Numerical simulation of the plasma double layer

A one-dimensional particle-in-cell computer simulation is used to model the formation of an electrostatic double layer. The conditions for the onset of the layer formation are explored and a relation between the length of the layer and the electrostatic potential difference across is found.     

Multi-model Bayesian assessment of climate change in the northern annular mode

A typical question in climate change analysis is whether a certain observed climate characteristic, like a pronounced anomaly or an interdecadal trend, is an indicator of anthropogenic climate change or still in the range of natural variability. Many climatic features are described by one-dimensional index time series, like for instance the global mean temperature or circulation indices. Here, we present a Bayesian classification approach applied to the time series of the northern annular mode (NAM), which is the leading mode of Northern Hemisphere climate variability. After a pronounced negative phase during the 1950s and 1960s, the observed NAM index reveals a distinct positive trend, which is also simulated by various climate model simulations under enhanced greenhouse conditions. The objective of this study is to decide whether the observed temporal evolution of the NAM may be an indicator of global warming. Given a set of prior probabilities for disturbed and undisturbed climate scenarios, the Bayesian decision theorem decides whether the observed NAM trend is classified in a control climate, a greenhouse-gas plus sulphate aerosol climate or a purely greenhouse-gas induced climate as derived from multi-model ensemble simulations.The three climate scenarios are well separated from each other in terms of the 30-year NAM trends. The multi-model ensembles contain a weak but statistically significant climate change signal in the form of an intensification of the NAM. The Bayesian classification suggests that the greenhouse-gas scenario is the most probable explanation for the observed NAM trend since 1960, even if a high prior probability is assigned to the control climate. However, there are still large uncertainties in this classification result because some periods at the end of the 19th century and during the “warm” 1920s are also classified in an anthropogenic climate, although natural forcings are likely responsible for this early NAM intensification. This demonstrates a basic shortcoming of the Bayesian decision theorem when it is based on one-dimensional index time series like the NAM index.     

Numerical computer simulation of cross-field propagation of a plasma stream in a magnetic field

A one-dimensional electrostatic particle simulation of plasma streaming perpendicular to a magnetic field with nonperiodic boundary condition has been carried out. When a bulk of plasma in injected across an ambient magnetic field, a stream of neutral plasma, consisting of equal numbers of ions and electrons, polarizes, and the resulting polarization electric field gives rise to the penetration of plasma across the magnetic field so that the integrity of plasma maintains. Computer simulation demonstrates the properties of cross-field propagation of plasma stream in a magnetic field with different plasma parameters.     

A universal vertical stellar density distribution law for the Galaxy

This article applies nonstandard analysis to derive jump conditions for one-dimensional, diverging, magnetogasdynamic shock waves emerging on the surface of a star. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions for the flow parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters. It is shown here that the equations modeling a family of magnetogasdynamic shock waves yield products of generalized functions that may be analyzed consistently using nonstandard predistributions.     

A generalized measurement equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry

We derive a generalized van Cittert-Zernike (vC-Z) theorem for radio astronomy that is valid for partially polarized sources over an arbitrarily wide field of view (FoV). The classical vC-Z theorem is the theoretical foundation of radio astronomical interferometry, and its application is the basis of interferometric imaging. Existing generalized vC-Z theorems in radio astronomy assume, however, either paraxiality (narrow FoV) or scalar (unpolarized) sources. Our theorem uses neither of these assumptions, which are seldom fulfiled in practice in radio astronomy, and treats the full electromagnetic field. To handle wide, partially polarized fields, we extend the two-dimensional (2D) electric field (Jones vector) formalism of the standard 'Measurement Equation' (ME) of radio astronomical interferometry to the full three-dimensional (3D) formalism developed in optical coherence theory. The resulting vC-Z theorem enables full-sky imaging in a single telescope pointing, and imaging based not only on standard dual-polarized interferometers (that measure 2D electric fields) but also electric tripoles and electromagnetic vector-sensor interferometers. We show that the standard 2D ME is easily obtained from our formalism in the case of dual-polarized antenna element interferometers. We also exploit an extended 2D ME to determine that dual-polarized interferometers can have polarimetric aberrations at the edges of a wide FoV. Our vC-Z theorem is particularly relevant to proposed, and recently developed, wide FoV interferometers such as Low Frequency Array (LOFAR) and Square Kilometer Array (SKA), for which direction-dependent effects will be important.     

Oscillatory α2-dynamo: numerical investigation

Linear and nonlinear equations describing the generation of a large-scale magnetic field (α²-dynamo) in a thin disc of turbulent conducting fluid are derived and discussed. The numerical procedure is based on a finite-difference implicit scheme for the corresponding nonlinear Cauchy problem with boundary conditions. In addition, the QR-algorithm for the linear eigenvalue problem is realized. It is demonstrated that the α²-dynamo is able to generate oscillatory magnetic fields. The periods of oscillation are typically of the order of or less than the diffusion time. These oscillations are suggested to be due to boundary effects. Dependence of the solutions on the generation efficiency and on the distribution of the mean helicity across the disc are discussed in detail. The period of oscillations only slightly depends on the specific form of distribution of the mean helicity across the disc and is determined mainly by the magnitude of the helicity and by the position of the helicity extremum: the nearer this point to the boundary, the greater the oscillation frequency. Nonlinear effects suppress oscillations when the mean helicity attains its maximum at a depth not more than a quarter of the disc thickness, and promote them otherweise. The one-dimensional system of nonlinear α²-dynamo equations is reduced to a single nonlinear equation of the Schrödinger type.     

Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

Numerical solutions are obtained from analytic dispersion relations for electrostatic waves in a self-consistent, one-dimensional magnetic neutral sheet. The dispersion relations are solved in the real wave number and complex frequency domain. The properties of wave modes will be described, with special emphasis on instability. Several regimes of instability are identified which may generally be divided into two classes. Wave growth is associated firstly with counterstreaming between ions and electrons, giving rise to low frequency waves similar to the usual electrostatic two-stream mode. In addition, high frequency growing waves occur, associated with harmonics of the electron oscillation frequency across the neutral plane.     

The structure of a prominence sheet

A one-dimensional analysis of Kippenhahn-Schlüter type is applied to a sheet of prominence material inclined at an angle, to the horizontal. It is found that the magnetic pressure across the prominence no longer has a symmetric profile, but is stronger on the lower side of the sheet. This excess in magnetic pressure is necessary to balance the component of prominence weight in that direction. A matching function is derived and allows for variations along the length of the sheet, enabling the internal prominence solution to be linked onto a given background potential field. In this way a curved prominence sheet in a potential field may be resolved. A smooth profile for the magnetic field and a continuous variation of plasma pressure across the prominence region is then possible. An example is given in which the analysis is applied to a polar-crown prominence configuration of inverse polarity and the basic properties of the prominence are determined.     

A note on adiabatic solutions of the one-dimensional current sheet problem

It has recently been shown that adiabatic solutions of the one-dimensional current sheet problem exist provided that magnetically trapped particles are included in the model together with the current-carrying untrapped “beam” particles. We show here that a formulation of the problem in terms of particle velocity and pitch angle is advantageous, and we derive some general properties of the solutions. In particular it is shown that there is, in general, no discontinuity in the value of the particle distribution function ? across the boundary in velocity space between “beam” and trapped particles, but that there will be a discontinuity in the gradients of ?. An example is given in which the beam population is of bi-Maxwellian form at the outer boundary of the current sheet.     

The virial theorem for subsystems: application to a globular cluster within a galaxy

A self‐similar evolution of a globular cluster within a galaxy, which implies a one‐component formulation of the virial theorem (Mouri & Taniguchi 2003), is extended to a two‐component formulation (Caimmi & Secco 2003). To this aim, the general case of an embedded sphere within an embedding sphere, both represented as truncated, singular isothermal spheres, is applied to the situation of interest. It is shown that, in the case under consideration, a two‐component formulation of the virial theorem reproduces the analytical results of a one‐component formulation. The process of energy change due to mass loss through the surface is analysed in detail, in connection with both a one‐component and a two‐component formulation of the virial theorem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Two-Dimensional Alfvén-Wave-Driven Solar Wind Model

This paper presents a two-dimensional, Alfvén-wave-driven solar wind model, in which the wave energy is assumed to cascade from the low-frequency Alfvén waves to high-frequency ion cyclotron waves and to be transferred to the solar wind protons by cyclotron resonance at the Kolmogorov rate. A typical structure in the meridional plane consisting of a coronal streamer near the Sun, a fast wind in high latitudes, and a slow wind across the heliospheric current sheet, is found. The fast wind obtained in the polar region is essentially similar to that derived by previous one-dimensional flow-tube models, and its density profile in the vicinity of the Sun roughly matches relevant observations. The proton conditions at 1 AU are also consistent with observations for both the fast and slow winds. The Alfvén waves appear in the fast- and slow-wind regions simultaneously and have comparable amplitudes, which agrees with Helios observations. The acceleration and heating of the solar wind by the Alfvén waves are found to occur mainly in the near-Sun region. It is demonstrated in terms of one-dimensional calculations that the distinct properties of the fast and slow winds are mainly attributed to different geometries of the flow tubes associated with the two sorts of winds. In addition, the 2-D and 1-D simulations give essentially the same results for both the fast and the slow winds.     

A five-wave Harten–Lax–van Leer Riemann solver for relativistic magnetohydrodynamics

We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine–Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten–Lax–van Leer solver or the recently proposed HLLC schemes.     

On the structure of azimuthally small-scale ulf oscillations of a hot space plasma in a curved magnetic field: Modes with discrete spectra

A one-dimensional inhomogeneous cylindrical plasma model with the magnetic field, whose field lines are concentric circles and the equilibrium parameters of the magnetic field and a medium change across magnetic shells, has been considered. In the scope of this model, it has been indicated that Alfvén modes can have discrete spectra. Such modes originate when resonators exist across magnetic shells, which can be implemented in the ring current area or near the outer edge of the plasmapause. The characteristics of the implementation of the modes with discrete spectra have been studied. The results are compared with the satellite observations. It has been concluded that poloidallypolarized pulsations in the Earth’s magnetosphere are largely oscillations with discrete spectra. It has been shown that the proposed model, which does not consider many properties of the magnetosphere, makes it possible to explain the main features in the experimentally observed generation of azimuthal small-scale ULF oscillations in the near-Earth plasma. The results can be used to interpret the satellite and SuperDARN radar measurements.     

Power spectrum distortions in CMB map one-dimensional cross-sections depending on the cosmological model

We examine the effect produced by the variation of parameters of the cosmological model on the power spectrum of one-dimensional cross-sections of the cosmic microwave background maps. We also investigate the possibility of determining these parameters in the analysis of one-dimensional data. The features of the component separation procedure, leading to additional restrictions on the accuracy of reconstruction of the original spectrum are discussed. When the low harmonics remain in the map, the power spectrum of a one-dimensional cross-section is poorly sensitive to the variations of a number of cosmological parameters. Still, the analysis of one-dimensional data could be useful in the search and study of anomalous effects.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

From planes to spheres: about gravitational lens magnifications

We discuss the classic theorem according to which a gravitational lens always produces at least one image with a magnification greater than unity. This theorem seems to contradict the conservation of total flux from a lensed source. The standard solution to this paradox is based on the exact definition of the reference 'unlensed' situation, in which the lens mass can be either removed or smoothly redistributed.
We calculate magnifications and amplifications (in photon number and energy flux density) for general lensing scenarios not limited to regions close to the optical axis. In this way the formalism is naturally extended from tangential planes for the source and lensed images to complete spheres. We derive the lensing potential theory on the sphere and find that the Poisson equation is modified by an additional source term that is related to the mean density and to the Newtonian potential at the positions of observer and source. This new term generally reduces the magnification, to below unity far from the optical axis, and ensures conservation of the total photon number received on a sphere around the source.
This discussion does not affect the validity of the focusing theorem , in which the unlensed situation is defined to have an unchanged affine distance between source and observer. The focusing theorem does not contradict flux conservation, because the mean total magnification (or amplification) directly corresponds to different areas of the source (or observer) sphere in the lensed and unlensed situation. We argue that a constant affine distance does not define an astronomically meaningful reference.
By exchanging source and observer, we confirm that magnification and amplification differ according to Etherington's reciprocity law, so that surface brightness is no longer strictly conserved. At this level we also have to distinguish between different surface brightness definitions that are based on photon number, photon flux and energy flux.     

Calculation of the sun's acoustic impulse response by multi-dimensional spectral factorization

Calculation of time-distance curves in helioseismology can be formulated as a blind-deconvolution (or system identification) problem. A classical solution in one-dimensional space is Kolmogorov's Fourier domain spectral-factorization method. The helical coordinate system maps two-dimensions to one. Likewise a three-dimensional volume is representable as a concatenation of many one-dimensional signals. Thus concatenating a cube of helioseismic data into a very long 1-D signal and applying Kolmogorov's factorization, we find we can construct the three-dimensional causal impulse response of the Sun by deconcatenating the Kolmogorov result. Time-distance curves calculated in this way have the same spatial and temporal bandwidth as the original data, rather than the decreased bandwidth obtained obtained by cross-correlating traces. Additionally, the spectral factorization impulse response is minimum phase, as opposed to the zero phase time-distance curves produced by cross-correlation.     

Element separation effects in the boundary region of a plasma surrounded by neutral gas

A one-dimensional model is being considered where a fully ionized plasma is separated from a neutral gas by a homogeneous magnetic field directed along the plasma boundary. The plasma and the neutral gas consist of two different types of ions and neutral particles. In a stationary state the outflux of plasma by diffusion across the magnetic field is compensated by an influx of neutrals which are ionized in a partially ionized boundary region. It is found that the ratio between the ion densities in the fully ionized region will in general differ from the density ratio of the two types of neutrals being present in the gas region. This provides a separation mechanism with applications both to cosmical and laboratory plasmas, such as in the following cases:

1. The abundance anomalies in magnetic variable stars and in the solar wind.
2. Separation processes of non-identical ions and neutral atoms in gas blanket systems.

     

A high-resolution study of Jupiter at a frequency of 30 GHz

We present the results of our study of Jupiter and its radiation belts with a resolution of 6 arcsec at a frequency of 30 GHz using the RATAN-600 radio telescope and a MARS matrix radiometer with a sensitivity of about 6 mK ^?1/2. We monitored the integrated emission from the Jovian disk with a signal-to-noise ratio of more than 1000 for 30 days and showed its radio emission to be highly stable (≈1%). Based on daily data for the one-dimensional radio brightness distribution over the disk, we mapped the longitudinal radio brightness distribution over 100 rotation periods of Jupiter around its axis. Neither hot nor cold spots with a temperature contrast of more than 1 K were detected; their contribution to the total radio flux from the Jovian disk was no more than 0.2%. The one-dimensional latitudinal (longitude-averaged) distribution obtained on VLA with a similar resolution is shown to be an order of magnitude less uniform than the one-dimensional longitudinal (latitude-averaged) distribution obtained on RATAN-600. We have studied the radiation belts at such high frequencies for the first time and estimated their intensities and variability levels under the effect of external factors. The variable component of the radiation belts was shown to have not exceeded 0.5% of the integrated spectrum of Jupiter over the entire period of its observations. We estimated the contribution of the Galilean satellites (“Galilean noise”) in low-resolution observations; the accuracy of allowing for this noise is determined by the accuracy of estimating the temperatures of the satellites at the observing frequency. The uncertainty in the total flux does not exceed 0.1%.     

Comment on element fractionation in the solar atmosphere driven by ionization-diffusion processes

It is emphasized that one-dimensional, steady-state models of a photoionization layer in which incoming photon fluxes ionize neutral particle fluxes cannot give rise to enhancements or depletions of one element over another. The so-called fractionation mechanism proposed by Marsch, von Steiger, and Bochler (1995) and Peter (1996, 1998) is shown to be a fallacy arising from applying an incorrect boundary condition at an arbitrary point.