Electron Vortex Research Articles

Nonquasineutral relativistic current filaments and their X-ray emission

Nonquasineutral electron current filaments with the azimuthal magnetic field are considered that arise due to the generation of electron vorticity in the initial (dissipative) stage of evolution of a current-carrying plasma, when the Hall number is small (σB/enec ≪ 1) because of the low values of the plasma conductivity and magnetic field strength. Equilibrium filamentary structures with both zero and nonzero net currents are considered. Structures with a zero net current type form on time scales of t < tsk = (r0ωpe/c)2tst, where tsk is the skin time, tst is the typical time of electron-ion collisions, and r0 is the radius of the filament. It is shown that, in nonquasineutral filaments in which the current is carried by electrons drifting in the crossed electric (Er) and magnetic (Bθ) fields, ultrarelativistic electron beams on the typical charge-separation scale rB = B/(4πene) (the so-called magnetic Debye radius) can be generated. It is found that, for comparable electron currents, the characteristic electron energy in filaments with a nonzero net current is significantly lower than that in zero-net-current filaments that form on typical time scales of t < tsk. This is because, in the latter type of filaments, the oppositely directed electron currents repel one another; as a result, both the density and velocity of electrons increase near the filament axis, where the velocities of relativistic electrons are maximum. Filaments with a zero net current can emit X rays with photon energies ℏ ω up to 10 MeV. The electron velocity distributions in filaments, the X-ray emission spectra, and the total X-ray yield per unit filament length are calculated as functions of the current and the electron number density in the filament. Analytical estimates of the characteristic lifetime of a radiating filament and the typical size of the radiating region as functions of the plasma density are obtained. The results of calculations are compared with the available experimental data.

Nonlinear Aspects of Quantum Plasma Physics: Nanoplasmonics and Nanostructures in Dense Plasmas

We present a short review of recent developments in nonlinear quantum plasma physics, including quantum hydrodynamic and effective nonlinear shrödinger equation formalisms, for describing collective phenomena in quantum plasmas. As examples we discuss simulation studies of the formation and dynamics of dark solitons and vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in dense in quantum electron plasmas. The electron dynamics of dark solitons and vortices is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson equations. Both dark solitons and singly charged electron vortices are robust, and the latter tend to form pairs of oppositely charged vortices. The two-dimensional quantum electron vortex pairs survive during collisions under the change of partners. The dynamics of the CPEM waves is governed by a nonlinear Schrödinger equation, which is nonlinearly coupled with the Schrödinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one spatial dimension admit stationary solutions in the form dark envelope solitons. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave envelopes in the electron density holes that are associated with positive potential profiles.

Using Global Interpolation to Evaluate the Biot-Savart Integral for Deformable Elliptical Gaussian Vortex Elements

This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios. When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and, unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptical fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement among the three approaches.

Water and Autocatalysis in Living Matter

Water plays a fundamental role in living organisms. Liquid water includes coherence domains (CD) where all molecules oscillate in unison in tune with a self-trapped electromagnetic field at a well-defined frequency. The coherent oscillations produce an ensemble of quasi-free electrons, able to collect noise energy from the environment and transform it into high-grade coherent energy in the form of electron vortices. This high-grade energy may activate the biomolecules resonating with the water CD. In this way, water CDs become dissipative structures in the sense of Prigogine and Froehlich, such that they are able to oscillate and coherence among them can be established. Thus, autocatalysis in living matter is made possible.

Experimental study of electron vortex structures in an electrostatic plasma lens

Results are presented from experimental studies of electron vortex bunches in a cold ion-beam plasma consisting of strongly magnetized electrons and a beam of almost free positive ions. The existence of electron vortex bunches was detected from local minima of the electric potential on surfaces perpendicular to the magnetic field lines. It is found that the vortices have the form of magnetic-field-aligned filaments, in which electrons rotate with a velocity significantly exceeding both the velocity of the vortex as a whole and the electron velocity in the ambient plasma. It is shown that, in a sufficiently strong magnetic field, the accumulation of electrons in the vortices terminates when the condition for the longitudinal confinement of electrons by the electric field fails to hold.

Electron transport and permittivity in a plasma with an arbitrary ionic charge

Based on the solution of a linearized kinetic equation for electrons with a Landau collision integral, we develop a theory of electron transport for small perturbations in a completely ionized plasma with an arbitrary ionic charge that is free from any constraints on the characteristic perturbation time and length scales. We calculate the potential and vortex electron fluxes for an arbitrary electron collision frequency that allow the spatial and temporal nonlocal transport to be described. We also derive expressions for the longitudinal and transverse electron permittivities of a collisional plasma with an arbitrary ionic charge that are suitable for describing the plasma response to small perturbations with an arbitrary frequency and wave vector. Using the transverse permittivity, which allows the absorption of an electromagnetic wave to be described in the entire range of plasma parameters (from the strongly collisional to the collisionless one), as an example, we provide a detailed comparison with previously known models.

Vortex structure of few-electron quantum dots

Exact diagonalizations are used to study the structure of the many-particle wavefunction in quantum dots containing up to six electrons. We are able to provide quantitative information on the correlated electron–vortex state that forms at strong magnetic fields and find that the electron–vortex distances scale as the square of the filling factor.

Giant electromagnetic vortex and MeV monoenergetic electrons generated by short laser pulses in underdense plasma near quarter critical density region

Very efficient generation of monoenergetic, about 1MeV , electrons from underdense plasma with its electron density close to the critical, when irradiated by an intense femtosecond laser pulse, is found via two dimensional particle-in-cell simulation. The stimulated Raman scattering of a laser pulse with frequency omega< or =2omega(pl max) gives rise to a giant electromagnetic vortex. In contrast to electron acceleration by the well-known laser pulse wake, injected plasma electrons are accelerated up to vortex ponderomotive potential forming a quite monoenergetic distribution. A relatively high charge of such an electron source makes very efficient generation of soft gamma rays with homega>300 keV .

Kinetic Alfvén waves and electron physics. II. Oblique slow shocks

One-dimensional (1D) particle-in-cell (PIC; kinetic ions and electrons) and hybrid (kinetic ions; adiabatic and massless fluid electrons) simulations of highly oblique slow shocks (θBn=84° and β=0.1) [Yin et al., J. Geophys. Res., 110, A09217 (2005)] have shown that the dissipation from the ions is too weak to form a shock and that kinetic electron physics is required. The PIC simulations also showed that the downstream electron temperature becomes anisotropic (Te‖&amp;gt;Te⊥), as observed in slow shocks in space. The electron anisotropy results, in part, from the electron acceleration/heating by parallel electric fields of obliquely propagating kinetic Alfvén waves (KAWs) excited by ion-ion streaming, which cannot be modeled accurately in hybrid simulations. In the shock ramp, spiky structures occur in density and electron parallel temperature, where the ion parallel temperature decreases due to the reduction of the ion backstreaming speed. In this paper, KAW and electron physics in oblique slow shocks are further examined under lower electron beta conditions. It is found that as the electron beta is reduced, the resonant interaction between electrons and the wave parallel electric fields shifts to the tail of the electron velocity distribution, providing more efficient parallel heating. As a consequence, for βe=0.02, the electron physics is shown to influence the formation of a θBn=75° shock. Electron effects are further enhanced at a more oblique shock angle (θBn=84°) when both the growth rate and the range of unstable modes on the KAW branch increase. Small-scale electron and ion phase-space vortices in the shock ramp formed by electron-KAW interactions and the reduction of the ion backstreaming speed, respectively, are observed in the simulations and confirmed in homogeneous geometries in one and two spatial dimensions in the accompanying paper [Yin et al., Phys. Plasmas 14, 062104 (2007)]. Results from this study conclude that the inability of the hybrid method to model the Landau resonance of KAW with electrons and the resulting time-evolving electron parallel heating lead to differences between the PIC and hybrid simulations.

Electrostatic coherent structures generation by local heating in a collisionless plasma

Abstract We propose a new mechanism for the generation of electrostatic coherent structures and Langmuir fluctuations in a stratified plasma. The model is base on open boundary 1D Vlasov simulations where heated electrons are injected by applying a temporal continuous periodic modification of the width of the electron distribution function at one boundary of the simulation box. To our knowledge, that is the first time that a “localized heating” mechanism is studied as a driver for the development of bi(multi)polar electric field with their associated electron density holes and vortices in the phase space. After the development of many electrostatic coherent structures, the injected fast particles are free to move along their ballistic limit, while electrons moving at nearly, or less than, the thermal speed are diffused in phase space by the local fields.

Formation of nonquasineutral vortex plasma structures with a zero net current

A nonquasineutral vortex structure with a zero net current is described that arises as a result of electron drift in crossed magnetic and electric fields, the latter being produced by charge separation on a spatial scale of about the magnetic Debye radius r B = |B|/(4πen e ). In such a structure with a radius of r ∼ r B , the magnetic field is maintained by a drift current on the order of the electron Alfven current J Ae = m e c 3/(2e) and can become as strong as B ≃ m e c 2/(er). Estimates show that, in a plasma with a density of n e = 1021−1023 cm−3 and with nonzero electron vorticity driven by high-power laser radiation on a time scale on the order of θ pe −1 , magnetic fields with a strength of B ∼ 108−109 G are generated on micron and submicron scales. The system with closed current that is considered in the present paper can also serve as a model of hot spots in the channel of a Z-pinch.

Formation and Dynamics of Dark Solitons and Vortices in Quantum Electron Plasmas

We present simulation studies of the formation and dynamics of dark solitons and vortices in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson system of equations, which conserves the number of electrons as well as their momentum and energy. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear structures presented here may serve the purpose of transporting information at quantum scales in ultracold micromechanical systems and dense plasmas, such as those created during intense laser-matter interactions.

Single-cycle high-intensity electromagnetic pulse generation in the interaction of a plasma wakefield with regular nonlinear structures

The interaction of regular nonlinear structures (such as subcycle solitons, electron vortices, and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultrashort electromagnetic pulses. The electromagnetic field of the nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the nonlinear structure. This process is illustrated with two-dimensional particle-in-cell simulations. The considered laser-plasma interaction regimes can be achieved in present day experiments and can be used for plasma diagnostics.

Electronic transport and vortex dynamics in the low-temperature liquid phase of an ultrathin Corbino-disk

We study the possible edge-pinning effects on the electronic transport and vortex-flow motion in the low-temperature (T) liquid phase of thin amorphous MoxSi1−x films with the Corbino-disk (CD) and strip(-like) contact geometries. For CD, we observe the two-dimensional (2D) field-driven superconductor–insulator transition (FSIT) at T=0 and anomalous vortex-flow motion at low T, suggestive of strong quantum fluctuations, which are similar to those observed in usual strip-shaped films. These results indicate that the edge effects are not important in our disordered films and that both the 2D FSIT and anomalous vortex motion at low T are intrinsic properties.

Large-scale electron vortex structure formation in a plasma lens

The first experimental data on the observation of electron vortices in an electrostatic plasma lens at a considerable radial gradient of electron density are reported. It is established that anharmonic potential waves of large amplitude appear and propagate in the azimuthal direction. The results of measurements of the electric field distribution show that electron bunches formed as a result of instability development contain trapped particles, which rotate at a large velocity around the centers of bunches, thus creating vortices. The main factor leading to limitation of the maximum amplitude of vortices in a strong magnetic field has been experimentally established.

Shifting and Pinning of a Magnetic Vortex Core in a Permalloy Dot by a Magnetic Field

Magnetic pinning in thin films seems to be a major research subject in the near future, as it is involved in all switching processes which include a movement of a domain wall or a magnetic vortex. We used Lorentz transmission electron microscopy and vortex pinning at artificial pinning sites to investigate the pinning behavior of magnetic vortices for the first time with high spatial resolution.

Electron vortices in semiconductors devices

The hydrodynamic model of electron transport in semiconductors is analyzed and, in analogy with vortices in fluid mechanics, the curl of electron velocity is defined as electron vorticity, and the transport equation for the electron vorticity is derived. Aside from the classical hydrodynamic sources of vorticity, collision terms in the continuity and momentum equations are identified as sources and sinks of electron vorticity. Similar to three-dimensional fluid flows there is a vortex stretching term in the vorticity equation. This term could be responsible for the possible cascade of electron kinetic energy to small scales and formation of chaotic turbulent electron transport regimes. A scale analysis of the electron vorticity equation is performed and the relative order of magnitude of each sources of vorticity is found. This analysis and the calculation of electron mean-free-path due to electron–electron and electron–phonon scatterings characterize a transport regime with significant electron vorticity effects. Furthermore, conditions for observation of electron vortices in semiconductor devices are predicted.

Electron‐acoustic solitary waves and double layers with an electron beam and phase space electron vortices in space plasmas

The nonlinear propagation of electron acoustic waves (EAWs) in a plasma composed of a cold electron fluid, hot electrons obeying trapped/vortex‐like distribution, warm electron beam, and stationary ions is considered. The streaming velocity of the beam, uo, plays the dominant role in changing the topology of the linear dispersion relation. For small but finite amplitude EAWs, a modified Korteweg de Vries (MKdV) equation is derived. It is found that the MKdV supports EAWs having a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The energy soliton amplitude decreases, though its width increases for any increase in the beam parameters. In the vicinity of the isothermal population, a nonlinear evolution equation with mixed nonlinearity is obtained. Its solution gives a (compressive/rarefactive) soliton or a compressive double layer (DL) depending on the system parameters. For arbitrary amplitude EAWs, the exact Sagdeev potential has been derived. The admitted Mach number regime widens due to an increase of the beam parameters. With a better approximation in the Sagdeev potential, more features of solitary waves, e.g., spiky and explosive, are also highlighted. The introduced effects modify significantly the wave velocity, the amplitude, and the width of the EAWs investigated numerically. This theoretical model is in good agreement with the broadband noise emission observed by Geotail spacecraft in the plasma sheet boundary layer of the Earth's magnetosphere.

Ion Acceleration in a Dipole Vortex in a Laser Plasma Corona

Particle-in-cell simulations show that the inhomogeneity scale of the plasma produced in the interaction of high-power laser radiation with gas targets is of fundamental importance for ion acceleration. In a plasma slab with sharp boundaries, the quasistatic magnetic field and the associated electron vortex structure produced by fast electron beams both expand along the slab boundary in a direction perpendicular to the plasma density gradient, forming an extended region with a quasistatic electric field, in which the ions are accelerated. In a plasma with a smooth density distribution, the dipole magnetic field can propagate toward the lower plasma density in the propagation direction of the laser pulse. In this case, the electron density in an electric current filament at the axis of the magnetic dipole decreases to values at which the charge quasineutrality condition fails to hold. In electric fields generated by this process, the ions are accelerated to energies substantially higher than those characteristic of plasma configurations with sharp boundaries.

Localization of magnetized electrons in current filaments as a fundamental cause of Coulomb explosion

Mechanisms for generating current filaments in a dense plasma under the action of focused laser pulses and in a Z-pinch configuration are discussed. The main properties of current filaments with a zero and nonzero electron vorticity Ωe=B−(c/e)∇×pe that originate at magnetic fields in the range 4πnemec2≪B2≪4πnimic2 are investigated under the conditions of Coulomb explosion at currents below the ion Alfven current. A study is made of the equilibrium configurations of nonquasineutral current filaments in a purely longitudinal (Bz) and a purely azimuthal (Bθ) magnetic field and also in a more general case of a helical magnetic field, having two components, under conditions such that the charge separation occurs on a spatial scale on the order of the magnetic Debye radius rB ≃ |B|/(4πene. It is shown that strong electric fields generated in the current filaments are comparable in magnitude to the atomic field and are capable of accelerating ions to energies of several tens of megaelectronvolts. The ion dynamics in strong electric fields of the filaments is calculated numerically and is shown to lead to the formation of collisionless shock waves on time scales on the order of several inverse ion plasma frequencies ωpi−1. The possible formation of current filaments on different spatiotemporal scales is considered.