arXiv subjects

R. A. Treumann

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

At least 55 records · Page 3Linked to original sources

arXiv2014

Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example

We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. Details can be found in arXiv:1406.6639

cond-mat.stat-mech↗

arXiv2014

"Gibbsian" Approach to Statistical Mechanics yielding Power Law Distributions

Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is derived and the physical temperature identified. Consistent expressions for the canonical partition function are given. In a first application, the corresponding Boltzmann, Fermi and Bose-Einstein distributions are obtained. It is shown that the latter lose their typical quantum properties, i.e. the degenerate Fermi state and Bose-Einstein condensation. These distributions apply only to states at finite temperature with correlations. As a by-product these results \emph{exclude any negative absolute temperatures} also in the Boltzmann limit.

cond-mat.stat-mech↗

arXiv2014

Superdiffusion revisited in view of collisionless reconnection

The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting orbits and break-out into ballistic motion lying at the bottom, for instance, of Lévy flights and the celebrated $κ$-distribution. A stringent derivation yields an anomalous diffusion coefficient increasing with time, thus describing superdiffusion. Contrary to wide belief, superdiffusion, though faster than classical, is a weak process. Absolute values of the coefficient are small due to the largeness of the anomalous collision frequency in waiting statistics compared with the infinitesimally small binary collision frequency. We provide parallel and perpendicular diffusion coefficients, determine the exponents of temporal increase, determine the power and $κ$ for two-dimensional diffusion by referring to published numerical particle-in-cell simulations, fix the range of permitted $κ$s, and construct a relation between the diffusion coefficients and the resistive scale. We furthermore find an expression for the anomalous collision frequency from the electron pseudo-viscosity in reconnection thus identifying reconnection as a localized diffusion process in satisfactory agreement with basic physical concepts.

physics.space-ph↗

arXiv2014

Fractional Laplace Transforms - A Perspective

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equations or problems in non-extensive statistical mechanics.

physics.data-an↗

arXiv2014

Plasma wave mediated electron pairing effects

Pairing of particles, in particular electrons, in high temperature plasma is generally not expected to occur. Here we investigate, based on earlier work, the possibility for electron pairing mediated in the presence of various kinds of plasma waves. We confirm the possibility for pairing in ion- and electron-acoustic waves, pointing out the importance of the former and the expected consequences. While electron-acoustic waves probably do not play any role, ion-acoustic waves may cause formation of heavy electron compounds. Lower hybrid waves also mediate pairing but under different conditions. Buneman modes which evolve from strong currents may cause pairing among trapped electrons constituting a heavy electron component that populates electron holes. All pairing processes are found to generate cold pair populations. They provide a mechanism of electron cooling which can be interpreted as kind of classical condensation, in some cases possibly accompanied by formation of current filaments, weak soft-X-ray emission and superfluidity which might affect reconnection physics.

physics.space-ph↗

arXiv2014

Collisionless Magnetic Reconnection in Space Plasmas

Magnetic reconnection requires the violation of the frozen-in condition which ties gyrating charged particles to the magnetic field inhibiting diffusion. Ongoing reconnection has been identified in near-Earth space as being responsible for the excitation of substorms, magnetic storms, generation of field aligned currents and their consequences, the wealth of auroral phenomena. Its theoretical understanding is now on the verge of being completed. Reconnection takes place in thin current sheets. Analytical concepts proceeded gradually down to the microscopic scale, the scale of the electron skin depth or inertial length, recognizing that current layers that thin do preferentially undergo spontaneous reconnection. Thick current layers start reconnecting when being forced by plasma inflow to thin. For almost half a century the physical mechanism of reconnection has remained a mystery. Spacecraft in situ observations in combination with sophisticated numerical simulations in two and three dimensions recently clarified the mist, finding that reconnection produces a specific structure of the current layer inside the electron inertial (also called electron diffusion) region around the reconnection site, the X line. Onset of reconnection is attributed to pseudo-viscous contributions of the electron pressure tensor aided by electron inertia and drag, creating a complicated structured electron current sheet, electric fields, and an electron exhaust extended along the current layer. We review the general background theory and recent developments in numerical simulation on collisionless reconnection. It is impossible to cover the entire field of reconnection in a short space-limited review. The presentation necessarily remains cursory, determined by our taste, preferences, and knowledge. Only a small amount of observations is included in order to support the few selected numerical simulations.

physics.space-ph↗

arXiv2014

Weibel, Firehose and Mirror mode Relations

Excitation of Weibel magnetic fields in an initially non-magnetized though anisotropic plasma may trigger other low-frequency instabilities fed by pressure anisotropy. It is shown that under Weibel-like-stable conditions the Weibel-like thermal fluctuation magnetic field allows for restricted Firehose-mode growth. In addition, low frequency Whistlers can also propagate in the plasma under certain anisotropic conditions. When the Weibel-like mode becomes unstable, Firehose instability ceases but Mirror modes take over. This will cause bubble structures in the Weibel-like field in addition to filamentation.

physics.space-ph↗

arXiv2013

QM theory of the thermal electron gyroradius

The average (thermal) gyroradius of charged particles is re-examined from a quantum-mechanical point of view. The straight quantum-mechanical calculation clearly reproduces its conventionally used random-mean-square (rms) expectation value. The quasi-classical approach reproduces its mean expectation value as well thus confirming the purely classical calculation. It shows that the fluctuations in the gyroradius amount to 21.5% of its rms value. This fluctuation is, however, within the usual $\sqrt{2}$-"freedom" range of choice in the definition of the rms gyroradius respectively the mean thermal speed on which the rms value is based, its correct (nonrelativistic) value $v_t^2= 2T_\perp/m_e$ and its simplified version $v_t^2=T_\perp/m_e$.

physics.plasm-ph↗

arXiv2013

A note on the structure and kinematics of Harris current sheets

The flat Harris current sheet model has become a powerful initial equilibrium in theory and simulation of magnetic reconnection in the magnetotail, at the magnetopause and also in multiple current sheet models of the heliosheath and astrophysics, where it is believed that such structures may become responsible for generation of turbulence and also high energy particles. Here we investigate the philosophy behind the Harris sheet in view of the physical conditions. The kinematic treatment in this note takes care of the different dynamics of ions and electrons.

physics.space-ph↗

arXiv2013

Incomplete-exclusion Statistical Mechanics in Non-collisional Violent Relaxation of Celestial Objects

Violent relaxation has been proposed half a century ago to bear responsibility for non-collisional dynamics and formation of gravitationally bound systems of extended celestial objects (agglomeration of stars, galaxies, clusters of galaxies) when reaching an approximate equilibrium state which can be described thermodynamically. The Lynden-Bell equilibrium distribution of such systems, resulting from a spatial exclusion principle, had been shown to be an analog to the Fermi distribution of states in solid state physics. Real extended objects like galaxies do not completely exclude each other, however. Permitting for partial exclusion leads to a modification of the equilibrium distribution. Here we show that this case can be treated in analogy to a hypothetical incomplete population of Fermi states. An incomplete-exclusion equilibrium distribution is obtained which enters the violent relaxation theory.

astro-ph.GA↗

arXiv2013

Fermi Statistics of Partially Populated States

Fermi statistics is formally extended to the case when energy levels are allowed to be partially occupied, which the Pauli principle does not categorically exclude. The partial Fermi distribution obtained depends on the partial occupation of states but otherwise has similar properties as the (integer) Fermi distribution. In the zero temperature limit both are identical.

cond-mat.stat-mech↗

arXiv2013

Electrons in Magnetic Mirror Geometry

Landau's theory of electron motion in stationary magnetic fields is extended to the inclusion of bouncing along the field between mirror points in an inhomogeneous field. The problem can be treated perturbation theoretically. As expected, bouncing is quantized, causes a weak shift in Landau levels, reduces parallel degeneracy, but does not contribute to diamagnetism.

quant-ph↗

arXiv2012

Downward transport of electromagnetic radiation by electron holes?

An attractive mechanism for radiation transport by electron holes from the magnetospheric auroral cavity source region down to the ionosphere and possibly even down to the atmosphere is examined. Because of the excitation and propagation properties of the X mode, this mechanism turns out to be highly improbable for the usual resonant excitation of radiation of frequency just below the local electron cyclotron frequency, $ω\lesssim ω_{ce}$. It could work only, if the auroral ionosphere would be locally perforated being of sufficiently low density for allowing electron holes riding down to low altitudes on the auroral electron beam. If resonant excitation of higher electron cyclotron harmonics, $ω\sim \ell ω_{ce}, ~\ell= 2,3,...$, becomes possible, a still unexplored mechanism, then radiation excited inside the hole could be transported to lower altitudes than generated. If this happens, radiation would provide another mechanism of coupling between the magnetospheric plasma and the atmosphere. Keywords: Electron cyclotron maser, electron holes, auroral acceleration, auroral radiation fine structure, auroral kilometric radiation, Jupiter radio emission, Planetary radio emission

physics.space-ph↗

arXiv2012

Collisionless reconnection: The sub-microscale mechanism of magnetic field line interaction

Magnetic field lines are quantum objects carrying one quantum $Φ_0=2π\hbar/e$ of magnetic flux and have finite radius $λ_m$. Here we argue that they possess a very specific dynamical interaction. Parallel field lines reject each other. When confined to a certain area they form two-dimensional lattices of hexagonal structure. We estimate the filling factor of such an area. Antiparallel field lines, on the other hand, attract each other. We identify the physical mechanism as being due to the action of the gauge potential field which we determine quantum mechanically for two parallel and two antiparallel field lines. The distortion of the quantum electrodynamic vacuum causes a cloud of virtual pairs. We calculate the virtual pair production rate from quantum electrodynamics and estimate the virtual pair cloud density, pair current and Lorentz force density acting on the field lines via the pair cloud. These properties of field line dynamics become important in collisionless reconnection, consistently explaining why and how reconnection can spontaneously set on in the field-free centre of a current sheet below the electron-inertial scale.

astro-ph.HE↗

arXiv2012

A note on the Weibel instability and thermal fluctuations

The thermal fluctuation level of the Weibel instability is recalculated. It is shown that the divergence of the fluctuations at long wavelengths, i.e. the Weibel infrared catastrophe, never occurs. At large wavelengths the thermal fluctuation level is terminated by the presence of even the smallest available stable thermal anisotropy. Weibel fields penetrate only one skin depth into the plasma. When excited inside, they cause layers of antiparallel fields of skin depth width and vortices which may be subject to reconnection.

astro-ph.CO↗

arXiv2012

Magnetic field amplification in electron phase-space holes and related effects

Three-dimensional electron phase space holes are shown to be positive charges on the plasma background which produce a radial electric field and force the trapped electron component into an azimuthal drift. In this way electron holes generate magnetic fields in the hole. We solve the cylindrical hole model exactly for the hole charge, electric potential and magnetic field. In electron holes, the magnetic field is amplified on the flux tube of the hole; equivalently, in ion holes the field would be decreased. The flux tube adjacent to the electron hole is magnetically depleted by the external hole dipole field. This causes magnetic filamentation. It is also shown that holes are massive objects, each carrying a finite magnetic moment. Binary magnetic dipole interaction of these moments will cause alignment of the holes into chains along the magnetic field or, in the three-dimensional case, produce a magnetic fabric in the volume of hole formation. Since holes, in addition to being carriers of charges and magnetic moments, also have finite masses, they behave like quasi-particles, performing ExB, magnetic field, and diamagnetic drifts. In an inhomogeneous magnetic field, their magnetic moments experience torque which causes nutation of the hole around the direction of the magnetic field presumably giving rise to low frequency magnetic modulations like pulsations. A gas of many such holes may allow for a kinetic description in which holes undergo binary dipole interactions. This resembles the polymeric behaviour. Both magnetic field generation and magnetic structure formation is of interest in auroral, solar coronal and shock physics, in particular in the problem of magnetic field filamentation in relativistic foreshocks and cosmic ray acceleration.

physics.space-ph↗

arXiv2012

Magnetopause displacements: The possible role of dust

Large compressions of the magnetopause are proposed to occasionally result from temporary encounters of the magnetosphere with dust streams in interplanetary space. Such streams may have their origin in cometary dust tails or asteroids which cross the inner heliosphere or in meteoroids in Earth's vicinity. Dust ejected from such objects when embedding the magnetosphere for their limited transition time should cause substantial global deformations of the magnetopause/magnetosphere due to the very large dust grain mass and momentum which compensates for the low dust density when contributing to the upstream pressure variation.

physics.space-ph↗

arXiv2011

Electron-cylotron maser radiation from electron holes: Downward current region

The electron-cyclotron maser emission from electron holes is applied to holes generated in the downstream current region of the aurora. We suggest that part of the fine structure observed in the auroral kilometric radiation is generated by the electron-cyclotron maser mechanism in the downstream current region. The argument goes that the main background auroral kilometric radiation source is still located in the partial electron ring (horseshoe) distribution of the upward current region while the fine structure is caused by electron holes generated predominantly in the downward current region. Since both regions always exist simultaneously they are acting in tandem in generating auroral kilometric radiation by the same mechanism though in different ways.

physics.space-ph↗