Vlasov Theory Research Articles

Non-classical plasma sheaths: space-charge-limited and inverse regimes under strong emission from surfaces

The collisionless plasma sheath represents an important example of Vlasov theory application. In this study, Particle-in-Cell/Monte Carlo Collision methodology has been used to study different examples of plasma sheaths under strong negative charge emission from surface. Secondary electrons emitted by primary electrons (acceleration region of Hall-effect discharge) and by photons (dusty plasma) are responsible for a complete inverse sheath: the potential monotonically increases toward a positively charged wall that is shielded by a single layer of negative charge. No ion-accelerating presheath exists in the bulk plasma region and the ion flux at the wall is zero. In the case of production of hydrogen negative ions by neutral conversion on the plasma grid in the extraction region of a negative ion source, a space-charge-limited regime occurs with the formation of a non-monotonic double layer in front of the grid.

Automatic analysis of thin-walled laminated composite sections

In this paper a computer program is developed for the determination of geometrical and material properties of composite thin-walled beams with arbitrary open cross-section and any arbitrary laminate stacking sequence. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The program is written in Fortran 77. Some numerical examples are given, with complete information about input and output.

A theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion

Results of a theoretical analysis of the local buckling in thin-walled bars with open cross-section subjected to warping torsion are presented. The local critical bimoment, which generates local buckling of a thin-walled bar and constitutes the limit of the applicability of the classical Vlasov theory, is defined. A method of determining local critical bimoment on the basis of critical warping stress is developed. It is shown that there are two different local critical bimoments with regard to absolute value for bars with an unsymmetrical cross-section depending on the sense of torsion load (sign of bimoment). However, for bars with bisymmetrical and monosymmetrical sections, the determined absolute values of local critical bimoments are equal to each other, irrespective of the sense of torsional load. Critical warping stresses, local critical bimoments and local buckling modes for selected cases of thin-walled bars with open cross-section are determined.

Nonminimal Einstein–Maxwell–Vlasov-axion model

We establish a new self-consistent system of equations accounting for a nonminimal coupling of the cooperative gravitational, electromagnetic and pseudoscalar (axion) fields in a multi-component relativistic plasma. The axionic extension of the nonminimal Einstein–Maxwell–Vlasov theory is based on two consistent procedures. First, we use the Lagrange formalism to obtain nonminimal equations for the gravitational, electromagnetic and pseudoscalar fields with the additional sources generated in plasma. Second, we use the Vlasov version of the relativistic kinetic theory of the plasma, guided by the cooperative macroscopic electromagnetic, gravitational and axionic fields, to describe adequately the response of the plasma on the variations of these fields. In order to show the self-consistency of this approach we check directly the compatibility conditions for the master equations for the cooperative fields. Using these compatibility conditions we reconstruct the ponderomotive force, which acts on the plasma particles, and discuss the necessary conditions for existence of the distribution function of the equilibrium type.

Linear and non-linear finite element analysis of shear-corrected composites box beams

The Updated Lagrangian formulation for non-linear finite element analysis is applied to the problem of thin-walled composites box beams undergoing large displacements. A shear correction factor for thin-closed rectangular sections is introduced into some terms of the variational formulation and its influence in the results is analyzed, in both linear and non-linear problems. The Vlasov's theory describing the coupled flexural-torsional phenomenon and the implementation of the FSDT theory in thin-walled beams is discussed, as well as the strains, stress resultants and constitutive relationships for composites box beams. The application of the Mechanic of Laminated Beam theory (MLB) to the calculation of the shear correction factors considering more constitutive terms for computing the shear flow in flanges and webs than those ones used in the original theory is also debated. The Updated Lagrangian finite element model applied in this work for non-linear analysis of box beams is described. A comparison of the numerical results with those obtained experimentally, analytically and by the numerical models proposed by other authors is done for both linear and non-linear problems. The assumptions made in this work and the formulation developed only applies to thin-walled beams that undergo large displacements, but small to moderate twist rotations.

Vlasov versus reduced kinetic theories for helically symmetric equilibria

A new constant of motion for helically symmetric equilibria in the vicinity of the magnetic axis is obtained in the framework of Vlasov theory. In view of this constant of motion the Vlasov theory is compared with drift kinetic and gyrokinetic theories near axis. It turns out that as in the case of axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18, 064507 (2011)] the Vlasov current density thereon can differ appreciably from the drift kinetic and gyrokinetic current densities. This indicates some limitation on the implications of reduced kinetic theories, in particular, as concerns the physics of energetic particles in the central region of magnetically confined plasmas.

Flexural-torsional vibration analysis of axially loaded thin-walled beam

The present paper considers the flexure-torsion coupled vibrations of axially loaded thin-walled beams with arbitrary open cross section, by means of an exact solution. The effects of axial force, warping stiffness and rotary inertia are included in the present formulations. In the case of simply supported thin-walled beam, a closed-form solution for the coupled natural frequencies of free harmonic vibrations was derived by using a general solution of the governing differential equations of motion based on Vlasov theory. The method is illustrated by its application to two test examples, to demonstrate the effects of bending-torsion coupling and axial force on the dynamic behavior of thin-walled beams. Compared with those available in the relevant literature, numerical results demonstrate the accuracy and effectiveness of the proposed method.

Kinetic model of electric potentials in localized collisionless plasma structures under steady quasi-gyrotropic conditions

Localized plasma structures, such as thin current sheets, generally are associated with localized magnetic and electric fields. In space plasmas localized electric fields not only play an important role for particle dynamics and acceleration but may also have significant consequences on larger scales, e.g., through magnetic reconnection. Also, it has been suggested that localized electric fields generated in the magnetosphere are directly connected with quasi-steady auroral arcs. In this context, we present a two-dimensional model based on Vlasov theory that provides the electric potential for a large class of given magnetic field profiles. The model uses an expansion for small deviation from gyrotropy and besides quasineutrality it assumes that electrons and ions have the same number of particles with their generalized gyrocenter on any given magnetic field line. Specializing to one dimension, a detailed discussion concentrates on the electric potential shapes (such as “U” or “S” shapes) associated with magnetic dips, bumps, and steps. Then, it is investigated how the model responds to quasi-steady evolution of the plasma. Finally, the model proves useful in the interpretation of the electric potentials taken from two existing particle simulations.

Kinetic Signatures and Intermittent Turbulence in the Solar Wind Plasma

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave-particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfven waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. We assume that (1) low-frequency Alfven and fast waves have the same spectral shape and the same amplitude of power spectral density; (2) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; (3) kinetic wave-particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha-proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfven-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfven-cyclotron wave at the same wave propagation angle \theta, particularly at $80^\circ$ < \theta < $90^\circ$. When Alfven-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by differential speed and temperature anisotropy of alpha particles via the self-consistently evolving wave-particle interaction. Therefore, fast-cyclotron waves as a result of linear mode coupling is a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.

Restrained torsion of open thin-walled beams including shear deformation effects

A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is estab- lished by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and free warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results. In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

On Problems of Torsion Analysis of Steel Members with Open Cross Section

This paper deals with the torsion analysis of steel members with thin-walled open cross section. The attention is paid mainly to the determination of resulting stresses accenting the different methods of their determination. Three basic approaches are discussed, namely the Vlasov's theory of thin-walled elastic members, the method based on modified bending and torsion analogy and the simplified method supplying the torsion by the effect of couple of forces. On the illustrative example the effect of torsion at steel crane girder has been analyzed using the confrontation of the aforesaid methods. Also some general notes and comments to the problem of torsion analysis and design of steel members are included.

A New Torsion Element of Thin-Walled Beams Including Shear Deformation

Restrained torsion analysis of open thin-walled beam is presented in this paper. A finite element model is developed. The element is based on the first-order torsion theory, which accounts for the warping deformation and shear deformation due to restrained torsion. The interpolation functions of total rotation and twist rate of free warping rotation of cross section are constructed respectively by using the relationship between these two rotations. Numerical example is illustrated to validate the current approach and the results of the current theory are compared with those obtained from classical Vlasov theory and first-order torsion theory.

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

[1] All Alfven waves in the solar wind have parallel electric fields, which enable Landau damping. The Alfven waves' Landau resonate with very low energy electrons; low-energy electrons are easily trapped in the Alfven waves, and at low energies electron-ion Coulomb scattering is very rapid. Analytic fluid theory and numerical solutions to the linear Vlasov equation are used to determine the properties of Alfven waves (and kinetic Alfven waves) in the solar wind. Electrostatic potentials associated with the waves' parallel electric fields are found to be relatively large. Owing to the large potentials, electrons over a broad range of velocities interact with the wave to produce Landau damping. Because of this broad range, linear Vlasov theory is invalid and the Landau-damping rates computed via linear Vlasov theory may not be accurate. Electron velocity diffusion owed to electron-ion Coulomb scattering is analyzed. Electron diffusion times in the Alfven wave Landau resonance are calculated and are found to be faster than wave periods and much faster than Landau-damping time scales. Coulomb collisions should prevent the electron distribution function from evolving away from a Maxwellian form, and thereby Coulomb collisions act to maintain Landau damping (although at a rate different than that given by linear Vlasov theory). Some complications of this Landau-damping picture arise from the interplanetary electric field competing with the Alfven wave parallel electric fields and from ion beams near the Landau resonance.

A comparison of Vlasov with drift kinetic and gyrokinetic theories

A kinetic consideration of an axisymmetric equilibrium with vanishing electric field near the magnetic axis shows that ∇f should not vanish on axis within the framework of Vlasov theory while it can either vanish or not in the framework of both a drift kinetic and a gyrokinetic theories (f is either the pertinent particle or the guiding center distribution function). This different behavior, relating to the reduction of phase space which leads to the loss of a Vlasov constant of motion, may result in the construction of different currents in the reduced phase space than the Vlasov ones. This conclusion is indicative of some limitation on the implications of reduced kinetic theories, in particular, as concerns the physics of energetic particles in the central region of magnetically confined plasmas.

Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams

The classical Vlasov theory for torsional analysis of thin-walled beams with open and closed cross-sections can be generalized by including distortional displacement fields. We show that the determination of adequate distortional displacement fields for generalized beam theory (GBT) can be found as part of a semi-discretization process. In this process the cross-section is discretized into finite cross-section elements and the axial variation of the displacement functions are solutions to the established coupled fourth order differential equations of GBT. We use a novel finite-element-based displacement approach in combination with a weak formulation of the shear constraints and constrained wall widths. The weak formulation of the shear constraints enables analysis of both open and closed cell cross-sections by allowing constant shear flow. We use variational analysis to establish and clearly identify the homogeneous differential equations, the eigenmodes, and the related homogeneous solutions. The distortional equations are solved by reduction of order and solution of the related eigenvalue problem of double size as in non-proportionally damped structural dynamic analysis. The full homogeneous solution is given as well as transformations between different degree of freedom spaces. This new approach is a considerable theoretical improvement, since the obtained GBT equations found by discretization of the cross-section are now solved analytically and the formulation is valid without special attention also for closed single or multi-cell cross-sections. Further more the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.

Lateral buckling of pultruded FRP beams

A mechanical model capable of taking into account the contribution of shear deformation on the lateral buckling behavior of open cross-sections pultruded FRP beams is presented. The total torsional rotation is divided into two parts: the first one, associated with axial warping and negligible shearing strains, the second one, associated entirely with shear strains. Through this approach it is therefore possible to consider with good approximation the shear strains, which are neglected by the classical Vlasov theory. The procedure is validated by comparing the results obtained via FEM with some numerical results available in literature. The effect of the normal to shear modulus ratio on the lateral buckling load is also investigated.

Static analysis of non-planar pierced shear walls with semi-rigid beam-wall connections using continuous connection technique

The lateral loads acting on high-rise reinforced concrete buildings are often resisted by specially arranged shear walls. Pierced shear walls weakened by doors, windows and corridors, necessitate particular attention, since they are highly indeterminate. In this study, the static analysis of non-planar pierced shear walls with yielded connections modelled as equivalent rotational springs is considered. To carry out a quick predesign of non-planar pierced shear walls, an elegant technique called Continuous Connection Technique (CCT) has been used in conjunction with Vlasov’s theory of thin-walled beams. The governing differential equations, in the CCT, are the compatibility equations written for the vertical displacements at the midpoints of the connecting beams. There is a contribution pertaining to the semi-rigid beam-wall connections in these equations. The connecting beams are assumed to have the same properties and spacing along the entire height of the wall and all rotational springs have equal constants. Key words: Non-planar, pierced shear wall, continuous connection technique, rotational spring, thin-walled beam, Vlasov theory.

A KINETIC ALFVÉN WAVE AND THE PROTON DISTRIBUTION FUNCTION IN THE FAST SOLAR WIND

Using one-dimensional test particle simulations, the effect of a kinetic Alfven wave on the velocity distribution function (VDF) of protons in the collisionless solar wind is investigated. We first use linear Vlasov theory to numerically obtain the property of a kinetic Alfven wave (the wave propagates in the direction almost perpendicular to the background magnetic field). We then numerically simulate how the wave will shape the proton VDF. It is found that Landau resonance may be able to generate two components in the initially Maxwellian proton VDF: a tenuous beam component along the direction of the background magnetic field and a core component. The streaming speed of the beam relative to the core proton component is about 1.2-1.3 Alfven speed.

Flushing effect in reconnection: Effects of minority species of oxygen ions

Effects of O + ions on magnetic reconnection in the magnetotail are examined in a Harris equilibrium using a combination of linear Vlasov theory and large-scale driven and non-driven two-dimensional fully kinetic particle simulations. Linear theory of multiple species plasma indicates that the growth rate is rather insensitive to the composition of the background (lobe) or its temperature but more sensitive to the properties of the current carriers. Thus O + can affect significant changes to the linear growth rate of tearing mode only as a current carrier. However, it is demonstrated that in the nonlinear stage reconnection can effectively move trace material from the lobes into the current sheet proper. If the supply of lobe markers (like O +) is sufficiently permanent in the lobe, an initially proton-dominated current sheet can be virtually replaced by the marker ions through this “flushing effect”. The dominance of marker ions introduces finite Larmor radius signatures with marker gyroradii scales rather than that of the protons. In this way, the presence of heavier marker species in the lobe can lead to (i) reduced efficiency of energy conversion, (ii) reduction in the number and repetition frequency of secondary islands, (iii) broadening of the quadrupole magnetic structure, (iv) slowing down of the coalescence process and (v) modification of the composition of the ion current carriers. Using Cluster observations, we show the evidence for the “flushing effect” in the data. Detailed comparison with observations is planned for future work.