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W. Baumjohann

Publications and source records attributed to W. Baumjohann.

At least 109 records · Page 6Linked to original sources
arXiv2017

The usefulness of Poynting's theorem in magnetic turbulence

We rewrite Poynting's theorem, already used in a previous publication (Treumann & Baumjohann 2017) to derive relations between the turbulent magnetic and electric power spectral densities, to make explicit where the mechanical contributions enter. We then make explicit use of the relativistic transformation of the turbulent electric fluctuations to obtain expressions which depend only on the magnetic and velocity fluctuations. Any electric fluctuations play just an intermediate role. Equations are constructed for the turbulent conductivity spectrum in Alfvénic and non-Alfvénic turbulence in extension of the results in the above citation. An observation-based discussion of their use in application to solar wind turbulence is given. The inertial range solar wind turbulence exhibits signs of chaos and self-organisation.

physics.space-ph↗
arXiv2017

Electron cyclotron maser instability (ECMI) in strong magnetic guide field reconnection

Reconnection in strong current-aligned magnetic guide fields allows for the excitation of the electron-cyclotron-maser instability and emission of electromagnetic radiationfrom the electron exhaust at the {\sf X} point. The electrons in the guide field remain magnetized, with reconnection barely affected. The guide field is responsible for the asymmetric properties of the {\sf X} point and exhaust. Asymmetry in the electron population results in conditions favorable for ECMI. Fundamental mission beneath the guide field cyclotron is similar to electron hole emission discussed elsewhere. It can be treated in the proper exhaust frame, and maps the local magnetic field when moving together with the exhaust along the guide field. Many applications of this mechanism can be imagined. We propose an outline of the mechanism and discuss some of its advantages and prospects. Among potential applications are AKR in auroral physics, various types of solar radio emissions during flares, planetary emissions and several astrophysical scenarios involving the presence of strong fields and field-aligned currents. Escape of radiation from {\sf X} is no problem. However, observation from remote requires traversing the stop-band of X modes and implies source displacements to weaker fields.

physics.space-ph↗
arXiv2017

Ultrarelativistic generalized Lorentzian thermodynamics and the differential cosmic ray energy flux

We apply the ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution to the energy spectrum of galactic cosmic ray fluxes. The inferred power law slopes contain a component which evolves with cosmic ray energy in steps of thirds, resembling the sequence of structure functions in fully developed Kolmogorov turbulence. Within the generalized thermodynamics the chemical potential can be estimated from the deviation of the fluxes at decreasing energy. Both may throw some light on the cosmic ray acceleration mechanism to very high energies.

astro-ph.HE↗
arXiv2017

Poynting's theorem in magnetic turbulence

Poynting's theorem is used to obtain an expression for the turbulent power-spectral density as function of frequency and wavenumber in low-frequency magnetic turbulence. No reference is made to Elsasser variables as is usually done in magnetohydrodynamic turbulence mixing mechanical and electromagnetic turbulence. We rather stay with an implicit form of the mechanical part of turbulence as suggested by electromagnetic theory in arbitrary media. All of mechanics and flows is included into a turbulent response function which by appropriate observations can be determined from knowledge of the turbulent fluctuation spectra. This approach is not guided by the wish of developing a complete theory of turbulence. It aims on the identification of the response function from observations as input into a theory which afterwards attempts its interpretation. Combination of both the magnetic and electric power spectral densities leads to a representation of the turbulent response function, i.e. the turbulent conductivity spectrum $σ_{ωk}$ as function of frequency $ω$ and wavenumber $k$. {It is given as the ratio of magnetic to electric power spectral densities in frequency space. This knowledge allows for formally writing down a turbulent dispersion relation. Power law inertial range spectra result in a power law turbulent conductivity spectrum. These can be compared with observations in the solar wind. Keywords: MHD turbulence, turbulent dispersion relation, turbulent response function, solar wind turbulence

physics.space-ph↗
arXiv2017

Electron scale structures and magnetic reconnection signatures in the turbulent magnetosheath

Collisionless space plasma turbulence can generate reconnecting thin current sheets as suggested by recent results of numerical magnetohydrodynamic simulations. The MMS mission provides the first serious opportunity to check if small ion-electron-scale reconnection, generated by turbulence, resembles the reconnection events frequently observed in the magnetotail or at the magnetopause. Here we investigate field and particle observations obtained by the MMS fleet in the turbulent terrestrial magnetosheath behind quasi-parallel bow shock geometry. We observe multiple small-scale current sheets during the event and present a detailed look of one of the detected structures. The emergence of thin current sheets can lead to electron scale structures where ions are demagnetized. Within the selected structure we see signatures of ion demagnetization, electron jets, electron heating and agyrotropy suggesting that MMS spacecraft observe reconnection at these scales.

physics.space-ph↗
arXiv2017

Causal Kinetic Equation of Non-equilibrium Plasmas

Statistical plasma theory far from thermal equilibrium is subject to Liouville's equation which is at the base of the BBGKY hierarchical approach to plasma kinetic theory from which in the absence of collisions Vlasov's equation follows. It is also at the base of Klimontovich's approach which includes single particle effects like spontaneous emission. All these theories have been applied to plasmas with admirable success even though they suffer from a fundamental omission in their use of the electrodynamic equations in the description of the highly dynamic interactions in many-particle particle conglomerations. In the following we extend this theory to taking into account that the interaction between particles separated from each other at a distance requires the transport of information. Action needs to be transported and thus in the spirit of the direct-interaction theory as developed by Wheeler and Feynman (1945) requires time. This is done by reference to the retarded potentials. We derive the fundamental Liouville equation for the phase space density of a system composed of a very large number of charged particles. Applying the approach of Klimontovich (1967) we obtain the retarded time evolution equation of the one-particle distribution function in plasmas which replaces Klimontovich's equation in cases when the direct-interaction effects have to be taken into account. This becomes important in all systems where the distance between two points $|Δ\vec{q} | \sim ct$ is comparable to the product of observation time and light velocity, which is typical in cosmic physics and astrophysics.

physics.space-ph↗
arXiv2017

The geomagnetic/magneto-telluric induction problem with spatial conductivity fluctuations

The electromagnetic induction equation (Helmholtz equation) for the electrically conducting Earth is generalised to the inclusion of a spatially fluctuating internal conductivity spectrum that is superimposed on a one-dimensional large-scale conductivity reference-profile which depends solely on the vertical coordinate z>0. This large-scale profile is assumed to be known. The distribution of the fluctuations is allowed to be arbitrary. The conductivity-fluctuation generalised Helmholtz equation depends on the spectral density of the fluctuations as function of the vertical and horizontal coordinates. Application to the inverse geomagnetic/magneto-telluric problem is discussed. We show analytically that the inverse problem yields the conductivity fluctuation spectrum. The relation between the spectral density and the obtained conductivity profile is given.

physics.space-ph↗
arXiv2017

Conductivity spectrum and dispersion relation in solar wind turbulence

Magnetic turbulence in the solar wind is treated from the point of view of electrodynamics. This can be done based on the use of Poynting's theorem attributing all turbulent dynamics to the spectrum of turbulent conductivity. For two directions of propagation of the turbulent fluctuations of the electromagnetic field with respect to the mean plus external magnetic fields an expression is constructed for the spectrum of turbulent dissipation. Use of solar wind observations of electromagnetic power spectral densities in the inertial subrange then allows determination of the conductivity spectrum, the dissipative response function, in this range. It requires observations of the complete electromagnetic spectral energy densities including electric power spectral densities. The dissipative response function and dispersion relation of solar wind inertial range magnetic turbulence are obtained. The dispersion relation indicates the spatial scale decay with increasing frequency providing independent support for the use of Taylor's hypothesis. The dissipation function indicates an approximate shot-noise spectrum of turbulent resistivity in the inertial range suggesting progressive structure formation in the inertial range which hints on the presence of discrete mode turbulence and nonlinear resonances.

physics.space-ph↗
arXiv2016

Inverse scattering problem in turbulent magnetic fluctuations

We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gel$'$fand-Levitan-Marchenko equation of quantum mechanical scattering theory.

physics.space-ph↗
arXiv2016

Generalised partition functions: Inferences on phase space distributions

The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition functions are obtained in straightforward way, from which the conventional Bose and Fermi distributions follow for $κ\to\infty$. For $κ\neq\infty$ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical $κ$-systems imply strong correlations which are absent at zero temperature where appart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable $κ$-distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

cond-mat.stat-mech↗
arXiv2016

Solar wind magnetic turbulence: Inferences from spectral shape

Some differences between theoretical, numerical and observational determinations of spectral slopes of solar wind turbulence are interpreted in the thermodynamical sense. Confirmations of turbulent Kolmogorov slopes in solar wind magnetic turbulence and magnetohydrodynamic simulations exhibit tiny differences. These are used to infer about entropy generation in the turbulent cascade and to infer about the anomalous turbulent collision frequency in the dissipative range as well as the average energy input in solar wind turbulence. Anomalous turbulent collision frequencies are obtained of the order of v < 200 Hz. The corresponding stationary solar wind magnetic energy input into magnetic turbulence in the Kolmogorov inertial range is obtained to be of the order of 50 eV/s. Its thermal fate is discussed.

physics.space-ph↗
arXiv2015

Fractional Mellin Transform -- A possible application in CFT

We propose a fractional variant of Mellin's transform which may find an application in the Conformal Field Theory. Its advantage is the presence of an arbitrary parameter which may substantially simplify calculations and help adjusting convergence.

physics.data-an↗
arXiv2015

Kinetic theory of information -- the dynamics of information

A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $\mathcal{I}_N$ in a Hamiltonian system of large particle number $N\gg 1$ is obtained. It is shown that the $N$-particle information is strictly conserved. Defining reduced particle number information densities in phase space should be possible to obtain a kinetic equation for the ordinary one-particle information $\mathcal{I}_1\equiv \mathcal{I}$ following the Bogoliubov prescription. The kinetic equation for $\mathcal{I}$ is a kind of generalized Boltzmann equation with interaction term depending on the hierarchy of reduced informations. This term in its general form is the most general expression for the Kolmogorov entropy rate of evolution of the information.

cond-mat.stat-mech↗
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↗