Perturbation Amplitude Research Articles

Effects of external kink and fishbone-like modes on energetic particle transport in tokamak plasmas

Transport and loss of beam injected energetic particles (EPs) due to three-dimensional perturbations, associated with the external kink (XK) instability and fishbone-like mode (FLM), are numerically investigated utilizing the guiding center following code ORBIT for static toroidal plasmas in HL-2A. The perturbation structure for the XK is computed by the MARS-F code and then mapped to the Boozer coordinates as defined in ORBIT. The simulation shows that the EP profile experiences a significant change in the middle of the plasma column, when the XK-induced radial magnetic field perturbation amplitude, normalized by the equilibrium field, exceeds a threshold value of about . The EP transport is found to be dominated by a diffusion process instead of convection. Furthermore, by scanning the perturbation frequency as a free parameter while maintaining the XK mode structure (thus mimicking the FLM as observed in DIII-D and JT-60U tokamaks), redistribution and loss of EPs are found to be substantially enhanced due to strong resonances between the FLM and EPs, when the mode frequency exceeds a threshold value of ∼2 kHz for the case considered. For either XK or FLM, the response of passing EPs to the perturbation is dominant due to the assumed tangential neutral beam injection. Most lost EPs due to these instabilities are initially passing particles but are eventually lost through trapped orbits.

The impact of the initial core temperature on protostellar disc fragmentation

ABSTRACT Ground-based and satellite observations have revealed dust temperatures as low as ∼5−7 K in the centre of low-mass, pre-stellar cloud cores, where star formation takes place. However, external heating may rise the outer core temperatures up to ∼15−20 K. Such low temperatures at the centre of pre-stellar cores are a key factor to constrain the conditions that lead to the formation of gravitationally bound protostellar systems as was recently captured by highly-resolved Atacama large millimeter/submillimeter array observations. Here, we report consistent smoothed particle hydrodynamics collapse calculations of cold cores that demonstrate the formation of close protobinary systems via small-scale fragmentation of a gravitationally unstable protostellar disc. The results indicate that mean binary separations, of tens of astronomical units, are a consequence of disc fragmentation in cold pre-stellar cores. Cloud cores initially with temperatures ≤6 K and a low amplitude (a = 0.1), m = 2 density perturbation formed close protobinaries that were followed deep into the non-isothermal collapse for several orbital periods and appeared to survive as independent stellar entities. At temperatures ≥7 K disc fragmentation is no longer observed and the calculations terminate with the formation of a wide protobinary, which may occasionally be accompanied by small substellar objects emerging by fragmentation of the circumbinary disc. When the perturbation amplitude is raised to a = 0.25, disc fragmentation occurs again only in cores with initial temperatures ≤6 K. Therefore, increasing the perturbation amplitude does not necessarily imply that there will be disc fragmentation at higher core temperatures.

Coronal seismology by slow waves in non-adiabatic conditions

Slow magnetoacoustic waves represent an important tool for probing the solar coronal plasma. The majority of seismological methods with slow waves are based on a weakly non-adiabatic approach, which assumes the coronal energy transport has only weak effects on the wave dynamics. Despite it significantly simplifies the application of coronal seismology by slow waves, this assumption omits a number of important and confidently observed effects and thus puts strong limitations on the reliability of seismological estimations. We quantitatively assess the applicability of the weak thermal conduction theory to coronal seismology by slow waves. We numerically model the linear standing slow wave in a 1D coronal loop, with field-aligned thermal conduction κ‖ as a free parameter and no restrictions on its efficiency. The time variations of the perturbed plasma parameters, obtained numerically with full conductivity, are treated as potential observables and analysed with the standard data processing techniques. The slow wave oscillation period is found to increase with κ‖ by about 30%, indicating the corresponding modification in the effective wave speed, which is missing from the weak conduction theory. Phase shifts between plasma temperature and density perturbations are found to be well consistent with the approximate weakly conductive solution for all considered values of κ‖. In contrast, the comparison of the numerically obtained ratio of temperature and density perturbation amplitudes with the weak theory revealed relative errors up to 30–40%. We use these parameters to measure the effective adiabatic index of the coronal plasma directly as the ratio of the effective slow wave speed to the standard sound speed and in the polytropic assumption, which is found to be justified in a weakly conductive regime only, with relative errors up to 14% otherwise. The damping of the initial perturbation is found to be of a non-exponential form during the first cycle of oscillation, which could be considered as an indirect signature of entropy waves in the corona, also not described by weak conduction theory. The performed analysis and obtained results offer a more robust scheme of coronal seismology by slow waves, with reasonable simplifications and without the loss of accuracy.

Experimental study on a light–heavy interface evolution induced by two successive shock waves

Richtmyer–Meshkov instability induced by two successive shock waves is experimentally studied in a specific shock tube. To create two successive shock waves synchronously, a driver section is added between the driver and driven sections of the standard shock tube, and an electronically controlled membrane rupture equipment is adopted. The shock-tube flow after the membranes rupture is well described by combining the shock relations, isentropic wave relations with compatibility relations across the contact surface (region). The new shock tube is capable of generating two successive shock waves with controllable strengths and time interval, and provides a relatively ‘clean’ wave system. Then the developments of single-mode light–heavy interfaces with different initial conditions induced by two successive shock waves are investigated. The initial amplitudes are all small enough such that the first-shocked interface is within the linear growth regime at the arrival of the second shock. The results show that if the pre-second-shock perturbation amplitude is small, the linear, nonlinear and modal evolutions of the double-shocked interface can be reasonably predicted by the existing models proposed for predicting the perturbation growth induced by a single shock. For the double-shocked interface, the second shock provides an additional perturbation velocity field to the original one introduced by the first shock impact. The validity of the linear superposition model indicates that the linear superposition of these two perturbation velocity fields is satisfied. Therefore, a double-shocked interface evolves similarly to a single-shocked interface provided that their postshock amplitudes and linear growth rates are the same.

Dynamics of a single-phase natural circulation system under harmonic excitation.

A natural circulation system (NCS) has a broad application in the sector of thermal engineering, for example, in nuclear reactors due to its capability in transferring heat without any support of external power or a mechanical device. NCSs, although designed for steady operation, have been found to exhibit dynamical behavior, such as periodic oscillations, depending on the input heater power. The heater power, otherwise assumed to be steady, can be fluctuating in practice. The present study focuses on the dynamics of a single-phase square NCS, which exhibits periodic dynamics and is subjected to an external harmonic perturbation (chosen as the simplest form of fluctuation) over the steady heater power. The objective of the study is to study the dynamics of NCS under external (harmonic) disturbances using the framework of forced synchronization. Toward that, a 1D transient model of a square-shaped NCS is simulated with harmonically forced input power. The transition in the nature of synchronization between mass flux oscillations and the external forcing has been characterized by varying the frequency and amplitude of external perturbation independently. We find different nonlinear effects of the harmonic forcing, such as exhibition of quasiperiodic dynamics, frequency pulling/pushing, and frequency locking or forced synchronization. The aforementioned characterization techniques open up an avenue for detailed analysis of the more complex type of fluctuating input heat in real systems.

Sensitivity of wave merging and mixing to initial perturbations in Holmboe instabilities

Initial perturbations are commonly used in direct numerical simulations (DNS) to trigger the shear instability of stratified fluids. We investigate the effects of initial perturbations on the evolution of Holmboe instabilities with DNS. In particular, we model the interaction between a primary Holmboe wave and a subharmonic component that has a wavelength double that of the primary wave. We show that the phase difference and the amplitude of the primary and subharmonic components of the initial perturbation control the merging of Holmboe instabilities, which, in turn, influence diapycnal mixing in stratified flows. The amplitude difference has a more significant effect on the merging of Holmboe instabilities compared to the initial phase difference. For a given amplitude of the primary perturbation, a larger subharmonic perturbation results in an earlier merging event. In three-dimensional simulations, this preference of the subharmonic initial perturbation increased the amplitude of Holmboe waves by a factor of two. Although the subharmonic mode grows slower, it grows for longer producing more net mixing.

Application of dislocation-based constitutive model into research of dynamic mechanical behavior under shock loading

To understand the plastic deformation mechanism of an FCC metal (pure aluminum) under shock loading and describe its dynamic mechanical behavior accurately, a multiscale constitutive model based on the dislocation substructure is developed, which comprehensively considers the controlling mechanisms of dislocation motion and dislocation evolution. Then, the model is extended to the loading of strong shock waves by incorporating the homogeneous nucleated dislocation within the constitutive framework. The model parameters are successfully determined by the normal plate impact experiments with different thicknesses of specimens. Additionally, shock front perturbation decay experiments are performed using a line velocity interferometer system for any reflector, where the modulated surface of the specimen is subjected to a laser-driven loading. Then, the model is applied to reproduce the perturbation decay of shock fronts in experiments. During the post-process of simulated results, the method based on the pressure gradient is used to determine the amplitude and the location of distributed shock fronts. The extended model shows promise as an effective method to figure out the role of strength (shear response) on the evolution of perturbation amplitude.

Perturbations in the interacting vacuum

In this study, we present the evolution of cosmological perturbations in a universe consisting of standard matter and interacting vacuum. We use the 1 + 3 covariant formalism in perturbation framework and consider two different models for the interacting vacuum; namely, a linear interacting model and interaction with creation pressure model. For both models, we derive the evolution equations governing the growth of linear perturbations for both radiation- and dust-dominated universe. We find numerical solutions in appropriate limits, namely long and short wavelengths. For both models, the perturbations grow with time (decay with redshift), showing that structure formation is possible in an accelerated cosmic background. The perturbation amplitudes — and their relative scalings with those of [Formula: see text]CDM — depend on the values of the interaction parameters considered, and in a way that can be used to constrain the models using existing and future large-scale structure data. In the vanishing limits of the coupling parameters of the interaction, we show that standard [Formula: see text]CDM cosmology, both background and perturbed, is recovered.

Ensemble quantification of short-term predictability of the ocean dynamics at a kilometric-scale resolution: a Western Mediterranean test case

Abstract. We investigate the predictability properties of the ocean dynamics using an ensemble of short-term numerical regional ocean simulations forced by prescribed atmospheric conditions. In that purpose, we developed a kilometric-scale, regional model for the Western Mediterranean sea (MEDWEST60, at 1/60∘ horizontal resolution). A probabilistic approach is then followed, where a stochastic parameterization of model uncertainties is introduced in this setup to initialize ensemble predictability experiments. A set of three ensemble experiments (20 members and 2 months) are performed, one with the deterministic model initiated with perturbed initial conditions and two with the stochastic model, for two different amplitudes of stochastic model perturbations. In all three experiments, the spread of the ensemble is shown to emerge from the smallest scales (kilometric scale) and progressively upscales to the largest structures. After 2 months, the ensemble variance saturates over most of the spectrum, and the small scales (<100 km) have become fully decorrelated across the ensemble members. These ensemble simulations can provide a statistical description of the dependence between initial accuracy and forecast accuracy for time lags between 1 and 20 d. The predictability properties are assessed using a cross-validation algorithm (i.e., using alternatively each ensemble member as the reference truth and the remaining 19 members as the ensemble forecast) together with a given statistical score to characterize the initial and forecast accuracy. From the joint distribution of initial and final scores, it is then possible to quantify the probability distribution of the forecast score given the initial score or reciprocally to derive conditions on the initial accuracy to obtain a target forecast accuracy. The misfit between ensemble members is quantified in terms of overall accuracy (CRPS score), geographical position of the ocean structures (location score) and spatial spectral decorrelation of the sea surface height 2-D fields (decorrelation score). With this approach, we estimate for example that, in the region and period of interest, the initial location accuracy required (necessary condition) with a perfect model (no model uncertainty) to obtain a location accuracy of the forecast of 10 km with a 95 % confidence is about 8 km for a 1 d forecast, 4 km for a 5 d forecast and 1.5 km for a 10 d forecast, and this requirement cannot be met with a 15 d or longer forecast.

POLARIZATION FEATURES OF ANISOTROPIC BRAGG LIGHT DIFFRACTION ON TRANSMISSIVE HOLOGRAPHIC PHASE GRATINGS

We established that for anisotropic Bragg light diffraction on holographic phase gratings for significant perturbation amplitudes of the refractive index of the medium, in the transmitted diffraction orders there is a significant rotation of the polarization plane of the diffracted wave, which is absent in the reflected diffraction orders. It is shown that periodic changes in the transmission coefficients of diffracted waves with a change in the azimuth of polarization of incident light are due to a significant difference in the Fresnel reflection coefficients at the layer boundaries for s- and p-components of incident light; these periodic changes are absent in the reflected diffraction orders.

Unitarizing non-relativistic Coulomb scattering

We compare the exactly solvable nonrelativistic Coulomb scattering with two recent unitarization methods for infinite-range forces. These methods require to calculate perturbatively the corresponding partial-wave amplitudes, which are then unitarized. We calculate the Coulomb partial-wave amplitudes up to the one-loop order. On the one hand, the unitarization method developed by Refs. [1,2] reproduces properly the exact solution, with an accuracy improving as the order in the perturbative calculation of the input perturbative partial-wave amplitudes increases. This is also shown to be the case for the pole position of the ground state. On the other hand, the method developed by the more recent Ref. [3] gives rise to partial-wave amplitudes that do not reproduce the known solvable solution, and gives rise to a pole position with zero binding energy.

Laminar–turbulent intermittency in pipe flow for an Herschel–Bulkley fluid: Radial receptivity to finite-amplitude perturbations

We investigate the laminar-to-turbulent transition for non-Newtonian Herschel–Bulkley fluids that exhibit either a shear-thinning or shear-thickening behavior. The reduced-order model developed in this study also includes the effect of yield-stress for the fluid. Within our model framework, we investigate how the Newtonian dynamics change when significant non-Newtonian effects are considered either via the flow index n or the yield-stress τ0 or both. We find that an increase in τ0 as well as a decrease in n lead to a delayed transition if a perturbation of the given turbulent intensity is injected at various radial locations. As the radial position of the injection for the perturbation is varied in this study, our reduced-order model allows for the investigation of the flow receptivity to the finite-amplitude perturbations and to their radial position of inception. We observe that, for a given mean flow profile, the same perturbation becomes more prone to induce turbulence the closer it approaches the wall because of its initial amplitude being relatively higher with respect to the local mean flow. An opposite trend is found when the perturbation amplitude is rescaled on the local mean flow.

A Large Database of Lightning‐Induced Electron Precipitation Events

AbstractLightning‐induced Electron Precipitation (LEP) events represent a known loss mechanism for radiation belt electrons. The quantitative role LEP events play in the radiation belt dyanmics, however, is not fully understood. Direct measurements of the D region of the ionosphere, where LEP electrons are deposited, are very limited. However, Very Low Frequency (VLF) remote sensing has for a long time been used to detect perturbations in the D region, in particular using the narrow‐frequency signals of VLF transmitting beacons. We present an automated neural‐network based search for LEP events using our network of VLF receivers in the continental US detecting, seeded by National Lightning Detection Network (NLDN) lightning strokes. We arrive at a database of nearly 26000 LEP events over a span of 18 months within the continental USA. We find several notable patterns in the occurrence and behavior of events, such as 30.1% of events only containing disturbances in phase, and a substantially greater probability of perturbations in phase and major axis amplitude being negative.

Seismic Induced Ground Deformation and Ionospheric Perturbations of the 29 July 2021, Mw 8.2 Chignik Earthquake, Alaska

AbstractThe subsurface, surface, and ionospheric characteristics associated with the 29 July 2021 Mw 8.2 Chignik Earthquake are studied in detail using continuous Global Positioning System (cGPS) data over Alaska. The cGPS‐inverted coseismic displacements demonstrate that the slip is distributed along the rupture area northeast of the epicenter with a maximum coseismic slip of ∼3.85 m occurring at a depth of ∼24.25 km. The vertical surface displacement estimated from the coseismic slip exhibits a similar deformation pattern with a maximum uplift of ∼1.0 m over the highly slip area. The ionospheric electron density perturbations associated with the Chignik earthquake were investigated using cGPS‐derived Total Electron Content (TEC) data. Unlike the northeast‐directed coseismic rupture and surface uplift, the ionospheric imprints of this event are more dominant southwest of the epicenter. This study reveals that the Earth's magnetic field and the ionospheric background electron density significantly controlled the TEC perturbation orientation and amplitudes rather than the rupture propagation and coseismic uplift pattern.

Resistive wall tearing mode disruptions in DIII-D and ITER tokamaks

Disruptions are a serious problem in tokamaks, in which thermal and magnetic energy confinement is lost. This paper uses data from the DIII-D experiment, theory, and simulations to demonstrate that resistive wall tearing modes (RWTMs) produce the thermal quench (TQ) in a typical locked mode shot. Analysis of the linear RWTM dispersion relation shows the parameter dependence of the growth rate, particularly on the resistive wall time. Linear simulations of the locked mode equilibrium show that it is unstable with a resistive wall and stable with an ideally conducting wall. Nonlinear simulations demonstrate that the RWTM grows to sufficient amplitude to cause a complete thermal quench. The RWTM growth time is proportional to the thermal quench time. The nonlinearly saturated RWTM magnetic perturbation amplitude agrees with experimental measurements. The onset condition is that the q = 2 rational surface is sufficiently close to the resistive wall. Collectively, this identifies the RWTM as the cause of the TQ. In ITER, RWTMs will produce long TQ times compared to present-day experiments. ITER disruptions may be significantly more benign than previously predicted.

Steady states stability features of the electron–positron plasma diode

Stationary states stability features of a planar geometry diode with electron and positron counter flows are studied. Such a diode may be considered as a model to elucidate the nature of the pulsar radio emission. The equation for the electric field perturbation amplitude is derived. The exact solution of this equation for the homogeneous stationary field is found. On the basis of the plasma dispersion relation, the stability threshold in terms of the electron current density is found above which the stationary solutions become unstable. This threshold turned out to be 2 times higher than the known Pierce threshold. It can be expected that the development of the detected instability will lead to the electric field oscillations that induce electromagnetic radiation.

Characterization of ensemble generation strategies: Application to three illustrative examples of Mediterranean high-impact weather

Predictability of high-impact weather constitutes a major challenge. In this study, we contribute to this relevant topic by analyzing the characteristics of multiple ensemble prediction systems aimed at sampling initial and/or model uncertainties for three exemplary heavy precipitation systems that occurred over the western Mediterranean. In particular, initial condition perturbations are generated by (i) directly downscaling the ensemble members from a global ensemble and (ii) creating perturbations by sampling a wide range of scales using an adaptation of the breeding methodology. Model error is sampled by applying stochastic perturbations to physical parameterizations and to microphysics parameters. A positive impact in terms of ensemble diversity is obtained when initial condition perturbations across a broad range of scales are applied, especially at low levels and for cases in which local factors are more relevant. Regarding stochastic model perturbations, they display very localized perturbations with low amplitude, which are insufficient to capture extreme scenarios, except when local factors play a dominant role. However, when combined with initial condition perturbations, they generally increase diversity and perturbation amplitude over areas characterized by deep moist convection. This outcome exhibits the positive impact of sampling both uncertainty sources, even in the extremely nonlinear regime that defines convective-scale phenomena.

A methodology for discriminating phase and amplitude effects on synchronization in tokamak pacing experiments

The control of macroscopic instabilities, such as Edge Localised Modes (ELMs) and sawteeth, is becoming an essential ingredient in the optimisation of scenarios in preparation for the next generation of tokamaks and the demonstrative reactor. Various pacing experiments have been indeed successfully carried out in many devices but various details of their interactions with the plasma remain poorly understood, in particular the assessment of the relative contribution of driver phase and amplitude to frequency synchronization. In this paper, a data analysis methodology for investigating the details of pacing experiments is proposed. The approach is based on the wavelet decomposition of the signals and the following implementation of information theoretic indicators, to determine the basic form of the interactions. The main analysis tool deployed is the conditional mutual information, equivalent to the informational transfer entropy, which can detect actual causal influences and not only statistical correlations between signals. The most flexible type of ELM pacing, the vertical kicks, permits to clearly confirm the potential of the analysis tools developed. In the dedicated experiments to optimise the ELMs pacing with pellets and sawteeth synchronization with ICRH modulation, the main effect is due to the influence of the amplitude of the external perturbations. Some evidence of phase synchronization has been found, in both JET and AUG, which indicates the direction of possible future optimization of the interventions. Indeed, adjusting the phase of the pacing schemes would free density and ICRH power to give more leeway to other feedback loops, an important aspect, particularly for the integrated control of the next generation of devices. The long-term objective of this line of research is therefore twofold. On the one hand, it is expected to contribute to better physical interpretation of the pacing experiments and possibly also of their target instabilities. From an operational perspective, hopefully these insights will help in the development of reactor relevant scenarios, as exemplified by examples of ELM a pacing with pellets carried out in preparation for the DT campaign on JET.

Transcranial direct current stimulation over the primary motor cortex improves speech production in post-stroke dysarthric speakers: A randomized pilot study.

PurposeThe current study investigated the therapeutic potential of transcranial direct current stimulation (tDCS) on speech intelligibility, speech-related physiological and vocal functions among post-stroke dysarthric patients.MethodNine chronic post-stroke dysarthric patients were randomly assigned to the stimulation or sham group. The stimulation group received 2mA of anodal tDCS over the left inferior primary motor cortex for 15 minutes, while the sham group received 30s of stimulation under the same settings. All the participants received 10 daily 15 minutes of individualized speech therapy targeting their dominant phonological process or phonemes with the greatest difficulty. The outcome measures included (1) perceptual analysis of single words, passage reading and diadochokinetic rate, (2) acoustic analysis of a sustained vowel, and (3) kinematic analysis of rapid syllable repetitions and syllable production in sentence, conducted before and after the treatment.ResultsThe results revealed that both the stimulation and sham groups had improved perceptual speech intelligibility at the word level, reduced short rushes of speech during passage reading, improved rate during alternating motion rate, AMR-kha1, and improved articulatory kinematics in AMR-tha1 and syllables /tha1/ and /kha1/ production in sentence. Compared to the sham group, the stimulation group showed significant improvement in articulatory kinematics in AMR-kha1 and syllable /kha1/ production in sentence. The findings also showed that anodal stimulation led to reduced shimmer value in sustained vowel /a/ phonation, positive changes in articulatory kinematics in AMR-tha1 and syllables /pha1/ and /kha1/ production in sentence at the post treatment measure. In addition to positive effects on articulatory control, reduced perturbation of voice amplitude documented in the stimulation group post treatment suggests possible tDCS effects on the vocal function.ConclusionsThe current study documented the beneficial effects of anodal tDCS over the primary motor cortex on speech production and suggested that combined tDCS and speech therapy may promote recovery from post-stroke dysarthria.

Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

The Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophysics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical methods cannot be applied to explain the long-time behavior of the Rayleigh-Taylor instability, and therefore, numerical simulation of the full problem is required. However, in order to capture the growth of amplitude of perturbations accurately, both the spatial and temporal discretizations need to be extremely fine for traditional numerical methods, and long-time simulation may become prohibitively expensive. In this paper, we propose efficient reduced order model techniques to accelerate the simulation of the Rayleigh-Taylor instability in compressible gas dynamics. We introduce a general framework for decomposing the solution manifold to construct the temporal domain partition and temporally-local reduced order model construction with varying Atwood number. We propose two practical approaches in this framework, namely decomposition by physical time and by penetration distance. Numerical results are presented to examine the performance of the proposed approaches.