Kinetic theory and simulation of electron-strahl scattering in the solar wind

2020 ◽  
Author(s):  
Daniel Verscharen ◽  
Seong-Yeop Jeong ◽  
Benjamin Chandran ◽  
Chadi Salem ◽  
Marc Pulupa ◽  
...  
Keyword(s):  
Solar Wind ◽  
Numerical Solutions ◽  
Mathematical Framework ◽  
Physical Mechanisms ◽  
The Core ◽  
Hot Plasma ◽  
Analytic Expressions ◽  
Core Electrons ◽  
Electron Gyrofrequency ◽  
Theoretical Results

<p>We investigate the scattering of strahl electrons by microinstabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven microinstabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fast-magnetosonic/whistler (FM/W) mode is the best candidate for a microinstability that scatters strahl electrons into the halo. We derive approximate analytic expressions for the FM/W instability threshold in two different β<sub>c </sub>regimes, where β<sub>c</sub> is the ratio of the core electrons' thermal pressure to the magnetic pressure, and confirm the accuracy of these thresholds through comparison with numerical solutions to the hot-plasma dispersion relation. We find that the strahl-driven oblique FM/W instability creates copious FM/W waves under low-β<sub>c</sub> conditions when U<sub>0s</sub>>3w<sub>c</sub>, where U<sub>0s</sub> is the strahl speed and w<sub>c </sub>is the thermal speed of the core electrons. These waves have a frequency of about half the local electron gyrofrequency. We also derive an analytic expression for the oblique FM/W instability for β<sub>c</sub>~1. The comparison of our theoretical results with data from the <em>Wind</em> spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. In addition, we find a good agreement between our theoretical results and numerical solutions to the quasilinear diffusion equation. We make predictions for the electron strahl close to the Sun, which will be tested by measurements from <em>Parker Solar Probe</em> and <em>Solar Orbiter</em>.</p>

scholarly journals Solar Wind Plasma Particles Organized by the Flow Speed

Solar Physics ◽  
2020 ◽  
Vol 295 (11) ◽  
Author(s):  
Viviane Pierrard ◽  
Marian Lazar ◽  
Stepan Štverák
Keyword(s):  
Solar Wind ◽  
Solar Wind Speed ◽  
Solar Wind Plasma ◽  
Flow Speed ◽  
Average Value ◽  
The Core ◽  
Fast Wind ◽  
Core Electrons ◽  
Reduced Mobility ◽  
Bulk Speed

AbstractRecent reports of the first data from Parker Solar Probe (PSP) have pointed to a series of links, correlations or anti-correlations between the solar wind bulk speed ($V_{\mathrm{SW}}$ V SW ) and physical properties of plasma particles from less than 0.25 AU in the corona. In the present paper, we describe corresponding and additional links of solar wind properties, at 0.4 AU and 1.0 AU, in an attempt to complement the PSP data and understand their evolution. A detailed analysis is carried out for the main electron populations, comparing the low-energy (thermal) core and the collisionless suprathermal halo. We show that the anti-correlation observed at 0.4 AU between $V_{\mathrm{SW}}$ V SW and the number density (average value) is maintained also at 1 AU for both the core and halo electrons. On the contrary, only the core electrons manifest a clear anti-correlation of the temperature with $V_{\mathrm{SW}}$ V SW , while the halo temperature does not vary much. We also describe the ions, protons and helium, which have a more reduced mobility and their properties exhibit different variations with the solar wind speed. The results are used to shed more light on the mechanisms leading to a differential acceleration of these species and the origin of slow and fast wind modulation.

scholarly journals Dynamics of nanodust particles emitted from elongated initial orbits

2018 ◽  
Vol 617 ◽  
pp. A43 ◽  
Author(s):  
A. Czechowski ◽  
I. Mann
Keyword(s):  
Solar Wind ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Dust Cloud ◽  
Theoretical Models ◽  
Ecliptic Plane ◽  
Parent Body ◽  
The Sun ◽  
Trapping Region ◽  
Eccentric Orbits

Context. Because of high charge-to-mass ratio, the nanodust dynamics near the Sun is determined by interplay between the gravity and the electromagnetic forces. Depending on the point where it was created, a nanodust particle can either be trapped in a non-Keplerian orbit, or escape away from the Sun, reaching large velocity. The main source of nanodust is collisional fragmentation of larger dust grains, moving in approximately circular orbits inside the circumsolar dust cloud. Nanodust can also be released from cometary bodies, with highly elongated orbits. Aims. We use numerical simulations and theoretical models to study the dynamics of nanodust particles released from the parent bodies moving in elongated orbits around the Sun. We attempt to find out whether these particles can contribute to the trapped nanodust population. Methods. We use two methods: the motion of nanodust is described either by numerical solutions of full equations of motion, or by a two-dimensional (heliocentric distance vs. radial velocity) model based on the guiding-center approximation. Three models of the solar wind are employed, with different velocity profiles. Poynting–Robertson and the ion drag are included. Results. We find that the nanodust emitted from highly eccentric orbits with large aphelium distance, like those of sungrazing comets, is unlikely to be trapped. Some nanodust particles emitted from the inbound branch of such orbits can approach the Sun to within much shorter distances than the perihelium of the parent body. Unless destroyed by sublimation or other processes, these particles ultimately escape away from the Sun. Nanodust from highly eccentric orbits can be trapped if the orbits are contained within the boundary of the trapping region (for orbits close to ecliptic plane, within ~0.16 AU from the Sun). Particles that avoid trapping escape to large distances, gaining velocities comparable to that of the solar wind.

scholarly journals Towards the Search for Thallium Nuclear Schiff Moment in Polyatomic Molecules: Molecular Properties of Thallium Monocyanide (TlCN)

Atoms ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 62 ◽  
Author(s):  
A. Kudrin ◽  
A. Zaitsevskii ◽  
T. Isaev ◽  
D. Maison ◽  
L. Skripnikov
Keyword(s):  
Inner Core ◽  
Molecular Properties ◽  
Basis Set ◽  
Cluster Method ◽  
Coupled Cluster ◽  
The Core ◽  
Complete Basis Set ◽  
Core Electrons ◽  
Complete Basis Set Limit ◽  
Potential Energy Minimum

Molecular properties of the thallium monocyanide (Tl·CN) system in its ground electronic state are studied using high-precision ab initio relativistic two-component pseudopotential replacing 60 inner-core electrons of Tl. A relativistic coupled-cluster method with single, double and perturbative triple amplitudes is employed to account for electronic correlations. Extrapolation of results to the complete basis set limit is used for all studied properties. The global potential energy minimum of Tl·CN corresponds to the linear cyanide (TlCN) isomer, while the non-rigid isocyanide-like (TlNC) structure lies by approximately 11 kJ/mol higher in energy. The procedure of restoration of the wavefunction in the “core” region of Tl atom was applied to calculate the interaction of the Tl nuclear Schiff moment with electrons. The parameter X of the interaction of the Tl nuclear Schiff moment with electrons in the linear TlCN molecule equals 7150 a.u. The prospects of using the TlCN molecule for the experimental detection of the nuclear Schiff moment are discussed.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

Convection in a rotating spherical fluid shell with an inhomogeneous temperature boundary condition at infinite Prandtl number

1993 ◽  
Vol 250 ◽  
pp. 209-232 ◽  
Author(s):  
Keke Zhang ◽  
David Gubbins
Keyword(s):  
Numerical Solutions ◽  
Unstable Mode ◽  
Mode Analysis ◽  
Mathematical Framework ◽  
Fluid Systems ◽  
Critical Wavelength ◽  
Resonance Solution ◽  
Inhomogeneous Temperature ◽  
Spherical Fluid ◽  
The Stability

We examine thermal convection in a rotating spherical shell with a spatially non-uniformly heated outer surface, concentrating on three distinct heating modes: first, with wavelength and symmetry corresponding to the most unstable mode of the uniformly heated problem; secondly, with the critical wavelength but opposite equatorial symmetry; and thirdly, with wavelength much larger than that of the most unstable mode. Analysis is focused on boundary-locked convection, the associated spatial resonance phenomena, the stability properties of the resonance solution, and time-dependent secondary convection. A number of new forms of instability and convection are found: the most interesting is perhaps the saddle-node bifurcation, which is the first to be found for realistic fluid systems governed by partial differential equations. An analogous Landau amplitude equation is also analysed, providing an important mathematical framework for understanding the complicated numerical solutions.

Electron Density Studies of Molecular Crystals

1997 ◽  
Author(s):  
Philip Coppens
Keyword(s):  
Charge Density ◽  
Electron Scattering ◽  
Experimental Studies ◽  
Molecular Crystals ◽  
Chemical Environment ◽  
Light Atom ◽  
Core Electron ◽  
The Core ◽  
Core Electrons ◽  
Electron Donor And Acceptor

Small molecules consisting of light-, few-electron atoms were the first species beyond atoms to yield to quantum-mechanical methods. Similarly, crystals of small light-atom molecules have served as most useful test cases of charge density mapping. The small number of core electrons in first-row atoms enhances the relative contribution of valence electron scattering to the diffraction pattern. Early studies, done just after automated diffractometers became widely available, were concerned with molecular crystals such as uracil (Stewart and Jensen 1967), s-triazine (Coppens 1967), oxalic acid dihydrate (Coppens et al. 1969), decaborane (Dietrich and Scheringer 1978), fumaramic acid (Hirshfeld 1971), glycine (Almlof et al. 1973), and tetraphenylbutatriene (Berkovitch-Yellin and Leiserowitz 1976). While thermal motion is often pronounced in molecular crystals, advances in low-temperature data collection have done much to alleviate this disadvantage. In recent years, subliquid-nitrogen cooling techniques have been increasingly applied. Among the most interesting aspects of molecular crystals are the influence of intermolecular interactions on the electronic structure. Physically meaningful Coulombic parameters pertinent to a molecule in a condensed environment can be obtained from the diffraction analysis, and can be used in the modeling of macromolecules. The enhancement of the electrostatic moments relative to those of the isolated species has been noted in chapter 7. But, beyond these considerations, molecular crystals are important in their own right. For example, crystals of aromatic molecules substituted with π-electron donor and acceptor groups are among the most strongly nonlinear optical solids known, considerably exceeding the nonlinearity of inorganic crystals such as potassium titanyl phosphate (KTP); while mixed-valence organic components of low-dimensional solids can become superconducting at low temperatures. The relation between such properties of molecular crystals and their charge distribution provides a continuing impetus for further study. The suitability of light-atom crystals for charge density analysis can be understood in terms of the relative importance of core electron scattering. As the perturbation of the core electrons by the chemical environment is beyond the reach of practically all experimental studies, the frozen-core approximation is routinely used. It assumes the intensity of the core electron scattering to be invariable, while the valence scattering is affected by the chemical environment, as discussed in chapter 3.

scholarly journals Multifractal analysis of low-latitude geomagnetic fluctuations

2009 ◽  
Vol 27 (2) ◽  
pp. 569-576 ◽  
Author(s):  
M. J. A. Bolzan ◽  
R. R. Rosa ◽  
Y. Sahai
Keyword(s):  
Solar Wind ◽  
High Latitude ◽  
Geomagnetic Field ◽  
Large Deviation ◽  
Multifractal Spectrum ◽  
Low Latitude ◽  
Physical Mechanisms ◽  
Wavelet Transform Modulus Maxima ◽  
Variability Pattern ◽  
Modulus Maxima

Abstract. The technique of large deviation multifractal spectrum has shown that the high-latitude (77.5° N, 69.2° W) geomagnetic fluctuations can be described from direct dissipation process or loading-unloading regimes of the solar wind-magnetosphere coupling. In this paper, we analyze the H-component of low-latitude (22.4° S, 43.6° W) geomagnetic field variability observed during the month of July 2000 at the Geomagnetic Observatory, Vassouras, RJ, Brazil. The variability pattern during this period is a mixture of quiet and disturbed days including the Bastille Day intense geomagnetic storm on 15 July. Due to the complexity of this data, we pursue a detailed analysis of the geomagnetic fluctuations in different time scales including a multifractal approach using the singular power spectrum deviations obtained from the wavelet transform modulus maxima (WTMM). The results suggest, as observed from high-latitude data, the occurrence of low-latitude multifractal processes driving the intermittent coupling between the solar wind-magnetosphere and geomagnetic field variations. On finer scales possible physical mechanisms in the context of nonlinear magnetosphere response are discussed.

Calculation of the Knight Shift in Palladium

1979 ◽  
Vol 34 (4) ◽  
pp. 523-524 ◽  
Author(s):  
R. Krieger ◽  
J. Voitländer
Keyword(s):  
Fermi Surface ◽  
Knight Shift ◽  
Enhancement Factor ◽  
Negative Contribution ◽  
Core Polarization ◽  
Conduction Electrons ◽  
The Core ◽  
Core Electrons ◽  
Palladium Metal ◽  
Good Agreement

The direct and core-polarization contributions to the Knight shift in palladium metal have been calculated taking an enhancement factor of 10 for d- and 1.28 for s-electrons. We found a large negative contribution of - 3.88% for the core electrons and a comparatively small direct contribution of 0.18% for s-electrons on the Fermi surface. Together with an estimated contribution of 0.36% for conduction electrons in s-orbitals, but not on the Fermi surface, the calculated total amount of - 3.34% is in good agreement with the experimental value of - 4% obtained by the Jaccarino plot for palladium at 0 K

Interactions of cell volume, membrane potential, and membrane transport parameters

1980 ◽  
Vol 238 (5) ◽  
pp. C196-C206 ◽  
Author(s):  
E. Jakobsson
Keyword(s):  
Membrane Potential ◽  
Cell Volume ◽  
Membrane Transport ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Time Varying ◽  
Transport Parameters ◽  
Animal Cells ◽  
Analytic Expressions ◽  
Solute Species

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

Structural Confinement and Safety Design of a Fast Reactor Core

1981 ◽  
Vol 103 (2) ◽  
pp. 289-294
Author(s):  
F. D. Ju ◽  
J. G. Bennett
Keyword(s):  
Fast Reactor ◽  
Lateral Pressure ◽  
Numerical Solutions ◽  
Homogeneous Medium ◽  
Safety Margin ◽  
Reactor Core ◽  
Gas Pressure ◽  
Equivalent Stiffness ◽  
Friction Forces ◽  
The Core

In certain fast-reactor designs, the core is an assemblage of a large number of containers of long, hexagonal, hollow cylinders mounted vertically. These so-called “hex-cans” sit individually on coolant nozzles held down by their own weight, and are held as a group laterally at two levels by two constraint rings. At operating temperature, the rings bear on the hex-can assembly because of differences in thermal expansion. The compression of the rings on the hex-can assembly serves to prevent lifting of the can individually or in groups because of any accidental buildup of gas pressure. In the analysis, it is observed that the large number of hexcans and the distribution of the temperature field are such that the cross section of the reactor core can be treated as in a locally uniform dilatational field. An approximate equation was developed relating the plane deformation of a hollow hex cylinder to the global lateral pressure. The parameters are the material constitution and the thickness index (the ratio of the interior and the exterior cross-flat dimensions). The effective range of the equation covers the thickness ratio from zero to the stability limit when the wall becomes too thin resulting in buckling under the lateral pressure. The design equation is exact for zero thickness index. For hollow hex cylinders, numerical solutions were also obtained by the finite element method as a comparison. For a thickness index of 0.9 to 0.95, the difference is less than 0.1 percent. The cylinder constitutive equation is then used to determine an equivalent stiffness for a solid hex cylinder that is to have the same deformation as the given hex-can. The entire planar core region is then analyzed as a homogeneous medium of the equivalent stiffness. The method was applied to the core confinement design for a fast reactor. The thermoelastic solution was then applied to a relatively simpler configuration than the actual case to give a measure of the lateral pressure. The available friction forces for various lift configurations were then obtained. The gas pressure necessary to overcome the minimum friction force thus resulted. In addition, using the lateral pressure, the safety margin of the wall thickness of the hex-can for stability failures was determined.

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