Perpendicular Scale Research Articles

Effects of wave damping and finite perpendicular scale on three-dimensional Alfvén wave parametric decay in low-beta plasmas

Effects of wave damping and finite perpendicular scale on three-dimensional Alfvén wave parametric decay in low-beta plasmas

New Regime of Inertial Alfvén Wave Turbulence in the Auroral Ionosphere.

We investigate a new regime of inertial Alfvén wave turbulence observed in the very low beta plasma of the auroral ionosphere using electric and magnetic field measurements by the TRICE-2 sounding rocket. Combining the observed features of the electric and magnetic field frequency spectra with the linear properties of inertial Alfvén waves, we deduce the path of the anisotropic turbulent cascade through wave vector space. We find a critically balanced cascade through the magnetohydrodynamic scales of the inertial range down to the perpendicular scale of the plasma skin depth, followed by a parallel cascade to the ion inertial length. We infer damping of the cascade by a combination of proton cyclotron damping and electron Landau damping.

Mind the gap: non-local cascades and preferential heating in high-β Alfvénic turbulence

ABSTRACT Characterizing the thermodynamics of turbulent plasmas is key to decoding observable signatures from astrophysical systems. In magnetohydrodynamic (MHD) turbulence, non-linear interactions between counter-propagating Alfvén waves cascade energy to smaller spatial scales where dissipation heats the protons and electrons. When the thermal pressure far exceeds the magnetic pressure, linear theory predicts a spectral gap at perpendicular scales near the proton gyroradius where Alfvén waves become non-propagating. For simple models of an MHD turbulent cascade that assume only local non-linear interactions, the cascade halts at this gap, preventing energy from reaching smaller scales where electron dissipation dominates, leading to an overestimate of the proton heating rate. In this work, we demonstrate that non-local contributions to the cascade, specifically large-scale shearing and small-scale diffusion, can bridge the non-propagating gap, allowing the cascade to continue to smaller scales. We provide an updated functional form for the proton-to-electron heating ratio accounting for this non-local energy transfer by evaluating a non-local weakened cascade model over a range of temperature and pressure ratios. In plasmas where the thermal pressure dominates the magnetic pressure, we observe that the proton heating is moderated compared to the significant enhancement predicted by local models.

Nonlinear electron scattering by electrostatic waves in collisionless shocks

We present a theoretical analysis of electron pitch-angle scattering by ion-acoustic electrostatic fluctuations present in the Earth's bow shock and, presumably, collisionless shocks in general. We numerically simulate electron interaction with a single wave packet to demonstrate the scattering through phase bunching and phase trapping and quantify electron pitch-angle scattering in dependence on the wave amplitude and wave normal angle to the local magnetic field. The iterative mapping technique is used to model pitch-angle scattering of electrons by a large number of wave packets, which have been reported in the Earth's bow shock. Assuming that successive electron scatterings are not correlated, we revealed that the long-term dynamics of electrons is diffusive. The diffusion coefficient depends on the ratio $\varPhi _0/W$ between the wave packet amplitude and electron energy, $D\propto (\varPhi _0/W)^{\nu }$ . A quasi-linear scaling ( $\nu \approx 2$ ) is observed for sufficiently small wave amplitudes, $\varPhi _0\lesssim 10^{-3}W$ , while the diffusion is nonlinear ( $1<\nu <2$ ) above this threshold. We show that pitch-angle diffusion of ${\lesssim }1$ keV electrons in the Earth's bow shock can be nonlinear. The corresponding diffusion coefficient scales with the intensity $E_{w}^{2}$ of the electrostatic fluctuations in a nonlinear fashion, $D\propto E_{w}^{\nu }$ with $\nu <2$ , while its expected values in the Earth's bow shock are $D\sim 0.1\unicode{x2013}100$ $(T_{e}/W)^{\nu -1/2}\,{\rm rad}^{2}\,{\rm s}^{-1}$ . We speculate that in the Earth's quasi-perpendicular bow shock the stochastic shock drift acceleration mechanism with pitch-angle scattering provided by the electrostatic fluctuations can contribute to the acceleration of thermal electrons up to approximately 1 keV. The potential effects of a finite perpendicular coherence scale of the wave packets on the efficiency of electron scattering are discussed.

Scale invariance and critical balance in electrostatic drift-kinetic turbulence

The equations of electrostatic drift kinetics are observed to possess a symmetry associated with their intrinsic scale invariance. Under the assumptions of spatial periodicity, stationarity, and locality, this symmetry implies a particular scaling of the turbulent heat flux with the system's parallel size, from which its scaling with the equilibrium temperature gradient can be deduced under some additional assumptions. This macroscopic transport prediction is then confirmed numerically for a reduced model of electron-temperature-gradient-driven turbulence in slab geometry. The system realises this scaling through a turbulent cascade from large to small perpendicular spatial scales. The route of this cascade through wavenumber space (i.e. the relationship between parallel and perpendicular scales in the inertial range) is shown to be determined by a balance between nonlinear-decorrelation and parallel-dissipation timescales. This type of ‘critically balanced’ cascade, which maintains a constant energy flux despite the presence of parallel dissipation throughout the inertial range (as well as order-unity dissipative losses at the outer scale) is expected to be a generic feature of plasma turbulence. The outer scale of the turbulence, on which the turbulent heat flux depends, is determined by the breaking of drift-kinetic scale invariance due to the existence of large-scale parallel inhomogeneity (the parallel system size).

Multi-scale dissection of wing transparency in the clearwing butterfly Phanus vitreus.

Optical transparency is rare in terrestrial organisms, and often originates through loss of pigmentation and reduction in scattering. The coloured wings of some butterflies and moths have repeatedly evolved transparency, offering examples of how they function optically and biologically. Because pigments are primarily localized in the scales that cover a colourless wing membrane, transparency has often evolved through the complete loss of scales or radical modification of their shape. Whereas bristle-like scales have been well documented in glasswing butterflies, other scale modifications resulting in transparency remain understudied. The butterfly Phanus vitreus achieves transparency while retaining its scales and exhibiting blue/cyan transparent zones. Here, we investigate the mechanism of wing transparency in P. vitreus by light microscopy, focused ion beam milling, microspectrophotometry and optical modelling. We show that transparency is achieved via loss of pigments and vertical orientation in normal paddle-like scales. These alterations are combined with an anti-reflective nipple array on portions of the wing membrane being more exposed to light. The blueish coloration of the P. vitreus transparent regions is due to the properties of the wing membrane, and local scale nanostructures. We show that scale retention in the transparent patches might be explained by these perpendicular scales having hydrophobic properties.

Lateral line abnormality in Common snook Centropomus undecimalis (Bloch, 1792) from The Southern Gulf of Mexico

The first cases of anomalous lateral line in 3 male Common Snook, Centropomus undecimalis, in the southern Gulf of Mexico are described. On October 12, 2022, August 15, 2023 and October 11, 2023, 3 adult male Common Snook were observed with obvious lateral line anomalies during the monitoring of artisanal fisheries in the state of Campeche, Mexico. One of the specimens presented a bi-branched lateral line; another specimen exhibited 2 perpendicular tubular scales under the lateral line with a similar shape to regenerating scales, and the last specimen had a secondary tubular scale on the upper lateral line. The cause of these anomalies could be environmental stress or poor health following an injury. More intensive monitoring of the commercial fishery is needed to determine the possible causes of these anomalies.

A novel approach to radially global gyrokinetic simulation using the flux-tube code stella

A novel approach to global gyrokinetic simulation is implemented in the flux-tube code stella. This is done by using a subsidiary expansion of the gyrokinetic equation in the perpendicular scale length of the turbulence, originally derived by Parra and Barnes (2015) [23], which allows the use of Fourier basis functions while enabling the effect of radial profile variation to be included in a perturbative way. Radial variation of the magnetic geometry is included by utilizing a global extension of the Grad-Shafranov equation and the Miller equilibrium equations which is obtained through Taylor expansion. Radial boundary conditions that employ multiple flux-tube simulations are also developed, serving as a more physically motivated replacement to the conventional Dirichlet radial boundary conditions that are used in global simulation. It is shown that these new boundary conditions eliminate much of the numerical artefacts generated near the radial boundary when expressing a non-periodic function using a spectral basis. We then benchmark the new approach both linearly and non-linearly using a number of standard test cases.

Large‐Scale High‐Speed Jets in Earth's Magnetosheath: Global Hybrid Simulations

AbstractHigh‐speed jets (HSJs) occur frequently in Earth's magnetosheath downstream of the quasiparallel bow shock. They have great impacts on the magnetosheath and the magnetosphere. Using two‐dimensional global hybrid simulations, we investigate the formation and evolution of HSJs with different solar wind conditions. When the quasi‐parallel shock is formed, HSJs begin to appear in the quasi‐parallel magnetosheath. Some elongated HSJs formed at the quasi‐parallel bow shock extend toward the quasi‐perpendicular magnetosheath along with the background magnetosheath flow. As the elongated HSJs moves in the magnetosheath, filamentary structures of the velocity, ion density, and temperature occur in the magnetosheath. The filamentary structures are the traces of HSJs moving in the magnetosheath. Moreover, the Kelvin‐Helmholtz instability can be excited at HSJs, which causes meandering of HSJs. When the interplanetary magnetic field is aligned to the solar wind velocity, the large‐scale HSJs with a parallel (perpendicular) scale size of about 2.5 RE (0.3 RE) are formed at the magnetosheath where the θBn is approaching zero. Then, some HSJs converge, leading to the formation of even larger HSJs with a parallel (perpendicular) scale size of 5 RE (0.6 RE).

Initiation of Alfvénic turbulence by Alfvén wave collisions: A numerical study

In the framework of compressional magnetohydrodynamics (MHD), we numerically studied the commonly accepted presumption that the Alfvénic turbulence is generated by the collisions between counter-propagating Alfvén waves (AWs). In the conditions typical for the low-beta solar corona and inner solar wind, we launched two counter-propagating AWs in the three-dimensional simulation box and analyzed polarization and spectral properties of perturbations generated before and after AW collisions. The observed post-collisional perturbations have different polarizations and smaller cross-field scales than the original waves, which supports theoretical scenarios with direct turbulent cascades. However, contrary to theoretical expectations, the spectral transport is strongly suppressed at the scales satisfying the classic critical balance of incompressional MHD. Instead, a modified critical balance can be established by colliding AWs with significantly shorter perpendicular scales. We discuss consequences of these effects for the turbulence dynamics and turbulent heating of compressional plasmas. In particular, solar coronal loops can be heated by the strong turbulent cascade if the characteristic widths of the loop substructures are more than ten times smaller than the loop width. The revealed new properties of AW collisions have to be incorporated in the theoretical models of AW turbulence and related applications.

On the formation of quasi-parallel shocks, magnetic and electric field turbulence, and the ion energization mechanism

ABSTRACT The analysis of four-point measurements by the NASA Magnetospheric Multiscalespacecraft reveals that the formation of quasi-parallel shocks is consistent with the counter-streaming ion–ion resonant right-handed instability. The counter-streaming occurs between the incoming solar wind and a diffuse hot ion population moving upstream. It is found that the onset of the instability is initiated by 30 s period oscillations, which steepen to shorter wavelengths and higher frequencies. The turbulent cascade in the electric field ranges from 0.01 Hz to a few kHz. The dominant frequency of the instability in the magnetic field is observed around the proton cyclotron frequency, consistent with the theoretical predictions. The instability produces large amplitude magnetic field and plasma density shocklets with the perpendicular scale length of 300 km (3 proton gyroradii) and the parallel scale length three times larger. The active acceleration regions are characterized by non-gyrotropic ion populations in the velocity space, in addition to the solar wind beam and a diffuse hot beam propagating upstream. We show that non-gyrotropic ion populations are consistent with the $ExB$ wave energization mechanism that can both heat bulk plasma and accelerate some ions to the observed energies of 200 keV.

Universal L−3 finite-size effects in the viscoelasticity of amorphous systems

We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus $G'$. The nonaffine contribution is written as a sum over modes in $k$-space. With a rigorous argument based on the analysis of the $k$-space integral over modes, it is shown that the confinement size $L$ in one spatial dimension, e.g. the $z$ axis, leads to a infrared cut-off for the modes contributing to the nonaffine (softening) correction to the modulus that scales as $L^{-3}$. Corrections for finite sample size $D$ in the two perpendicular dimensions scale as $\sim (L/D)^4$, and are negligible for $L \ll D$. For liquids it is predicted that $G'\sim L^{-3}$ in agreement with a previous more approximate analysis, whereas for amorphous materials $G' \sim G'_{bulk} + \beta L^{-3}$. For the case of liquids, four different experimental systems are shown to be very well described by the $L^{-3}$ law.

MMS Observations of Broadband Electrostatic Waves in Electron Diffusion Region of Magnetotail Reconnection

AbstractIn this study, the broadband electrostatic waves are observed in electron diffusion region (EDR). Detailed analysis has shown that the parallel electric field of these waves have a bipolar or continuous steepening waveform. The bipolar structures of the parallel electric field are usually accompanied by electron holes (EHs) in phase space. The parallel spatial scales of EHs are ∼3–5 ( is the Debye length), and the perpendicular spatial scales are larger than ∼18.6 . Therefore, the length ratios are larger than ∼3.7–6.2, which means that the EHs have oblate shapes. Associated with these plasma waves, electron beams propagating away from the X‐line have been observed. By performing a one‐dimensional (1‐D) electrostatic particle‐in‐cell simulation of the bump‐on‐tail instability, we reproduce two types of waveforms similar to those observed in the EDR during the different evolution stage of the instability, which implies that these electrostatic waves are generated by the bump‐on‐tail instabilities.

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the arbitrarily large deviations from thermal equilibrium that are present in the plasma periphery of tokamak devices. The formulation of the gyrokinetic model is based on a second-order accurate description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behaviour of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function. The collisional effects are included by a nonlinear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a Hermite–Laguerre velocity-space polynomial basis. Then, the gyrokinetic equation is projected onto the same basis yielding the spatial and temporal evolution of the Hermite–Laguerre expansion coefficients. A closed set of fluid equations for the lowest-order coefficients is presented. The Hermite–Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell equations derived from a variational principle where the velocity integrals are explicitly evaluated.

The Relationship Between Cusp Region Ion Outflows and East‐West Magnetic Field Fluctuations at 4,000‐km Altitude

AbstractA number of interdependent conditions and processes contribute to ionospheric‐origin energetic ( 10 eV to several keV) ion outflows. Due to these interdependences and the associated observational challenges, energetic ion outflows remain a poorly understood facet of atmosphere‐ionosphere‐magnetosphere coupling. Here we demonstrate the relationship between east‐west magnetic field fluctuations ( ) and energetic outflows in the magnetosphere‐ionosphere transition region. We use dayside cusp region FAST satellite observations made near apogee ( 4,180‐km altitude) near fall equinox and solstices in both hemispheres to derive statistical relationships between ion upflow and spectral power as a function of spacecraft frame frequency bands between 0 and 4 Hz. Identification of ionospheric‐origin energetic ion upflows is automated, and the spectral power in each frequency band is obtained via integration of power spectral density. Derived relationships are of the form for upward ion flux at 130‐km altitude, with the mapped upward ion flux for a nominal spectral power nT . The highest correlation coefficients are obtained for spacecraft frame frequencies 0.1–0.5 Hz. Summer solstice and fall equinox observations yield power law indices 0.9–1.3 and correlation coefficients , while winter solstice observations yield 0.4–0.8 with . Mass spectrometer observations reveal that the oxygen/hydrogen ion composition ratio near summer solstice is much greater than the corresponding ratio near winter. These results reinforce the importance of ion composition in outflow models. If observed perturbations result from Doppler‐shifted wave structures with near‐zero frequencies, we show that spacecraft frame frequencies 0.1–0.5 Hz correspond to perpendicular spatial scales of several to tens of kilometers.

Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

In an earlier paper (Wan et al., J. Fluid Mech., vol. 697, 2012, pp. 296–315), the authors showed that a similarity solution for anisotropic incompressible three-dimensional magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\boldsymbol{B}_{0}$, exists if the ratio of parallel to perpendicular (with respect to $\boldsymbol{B}_{0}$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor–Kármán-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, mean field strength, and cross-helicity, on the nature of similarity decay is discussed.

Hybrid Simulations of Magnetodisc Transport Driven by the Rayleigh‐Taylor Instability

AbstractPlasma transport in the rapidly rotating giant magnetospheres is thought to involve a centrifugally driven flux tube interchange instability, similar to the Rayleigh‐Taylor (RT) instability. In three dimensions, the convective flow patterns associated with the RT instability can produce strong guide field reconnection, allowing plasma mass to move radially outward while conserving magnetic flux (Ma et al., 2016, https://doi.org/10.1002/2015JA022122). We present a set of hybrid (kinetic ion/fluid electron) plasma simulations of the RT instability using high plasma beta conditions appropriate for the inner and middle magnetosphere at Jupiter and Saturn. A density gradient, combined with a centrifugal force, provide appropriate RT onset conditions. Pressure balance requires only a temperature gradient as the magnetic pressure is constant. Pressure balance is achieved with a temperature gradient in a fixed magnetic field. The three‐dimensional simulation domain represents a local volume of the magnetodisc resonant cavity. Simulated RT growth rates compare favorably with linear theory, where the fundamental mode of the resonant cavity determines the largest (stabilizing) parallel wavelength. We suggest that the perpendicular scale of RT structures is determined by the fundamental mode, which limits growth due to magnetic tension. Finally, we investigated strong guide field magnetic reconnection and diffusive processes as plausible mechanisms to facilitate kinetic‐scale radial transport.

Multispacecraft Analysis of Electron Holes

AbstractElectron holes (EHs) are nonlinear electrostatic structures in plasmas. Most previous in situ studies of EHs have been limited to single‐ and two‐spacecraft methods. We present statistics of EHs observed by Magnetospheric Multiscale on the magnetospheric side of the magnetopause during October 2016 when the spacecraft separation was around 6 km. Each EH is observed by all four spacecraft, allowing EH properties to be determined with unprecedented accuracy. We find that the parallel length scale, l∥, scales with the Debye length. The EHs can be separated into three groups of speed and potential based on their coupling to ions. We present a method for calculating the perpendicular length scale, l⊥. The method can be applied to a small subset of the observed EHs for which we find shapes ranging from almost spherical to more oblate. For the remaining EHs we use statistical arguments to find l⊥/l∥≈5, implying dominance of oblate EHs.

Simultaneous Multispacecraft Probing of Electron Phase Space Holes

AbstractWe present a series of electron holes observed simultaneously on four Magnetospheric Multiscale spacecraft in the plasma sheet boundary layer. The multispacecraft probing shows that the electron holes propagated quasi‐parallel to the local magnetic field with velocities of a few thousand kilometers per second with parallel spatial scales of a few kilometers (a few Debye lengths). The simultaneous multispacecraft probing allows analyzing the 3‐D configuration of the electron holes. We estimate the electric field gradients and charge densities associated with the electrons holes. The electric fields are fit to simple 3‐D electron hole models to estimate their perpendicular scales and demonstrate that the electron holes were generally not axially symmetric with respect to the local magnetic field. We emphasize that most of the electron holes had a complicated structure not reproduced by the simple models widely used in single‐spacecraft studies.

A Model for Solar Wind Structure and Dynamics Based on Alfvén Wave Turbulence

We present a 3D reduced magnetohydrodynamic (RMHD) model of reflection-driven Alfvén wave turbulence in an open magnetic field at the center of a coronal hole. The non-linear interactions between outward (dominant) and inward (minority) propagating waves generate turbulence. The RMHD equations describing the turbulence include the effects of solar wind outflow velocity on the dissipation of waves. The Alfvén wave turbulence results in the transfer of energy to small perpendicular scales (“direct cascade”) or to larger scales (“inverse cascade”). We first show the result of our calculation for a model where there is smooth variation of plasma parameters such as Alfvén speed and density with height along the flux tube. However, this model does not produce the required energy to heat the plasma and accelerate the fast solar wind. Therefore, we introduce our second model, where we include additional density fluctuation along the open field. These density variations simulate the effects of compressive MHD waves in the solar wind. We find that these variations in density enhance the turbulence dissipation rates, and thereby increase the heating rate and the acceleration of the solar wind.