Short-wavelength Fluctuations Research Articles

Fractonic plaquette-dimer liquid beyond renormalization

We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a z-link or a plaquette in the x-y plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type `higher-rank electrostatics', which can exhibit a plaquette-dimer liquid and an ordered phase. We analyse this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.

Weak line discovered by Voyager 1 in the interstellar medium: Quasi-thermal noise produced by very few fast electrons

A weak continuous line has been recently discovered onboard Voyager 1 in the interstellar medium, whose origin raised two major questions. First, how can this line be produced by plasma quasi-thermal noise on the Voyager short antenna? Second, why does this line emerge at some distance from the heliopause? We provide a simple answer to these questions, which elucidates the origin of this line. First, a minute quantity of supra-thermal electrons, as generally present in plasmas – whence the qualifier ‘quasi-thermal’ – can produce a small plasma frequency peak on a short antenna, of amplitude independent of the concentration of these electrons; furthermore, the detection required long spectral averages, alleviating the smallness of the peak compared to the background. We therefore attribute the observed line to a minute proportion of fast electrons that contribute negligibly to the pressure. Second, we suggest that, up to some distance from the heliopause, the large compressive fluctuations ubiquitous in this region prevent the line to emerge from the statistical fluctuations of the receiver noise because it is blurred out by the averaging required for detection, especially in the presence of short-wavelength density fluctuations. These results open up novel perspectives for interstellar missions, by showing that a minute proportion of fast electrons may be sufficient to measure the density even with a relatively short antenna, because the quietness of the medium enables a large number of spectra to be averaged.

A Statistical Model for Short-Wavelength Collective Chain Fluctuations in a Lipid Bilayer under a High External Electric Field

A Statistical Model for Short-Wavelength Collective Chain Fluctuations in a Lipid Bilayer under a High External Electric Field

Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma

Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.

Influence of fault roughness on surface displacement: from numerical simulations to coseismic slip distributions

SUMMARYField studies have characterized natural faults as rough, non-planar surfaces at all scales. Fault roughness induces local stress perturbations during slip, which dramatically affect rupture behaviour, resulting in slip heterogeneity. However, the relation between fault roughness and slip heterogeneity remains a key knowledge gap between current numerical and field studies. In this study, we analyse numerical simulations of earthquake rupture to determine how roughness influences final slip. Using a rupture catalogue containing thousands of dynamic rupture simulations on band-limited self-similar fractal fault profiles with varying roughness and background shear stress levels, we quantify how fault roughness affects the spectral characteristics of the resulting slip distribution. We find that slip distributions become increasingly more self-affine, that is, containing more short wavelength fluctuations as compared to the self-similar fault profiles, as roughness increases. We also find that, at very short wavelengths (<1 km), the fractal dimension of the slip distributions dramatically changes with increasing roughness, background shear stress, and rupture speed (sub-Rayleigh versus supershear). The existence of a critical wavelength around 1 km, under which more short wavelengths are either preserved or created, suggests the role of rupture process and dynamic effects, together with fault geometry, in controlling the final slip distributions. The same spectral analysis is performed on high-resolution coseismic surface slip distributions from a catalogue of real strike-slip earthquakes. Compared to numerical simulations, all earthquakes feature slip distributions that are much more self-affine than the slip distributions from numerical simulations. A different critical wavelength, here around 5–6 km, appears, potentially informing about a critical asperity length. While we show here that the relation between fault roughness and slip is much more complex than expected, this study is a first attempt at using statistical analyses of numerical simulations on rough faults to investigate observed coseismic slip distributions.

Validation of gyrokinetic simulations of a National Spherical Torus eXperiment H-mode plasma and comparisons with a high-k scattering synthetic diagnostic

A new extensive validation study performed for a modest-beta National Spherical Torus eXperiment (NSTX) neutral beam injection-heated H-mode discharge predicts that electron thermal transport can be entirely explained by short-wavelength electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in conditions of strong and weak ETG turbulence drive. Quantitative comparisons between high-k fluctuation measurements (Smith et al 2008 Rev. Sci. Instrum. 79 123501) and simulations are performed via a novel synthetic high-k diagnostic. Computationally intensive electron-scale simulations featuring an unusually large domain (Lr, Lθ) ∼ (20, 20)ρs are shown to be required for accurate deployment of the synthetic diagnostic. Ion thermal transport is shown to be close to neoclassical levels, consistent with stable ion-scale turbulence simulations conducted with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). Electron-scale GYRO simulations are shown to match the thermal power-balance estimates from TRANSP. The frequency spectra characteristics of electron-scale turbulence (spectral peak and width) can be consistently reproduced by the synthetic spectra, but these reveal not to be a critical constraint on the simulation model. The shape of the high-k wavenumber spectrum and the fluctuation level ratio between the strong and weak ETG conditions can also be simultaneously matched by electron-scale simulations within sensitivity scans about the experimental profile values, and result to be great discriminators of the turbulence models analyzed. Together, electron thermal power comparisons and quantitative agreement of electron-scale turbulence spectra give strong evidence supporting electron-scale ETG fluctuations as the main mechanism driving anomalous electron thermal transport in the two outer-core conditions of the modest-beta NSTX H-mode analyzed.

Cosmological backreaction in spherical and plane symmetric dust-filled space-times

We examine the implementation of Buchert’s and Green & Wald’s averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert’s averaging scheme gives a faithful way of interpreting the large-scale expansion of space, and explicit terms that precisely quantify deviations from the behaviour expected from the Friedmann equations of homogeneous and isotropic cosmological models. The Green & Wald formalism, on the other hand, does not appear to yield any information about the large-scale properties of a given inhomogeneous space-time. Instead, this formalism is designed to calculate the back-reaction effects of short-wavelength fluctuations around a given ‘background’ geometry. We find that the inferred expansion of space in this approach is entirely dependent on the choice of this background, which is not uniquely specified for any given inhomogeneous space-time, and that the ‘back-reaction’ from small-scale structures vanishes in every case we study. This would appear to limit the applicability of Green & Wald’s formalism to the study of large-scale expansion in the real Universe, which also has no pre-defined background. Further study is required to enhance the evaluation and comparison of these averaging formalisms, and determine whether the same difficulties exist, in less idealized space-time geometries.

Micro instabilities and rotating spokes in the near-anode region of partially magnetized plasmas

Electron and ion transport in the near-anode region of a partially magnetized plasma under conditions typical of Hall thrusters or magnetron discharges is studied with fully kinetic, Particle-In-Cell Monte Carlo Collision (PIC-MCC) simulations assuming a uniform magnetic field and no ionization. We derive a simple relation that defines the magnetic field at the transition point between negative and positive sheaths. For magnetic fields around or above this transition point, PIC-MCC simulations show the development of short wavelength azimuthal instabilities that cascade to longer wavelengths (“rotating spokes”) as the magnetic field is increased. Both short-wavelength and large-wavelength fluctuations can coexist under some conditions. A detailed study of the fluid dispersion relation is used to analyze the PIC-MCC results. Small coherent structures can be associated with the destabilization of ion sound waves by density gradient and collisions. Longer wavelengths or rotating spokes are characteristic of the collisionless Simon-Hoh instability. The small structures are dominant for larger plasma density gradients, while the larger structures correspond to smaller density gradients and larger magnetic fields. Anomalous transport associated with these instabilities can be significant, with effective collision frequencies larger than 2×107 s−1 in xenon for magnetic fields above the transition point.

Evolution of statistical properties of microturbulence during transient process under electron cyclotron resonance heating of the L-2M stellarator plasma

The formalism of compound Cox processes was used for statistical analysis of turbulent density fluctuations of plasma during a transient process at electron cyclotron resonance heating of L-2M stellarator plasmas. Short-wavelength (k = 20–30 cm−1) density fluctuations in the central region of the plasma column were measured by the collective backscattering technique. The transient process was caused by sputtering of wall coating and subsequent pulsed impurity injection into the plasma after a step-like increase of the heating power. The evolution of the following parameters was studied: probability density function (PDF) and dynamic and diffusive components of variance of density fluctuations increments. It was found that density fluctuations increments increase simultaneously with average electron density increase and electron temperature decrease during the transient process. It was shown that the PDF of fluctuation increments is characterized by the existence of heavy tails and it can be represented as a composition of four normal laws. Deviation from normal law that happens in the form of random bursts was observed. Duration and frequency of the bursts increases with the level of fluctuation increments and this increase is accompanied by the increase of both components of the variance.

Fluctuations on vertical profiles of the ionospheric electron density perturbed by the March 11, 2011 M9.0 Tohoku earthquake and tsunami

The GPS radio occultation (RO) of FORMOSAT-3/COSMIC (F3/C) with 1–2.5-km-altitude resolution is used to scan fluctuations on vertical profiles of the ionospheric electron density induced by seismic and tsunami waves of the March 11, 2011 M9.0 Tohoku earthquake. The Hilbert–Huang transform is applied to derive the instantaneous wave number and amplitude of the fluctuations in 22 (7 before and 15 after) F3/C profiles within 3000 km in radius from the epicenter during the earthquake. Fluctuations of the vertical electron density profile induced by underneath Rayleigh and tsunami waves and their post-waves are examined. It is found that the right underneath Rayleigh wave can induce significant long-wavelength fluctuations of 50–105 km on the vertical profile of the electron density, while tsunami and their post-waves activate the prominent short-wavelength fluctuations less than 16 km on those profiles in the poleward side of the epicenter. Results show that RO is a powerful tool which is suitable to probe vertical fluctuations in the ionospheric electron density.

Effect of Ni substitute in off-stoichiometric Bi(Pb)-Sr-Ca-Cu(Ni)-O superconductor. Excess conductivity, XRD analysis and thermal behaviour

Two phases (2223 and 2212) are identified in Bi1.8Pb0.3Sr2Ca2(Cu1-xNix)3.3Oy superconductor system, sintered at 847 °C for 322 h, in partial nitrogen atmosphere. The volume fraction of 2223-phase is strongly dependent on Ni doping: 78.37% for x = 0.002, 70.29% for x = 0.005% and 51.13% for x = 0.015. The unit cells of 2223 and 2212 phases were indexed as tetragonal structures, having different lattice constants. Plots of resistance versus temperature (four points method) on cooling to 77 K, evidenced that the critical temperature for the transition to the superconductor phase, Tc, is linearly decreasing from 106.21 to 93.47 K when the Ni content is varying from x = 0.002 to x = 0.03. From log-log plots of the excess-conductivity we calculated the cross-over temperatures between 3D and 2D dimensionality as well as from 2D to SWF (short wavelength fluctuation) behaviour, the coupling factor and the coherence length for all the samples. Thermal analysis of the resulting samples (after the last sintering) was performed by heating each sample from room temperature (RT) to 1000 °C at a rate of 10 K min−1 in dynamic air atmosphere (150 cm3 min−1). A clear dependence on Ni content is seen by TG and DSC, but a relative thermal equilibrium between the two phases, 2223 and 2212, in RT-869 °C range, is observed. Strong endothermic effects (melting accompanied by small decomposition processes) begin at around 869 °C for all Ni doped samples. The results for the specific heat capacities, calculated from DSC plots, are also presented. Contribution of the crystal lattice to the estimated specific heat capacity was in conformity with the Einstein model, the Einstein temperature values being dependent on Ni content.

The Possibility of Measuring Radial-Velocity Fluctuations in a Tokamak Plasma with the Aid of Enhanced Microwave-Scattering Diagnostics

We propose implementing the diagnostics of long-wavelength fluctuations of the radial velocity of tokamak plasma, which is based on Doppler-enhanced microwave scattering by short-wavelength fluctuations entrained by large-scale turbulent flow in the equatorial plane of a tokamak.

Возможность измерения флуктуаций радиальной скорости плазмы в токамаке с помощью диагностики усиленного микроволнового рассеяния

AbstractWe propose implementing the diagnostics of long-wavelength fluctuations of the radial velocity of tokamak plasma, which is based on Döppler-enhanced microwave scattering by short-wavelength fluctuations entrained by large-scale turbulent flow in the equatorial plane of a tokamak.

Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas

Density fluctuations in the large-density-gradient region of improved confinement Madison Symmetric Torus reversed field pinch (RFP) plasmas exhibit multiple features that are characteristic of the trapped-electron mode (TEM). Core transport in conventional RFP plasmas is governed by magnetic stochasticity stemming from multiple long-wavelength tearing modes. Using inductive current profile control, these tearing modes are reduced, and global confinement is increased to that expected for comparable tokamak plasmas. Under these conditions, new short-wavelength fluctuations distinct from global tearing modes appear in the spectrum at a frequency of f ∼ 50 kHz, which have normalized perpendicular wavenumbers k⊥ρs≲0.2 and propagate in the electron diamagnetic drift direction. They exhibit a critical-gradient threshold, and the fluctuation amplitude increases with the local electron density gradient. These characteristics are consistent with predictions from gyrokinetic analysis using the Gene code, including increased TEM turbulence and transport from the interaction of remnant tearing magnetic fluctuations and zonal flow.

Toroidal inhomogeneity of plasma density fluctuations during ECR plasma heating in the L-2M stellarator

Correlation between short-wavelength (k⊥ ≈ 20–30 cm–1) and long-wavelength (k⊥ ≈ 1–2 cm–1) plasma density fluctuations in two poloidal cross sections of the stellarator chamber separated by 1/14 or 5/14 of the torus perimeter was studied using collective scattering of radiation of two 75-GHz gyrotrons and radiation of a 37-GHz Doppler reflectometer at an ECR heating power density of 1.6–3.2 MW/m3. It is found that excitation of turbulent fluctuations is bursty in character and that fluctuations excited in different L-2M cross sections are uncorrelated. It is shown that the energy of turbulent fluctuations is modulated by a low frequency of 5–20 kHz. An idea is put forward that anomalous transport is toroidally inhomogeneous.

Dynamical Instability Causes the Demise of a Supercooled Tetrahedral Liquid

We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric (NPT) Monte Carlo simulations. In similarity with systems which are far from equilibrium but near the onset of jamming (O’Hern et al. in Phys Rev Lett 93:165702, 2004), we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the slope $$[\partial (G/N)/\partial \phi ]$$ of the Gibbs free energy (G) at a unique value of per particle potential energy $$\phi = \phi _{{\tiny mid}}$$ . The short-wavelength (fast) fluctuations are controlled by the bath temperature T. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than $$\phi _{{\tiny mid}}$$ . The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate stage of relaxation). Because of the condition [ $$\partial ^2 (G/N)/\partial \phi ^2 = 0$$ ] at $$\phi = \phi _{{\tiny mid}}$$ , the slope $$[\partial (G/N)/\partial \phi ]$$ has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at $$\phi _{{\tiny mid}}$$ , i.e., the condition that G decreases as configurations with potential energies lower than $$\phi _{{\tiny mid}}$$ are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.

Reaction of turbulence at the edge and in the center of the plasma column to pulsed impurity injection caused by the sputtering of the wall coating in L-2M stellarator

Impurity injection into plasma caused by the sputtering of the wall coating in the L-2M stellarator during auxiliary electron cyclotron resonance heating leads to a change in the level of plasma density fluctuations with frequencies above 0.25 MHz: suppression of long-wavelength (k ⊥ = 2 cm–1) density fluctuations in the edge plasma, intensification of short-wavelength (k ⊥ = 30 cm–1) and long-wavelength (k ⊥ = 1 cm–1) fluctuations at the midradius of the plasma column, and intensification of short-wavelength fluctuations (k ⊥ = 20 cm–1) in the plasma center (including the gyroresonance region). At the same time, the level of fluctuations with frequencies below 0.25 MHz remains unchanged. In the edge plasma, a decrease in the plasma potential and suppression of its fluctuations is observed during impurity injection, which also causes an increase in MHD activity.

2D particle-in-cell simulations of the electron drift instability and associated anomalous electron transport in Hall-effect thrusters

In this work we study the electron drift instability in Hall-effect thrusters (HETs) using a 2D electrostatic particle-in-cell (PIC) simulation. The simulation is configured with a Cartesian coordinate system modeling the radial-azimuthal () plane for large radius thrusters. A magnetic field, , is aligned along the Oy axis (r direction), a constant applied electric field, , along the Oz axis (perpendicular to the simulation plane), and the direction is along the Ox axis (θ direction). Although electron transport can be well described by electron–neutral collisions for low plasma densities, at high densities (similar to those in typical HETs), a strong instability is observed that enhances the electron cross-field mobility; even in the absence of electron–neutral collisions. The instability generates high frequency (of the order of MHz) and short wavelength (of the order of mm) fluctuations in both the azimuthal electric field and charged particle densities, and propagates in the direction with a velocity close to the ion sound speed. The correlation between the electric field and density fluctuations (which leads to an enhanced electron–ion friction force) is investigated and shown to be directly responsible for the increased electron transport. Results are compared with a recent kinetic theory, showing good agreement with the instability properties and electron transport.

Mutual synchronization of nano-oscillators driven by pure spin current

We report the experimental observation of mutual synchronization of magnetic nano-oscillators driven by pure spin current generated by nonlocal spin injection. We show that the oscillators efficiently synchronize due to the direct spatial overlap of the dynamical modes excited by the spin current, which is facilitated by the large size of the auto-oscillation area inherent to these devices. The synchronization occurs within an interval of the driving current determined by the competition between the dynamic nonlinearity that facilitates synchronization and the short-wavelength magnetic fluctuations enhanced by the spin current that suppress synchronization. The demonstrated synchronization effects can be utilized to control the spatial and spectral characteristics of the dynamical states induced by the spin currents.

Reflection and backscattering of microwaves under doubling of the plasma density and displacement of the gyroresonance region during electron cyclotron resonance heating of plasma in the l-2M stellarator

Reflection and backscattering of high-power (400 kW) gyrotron radiation creating and heating plasma at the second harmonic of the electronic cyclotron frequency in the L-2M stellarator have been investigated experimentally. The effect of the displacement of the gyroresonance region from the axis of the plasma column under doubling of the plasma density on the processes of reflection and backscattering of microwave radiation has been examined. A near doubling of short-wavelength (k⊥ ≈ 30 cm–1) turbulent density fluctuations squared is observed. The change in the energy confinement time under variations of plasma parameters and characteristics of short-wavelength turbulence is discussed. A discrepancy between the measured values of the reflection coefficient from the electron cyclotron resonance heating region and predictions of the one-dimensional model is revealed.