode junctions as sources of radiation

Mirror modes in collisionless high-temperature plasmas represent macroscopic high-temperature quasi-superconductors with bouncing electrons in discrete-particle resonance with thermal ion-sound noise contributing to the ion-mode growth beyond quasilinear stability. In the semi-classical GL approximation the conditions for phase transition are given. The quasi-superconducting state is of second kind causing a magnetically perforated plasma texture. Focussing on the interaction of mirror bubbles we apply semi-classical Josephson conditions and show that a mirror perforated plasma emits weak electromagnetic radiation which in the magnetosheath is in the sub-millimeter respectively infrared range.

physics.plasm-ph↗

arXiv2020

Possible phase transition in plasma mirror modes

Mirror modes in collisionless high-temperature plasmas represent macroscopic high-temperature quasi-superconductors. We explicitly calculate the bouncing electron contribution to the ion-mode growth rate, diamagnetic surface current responsible for the Meissner effect, and the weak attracting electric field. The mean electric field turns out to be negligible. Pairing is a second-order effect of minor importance. The physically important effect is the resonant interaction between bouncing electrons and the thermal ion-sound background. It is responsible for the mirror mode to evolve as a phase transition from normal to quasi-superconducting state.

physics.space-ph↗

arXiv2020

Olbertian partition function in scalar field theory

The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau-Ginzburg action, respectively Hamiltonian. In order do make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau-Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, i.e. once the field equations are written down such that the interactions can be formulated.

physics.class-ph↗

arXiv2020

Topside Reconnection

It is proposed that reconnection would be a main mechanism governing the plasma processes on auroral time scales in the topside ionosphere/high-latitude magnetosphere transition. It occurs in the downward current region between two narrow parallel closely spaced though separated downward current sheets. The field-aligned currents are carried by upward cold upper-ionospheric electrons closing the upward current in an adjacent region. This local process does primarily not affect the ambient field but generates an anomalous diffusivity.

physics.space-ph↗

arXiv2020

Auroral kilometric radiation and electron pairing

We suggest that pairing of bouncing medium-energy electrons in the auroral upward current region close to the mirror points may play a role in driving the electron cyclotron maser instability to generate an escaping narrow band fine structure in the auroral kilometric radiation. We treat this mechanism in the gyrotron approximation, for simplicity using the extreme case of a weakly relativistic Dirac distribution instead the more realistic anisotropic Jüttner distribution. Promising estimates of bandwidth, frequency drift and spatial location are given.

physics.space-ph↗

arXiv2020

Lorentzian Entropies and Olbert's $κ$-distribution

This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $κ$-distributions) which are frequently observed particularly in high temperature plasmas. The general expression of the partition function in such systems is given as well in a form similar to the Boltzmann-Gibbs probability distribution, including a possible exponential high energy truncation. We find the representation of the mean energy as function of probability, and provide the implicit form of Olbert (Lorentzian) entropy as well as its high temperature limit. The relation to phase space density of states is obtained. We then find the entropy as function of probability, an expression which is fundamental to statistical mechanics and here to its Olbertian version. Lorentzian systems through internal collective interactions cause correlations which add to the entropy. Fermi systems do not obey Olbert statistics, while Bose systems might at temperatures sufficiently far from zero.

cond-mat.stat-mech↗

arXiv2019

Seeds for collisionless reconnection

A stationary, two-dimensional, and non-driven antiparallel magnetic field configuration consisting of a central current film, flanked by two non-magnetic domains of electron inertial scale, resembling the Josephson model. Landau-Ginsburg conditions apply at the boundaries to the oppositely directed external magnetic fields, whose sources are located at infinity. On the microscopic level sufficiently large magnetic islands and X points form from exchange of small numbers of elementary magnetic fluxes without reference to any plasma instabilities which on these scales are purely electrostatic. These may serve as seeds to ignite large-scale collisionless reconnection.

physics.space-ph↗

arXiv2019

Electron pairing in mirror modes: Surpassing the quasilinear limit

The mirror mode evolving in collisionless magnetised high-temperature thermally anisotropic plasmas is shown to develop an interesting macro-state. Starting as a classical zero frequency ion fluid instability it saturates quasi-linearly at very low magnetic level, while forming elongated magnetic bubbles which trap the electron component to perform an adiabatic bounce motion along the magnetic field. {Further evolution of the mirror mode towards a stationary state is determined by the bouncing trapped electrons which interact with the thermal level of ion sound waves, generate attractive wake potentials which give rise to formation of electron pairs in the lowest-energy singlet state of two combined electrons. Pairing takes preferentially place near the bounce-mirror points where the pairs become spatially locked with all their energy in the gyration. The resulting large anisotropy of pairs enters the mirror growth rate in the quasi-linearly stable mirror mode. It breaks the quasilinear stability and causes further growth. Pressure balance is either restored by dissipation of the pairs and their anisotropy or inflow of plasma from the environment. In the first case new pairs will continuously form until equilibrium is reached. In the final state the fraction of pairs can be estimated. This process is open to experimental verification. To our knowledge it is the only process where in high temperature plasma pairing may occur and has an important observable macroscopic effect: breaking the quasilinear limit and generation of localised diamagnetism.}

physics.space-ph↗

arXiv2019

A Note on the Entropy Force in Kinetic Theory and Black Holes

The entropy force is the collective effect of inhomogeneity in disorder in a statistical many particle system. We demonstrate its presumable effect on one particular astrophysical object, the black hole. We then derive the kinetic equations of a large system of particles including the entropy force. It adds a collective therefore integral term to the Klimontovich equation for the evolution of the one-particle distribution function. Its integral character transforms the basic one particle kinetic equation into an integro-differential equation already on the elementary level, showing that not only the microscopic forces but the hole system reacts to its evolution of its probability distribution in a holistic way. It also causes a collisionless dissipative term which however is small in the inverse particle number and thus negligible. However it contributes an entropic collisional dissipation term. The latter is defined via the particle correlations but lacks any singularities and thus is large scale. It allows also for the derivation of a kinetic equation for the entropy density in phase space. This turns out to be of same structure as the equation for the phase space density. The entropy density determines itself holistically via the integral entropy force thus providing a self-controlled evolution of entropy in phase space.

cond-mat.stat-mech↗

arXiv2019

On the applicability of Taylor's hypothesis in streaming magnetohydrodynamic turbulence

We examine the range of applicability of Taylor's hypothesis used in observations of magnetic turbulence in the solar wind. We do not refer to turbulence theory. We simply ask whether in a turbulent magnetohydrodynamic flow the observed magnetic frequency spectrum can be interpreted as mapping of the wavenumber turbulence into the stationary spacecraft frame. In addition to the known restrictions on the angle of propagation with respect to the fluctuation spectrum and the question on the wavenumber dependence of the frequency in turbulence which we briefly review, we show that another restriction concerns the inclusion or exclusion of turbulent fluctuations in the velocity field. Taylor's hypothesis in application to magnetic (MHD) turbulence encounters its strongest barriers here. It is applicable to magnetic turbulence only when the turbulent velocity fluctuations can practically be completely neglected against the bulk flow speed. For low flow speeds the transformation becomes rather involved. This account makes even no use of the additional scale dependence of the turbulent frequency, viz. the existence of a "turbulent dispersion relation".

physics.space-ph↗

arXiv2019

On the ion-inertial range density power spectra in solar wind turbulence

A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. De-magnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov-Kraichnan (IK) inertial-range velocity turbulence power spectra via the spectrum of the velocity-turbulence-related random-mean-square induction-electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Kolmogorov inertial range spectra in solar wind velocity turbulence and observations of density power spectra suggest that the occasionally observed scale-limited bumps in the density-power spectrum may be traced back to the electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This approach still neglects contribution of Hall currents and is restricted to the ion-inertial range scale. While both density and magnetic turbulence spectra in the affected range of ion-inertial scales deviate from Kolmogorov or Iroshnikov-Kraichnan, the velocity turbulence preserves its inertial range shape in this process to which spectral advection turns out to be secondary but may become observable under special external conditions. One such case observed by WIND is analysed. We discuss various aspects of this effect including the affected wavenumber scale range, dependence on angle between mean flow velocity and wavenumber and, for a radially expanding solar wind flow when assuming adiabatic expansion at fast solar wind speeds and a Parker dependence of the solar wind magnetic field on radius, also the presumable limitations on the radial location of the turbulent source region.

physics.space-ph↗