Wave Vector Anisotropy Research Articles

Whistler turbulence at variable electron beta: Three‐dimensional particle‐in‐cell simulations

Three‐dimensional particle‐in‐cell (PIC) simulations of whistler turbulence at three different initial values of βe are carried out on a collisionless, homogeneous, magnetized plasma model. The simulations begin with an initial ensemble of relatively long‐wavelength whistler modes and follow the temporal evolution of the fluctuations as wave‐wave interactions lead to a forward cascade into a broadband, turbulent spectrum at shorter wavelengths with a wave vector anisotropy in the sense of k⟂>k∥. Here ⟂ and ∥ denote directions perpendicular and parallel to the background magnetic field, respectively. In addition, wave‐particle interactions lead to fluctuating field dissipation and electron heating with a temperature anisotropy in the sense of T∥>T⟂. At early times, the wave‐wave cascade dominates energy transport, whereas wave‐particle Landau damping dominates at late simulation times. Larger values of βe correspond to a faster forward cascade in wave number and to a faster rate of electron heating, as well as to a less anisotropic wave vector distribution and to a less anisotropic electron velocity distribution.

Formation of X-pulses in periodically gain/loss modulated materials

We propose a versatile and efficient technique for the formation of X-pulses in materials with a periodical gain/loss modulation on the wavelength scale. We show that in such materials the strong wave-vector anisotropy of amplification/attenuation of the Bloch modes enables the shaping of ultra-short light pulses around the edges of the first Brillouin zone. X-pulses generation is numerically demonstrated and the optimum conditions are derived; specific characteristics of X-pulses can be tailored by appropriate selection of the geometry and modulation depth.

Constructing a large variety of Dirac-cone materials in the Bi1−xSbx thin film system

We theoretically predict that a large variety of Dirac-cone materials can be constructed in Bi${}_{1-x}$Sb${}_{x}$ thin films, and we here show how to construct single-, bi- and tri- Dirac-cone materials with various amounts of wave vector anisotropy. These different types of Dirac cones can be of special interest to electronic devices design, quantum electrodynamics and other fields.

Whistler turbulence forward cascade: Three-dimensional particle-in-cell simulations

[1] The first fully three-dimensional particle-in-cell (PIC) simulation of whistler turbulence in a magnetized, homogeneous, collisionless plasma has been carried out. An initial relatively isotropic spectrum of long-wavelength whistlers is imposed upon the system, with an initial electron β = 0.10. As in previous two-dimensional simulations of whistler turbulence, the three-dimensional system exhibits a forward cascade to shorter wavelengths and broadband, turbulent spectra with a wave vector anisotropy in the sense of stronger fluctuation energy at k⊥ than at comparable k∥ where the respective subscripts represent directions perpendicular and parallel to the background magnetic field Bo. However, the three-dimensional (3D) simulations display quantitative differences with comparable two-dimensional (2D) computations. In the 3D runs, turbulence develops a stronger anisotropic cascade more rapidly than in 2D runs. Furthermore, reduced magnetic fluctuation spectra in 3D runs are less steep functions of perpendicular wave numbers than those from 2D simulations. The much larger volume of perpendicular wave vector space in 3D appears to facilitate the transfer of fluctuation energy toward perpendicular directions.

WHISTLER TURBULENCE WAVEVECTOR ANISOTROPIES: PARTICLE-IN-CELL SIMULATIONS

Two-dimensional electromagnetic particle-in-cell simulations of whistler turbulence in a magnetized, homogeneous, collisionless plasma of electrons and protons are carried out. Enhanced magnetic fluctuation spectra are initially imposed at relatively long wavelengths, and, as in previous such simulations, the temporal evolution shows a forward cascade of magnetic fluctuation energy to shorter wavelengths, with more fluctuation energy at a given wavenumber perpendicular to B o than at the same wavenumber parallel to the background field. The new result here is that the wavevector anisotropy is very different for each of the three components of the fluctuating magnetic field. Here, ∥ denotes the direction parallel to the background magnetic field B o , ⊥ indicates the direction perpendicular to B o and in the simulation plane, and the symbol ⊥⊥ denotes the direction perpendicular to both B o and the simulation plane. The parallel magnetic fluctuations show more energy at than at , whereas the perpendicular in-plane magnetic fluctuations show more energy at than at . Finally, the out-of-plane magnetic fluctuations, , strongly prefer to propagate in the direction.

Wave-Vector Dependence of Magnetic-Turbulence Spectra in the Solar Wind

Using four-point measurements of the Cluster spacecraft, the energy distribution was determined for magnetic field fluctuations in the solar wind directly in the three-dimensional wave-vector domain in the range |k|<or=1.5x10{-3} rad/km. The energy distribution exhibits anisotropic features characterized by a prominently extended structure perpendicular to the mean field preferring the ecliptic north direction and also by a moderately extended structure parallel to the mean field. From the three-dimensional energy distribution wave vector anisotropy is estimated with respect to directions parallel and perpendicular to the mean magnetic field, and the result suggests the dominance of quasi-two-dimensional turbulence toward smaller spatial scales.

INTERPRETING POWER ANISOTROPY MEASUREMENTS IN PLASMA TURBULENCE

A relationship is derived between power anisotropy and wavevector anisotropy in turbulent fluctuations. This can be used to interpret plasma turbulence measurements, for example in the solar wind. If fluctuations are anisotropic in shape then the ion gyroscale break point in spectra in the directions parallel and perpendicular to the magnetic field would not occur at the same frequency, and similarly for the electron gyroscale break point. This is an important consideration when interpreting solar wind observations in terms of anisotropic turbulence theories. Model magnetic field power spectra are presented assuming a cascade of critically balanced Alfven waves in the inertial range and kinetic Alfven waves in the dissipation range. The variation of power anisotropy with scale is compared to existing solar wind measurements and the similarities and differences are discussed.

On shear viscosity and the Reynolds number of magnetohydrodynamic turbulence in collisionless magnetized plasmas: Coulomb collisions, Landau damping, and Bohm diffusion

For a collisionless plasma, the magnetic field Ḇ enables fluidlike behavior in the directions perpendicular to B; however, fluid behavior along Ḇ may fail. The magnetic field also introduces an Alfven-wave nature to flows perpendicular to Ḇ. All Alfven waves are subject to Landau damping, which introduces a flow dissipation (viscosity) in collisionless plasmas. For three magnetized plasmas (the solar wind, the Earth’s magnetosheath, and the Earth’s plasma sheet), shear viscosity by Landau damping, Bohm diffusion, and by Coulomb collisions are investigated. For magnetohydrodynamic turbulence in those three plasmas, integral-scale Reynolds numbers are estimated, Kolmogorov dissipation scales are calculated, and Reynolds-number scaling is discussed. Strongly anisotropic Kolmogorov k−5∕3 and mildly anisotropic Kraichnan k−3∕2 turbulences are both considered and the effect of the degree of wavevector anisotropy on quantities such as Reynolds numbers and spectral-transfer rates are calculated. For all three plasmas, Braginskii shear viscosity is much weaker than shear viscosity due to Landau damping, which is somewhat weaker than Bohm diffusion.

Spacecraft observations of solar wind turbulence: an overview

Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic (MHD) turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfvén waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and the presence of intermittency similar to that in neutral fluids. We also discuss the presence of anisotropy in wavevector space relative to the local magnetic field direction. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wavevectors either parallel to the magnetic field (‘slab’ fluctuations) or approximately perpendicular to it (‘2D’). We review the existing evidence for such anisotropy, which has important consequences for the transport of energetic particles. Finally, we present the first results of a new analysis which provides the most accurate measurements to date of the wave-vector anisotropy of wavevector power in solar wind MHD turbulence.

Leaky helical flexural wave scattering contributions from tilted cylindrical shells: ray theory and wave-vector anisotropy.

At sufficiently high frequencies, cylindrical shells support a wave whose properties are analogous to those of the lowest antisymmetric Lamb wave on plates. When the shell is in water and the frequency exceeds the coincidence frequency, the flexural wave is a leaky wave that can be a major contributor to the scattering by tilted shells [G. Kaduchak, C. M. Wassmuth, and C. M. Loeffler, J. Acoust. Soc. Am. 100, 64-71 (1996)]. While the meridional ray-scattering contributions for such leaky flexural waves were previously modeled, the helical contribution can also be significant. A ray theory for those contributions is compared with the exact partial wave series (PWS) solution for infinitely long empty shells. The agreement between the ray theory and the PWS is only possible when a weak anisotropy of the flexural wave parameters is included in the evaluation of the ray theory. The anisotropy is determined numerically from the roots of a denominator in the PWS because approximations for the anisotropy from thin-shell mechanics are not applicable significantly above the coincidence frequency.

Theoretical calculation of impact ionization rate in SiO2

Impact ionization rate in SiO2 was numerically calculated using both pseudo-wave functions and energy band structure based on a self-consistent pseudopotential method. To avoid numerical complexity due to amorphous structure, SiO2 was assumed to be a crystalline α-quartz. The calculated impact ionization rate shows a strong wave vector anisotropy near a threshold energy regime, primary electrons existing at Γ point yield the strongest impact ionization rate. It was found that calculated results are not expressed by a Keldysh formula since SiO2 has complex band structure (e.g., indirect transition gap and nonparabolic bands). The magnitude of the theoretical impact ionization rate was very close to the experimental results recently reported by E. Cartier and F.R. McFeely [Phys. Rev. B 44, 10689 (1991)]. Detailed theoretical study clearly demonstrates that the average energy of secondary generated carriers depends linearly on the energy of primary electrons.

Magnetic Steering of Magnetostatic Waves in Epitaxial YIG Films

High quality epitaxial YIG films grown on gadolinium gallium garnet have certain geometrical advantages over flux-grown material for refined investigation of basic magnetic wave propagation phenomena. Better uniformity of internal field under magnetic bias and convenience for placement of spatially periodic current-carrying couplers on the free YIG surface, ensures enhanced field uniformity by confining the region of propagation. Surface magnetostatic waves are dispersive and exhibit wave vector anisotropy so that, in general, the phase and group velocity vectors are noncollinear, with the beam steering angle variable by the magnetic bias field. Scanning magnetic probe experiments were conducted at 3 GHz on 10-μm thick films wherein beam steering angles were observed up to ∼50° for a wave number approximating 830 cm−1, for a 10° rotation of the bias field from the collinear situation. Use of the theoretical model applicable to thin film media, which neglects exchange effects, led to good agreement with the experimental results within measurement error.