Quasilinear Effects Research Articles

Electrically induced and controlled piezoelectricity

The quasi-linear electromechanical effect, which resembles piezoelectricity, can be induced by strong electric field in any solid dielectric. This effect is defined as linearized electrostriction, which is observed in the biasing electric field and is proportional to the square of the dielectric permittivity. The present work analyses physical mechanisms of the occurrence of such an effect in the piezoelectrics, the paraelectrics and the relaxor ferroelectrics, taking into account the inertia of electromechanical response. Hysteresis-less electromechanical control of deformation is used in actuators and tuneable microwave devices. The efficiency of the induced piezoelectricity is maximal in dielectrics with high permittivity, while the efficiency is ensured by mechanisms of low-inertia quasi-elastic polarization. To assess the maximum performance of piezoelectric actuators made of different materials, the method of dielectric spectroscopy is used.

A two-dimensional numerical study of ion-acoustic turbulence

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

Application of linear electron Bernstein current drive models in reactor-relevant spherical tokamaks

Electron Bernstein current drive (EBCD) systems in spherical tokamaks are sensitive to plasma and launch conditions, and therefore require large parametric scans to optimise their design. One particular bottleneck in the simulation workflow is quasilinear modelling of current drive efficiency. Linear adjoint models are an attractive alternative, offering a ∼103 × speed-up compared to quasilinear codes. While linear models are well-tested and commonly used for electron cyclotron current drive (ECCD), they have seen little use in EBCD modelling. In this work, variants of the linear model are applied to EBCD and compared to quasilinear results in a reactor-relevant plasma, i.e. Spherical Tokamak for Energy Production (STEP). This comparison reveals it is important to accurately model the collision operator and finite Larmor radius effects in the linear model. When done properly, good agreement is found with quasilinear calculations, at least for normalised minor radii ρ < 0.7 and at low power densities. The power density threshold for quasilinear effects during EBCD is found to be significantly lower than that of ECCD. This is attributed to the much lower group velocity of the electron Bernstein wave (EBW). Thus, the linear model is only valid for EBCD modelling at low power densities (e.g. ≲ 1 MW launched EBW power in STEP). This may be satisfied in present-day experimental devices, but certainly not in reactors targeting non-inductive operation.

Mixed-effect models with trees

Tree-based regression models are a class of statistical models for predicting continuous response variables when the shape of the regression function is unknown. They naturally take into account both non-linearities and interactions. However, they struggle with linear and quasi-linear effects and assume iid data. This article proposes two new algorithms for jointly estimating an interpretable predictive mixed-effect model with two components: a linear part, capturing the main effects, and a non-parametric component consisting of three trees for capturing non-linearities and interactions among individual-level predictors, among cluster-level predictors or cross-level. The first proposed algorithm focuses on prediction. The second one is an extension which implements a post-selection inference strategy to provide valid inference. The performance of the two algorithms is validated via Monte Carlo studies. An application on INVALSI data illustrates the potentiality of the proposed approach.

Theory of Solutions for an Inextensible Cantilever

Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin–Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.

Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient , where and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ∼ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

Interaction Between Two Jackiw-Rebbi States in Interfaced Binary Waveguide Arrays with Cubic-quintic Nonlinearity

We study the coupling and switching effects of two discrete relativistic quantum Jackiw-Rebbi states in interfaced binary waveguide arrays with cubic-quintic nonlinearity. Like in the case with Kerr nonlinearity, two Jackiw-Rebbi states can couple efficiently to each other in the low-power regime, show the switching effect in the intermediate-power regime, and possess the trapping effect in the high-power regime. However, in the case with cubic-quintic nonlinearity, if the input Jackiw-Rebbi state power is increased further, one can observe the quasi-linear coupling effect between two Jackiw-Rebbi states which has not been found between two Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity.

Simulation of the Ohkawa-mechanism- dominated current drive of electron cyclotron waves using linear and quasi-linear models

Simulation on the Ohkawa-mechanism-dominated current drive (OKCD) of electron cyclotron (EC) waves is performed using TORAY-GA linear code, and the results are compared with those calculated by CQL3D quasi-linear code. It is found that the radial location of the OKCD profile is almost identical between the linear and the quasi-linear calculations. However, there are significant differences in the calculation of the total driven current and the peak value of the driven current profile between the two models. The calculated by the CQL3D code is at least 1.4 times larger than the results from the TORAY-GA code. For the calculation of , the results from CQL3D are at least 1.6 times larger than that calculated by TORAY-GA. With increasing electron temperature, the two models further enlarge the total driven current scaling factor and the peak driven current density scaling factor . This is mainly because the collision operator in TORAY-GA code adopts a high-speed model and does not retain the first-order Legendre expansion term for momentum conservation of electron self-collision. The quasi-linear effect does not have a significant influence on the total driven current of OKCD when the EC power level does not meet > 0.5. Therefore, in practical engineering, the TORAY-GA code can be used to calculate OKCD quickly and accurately by multiplying with appropriate scaling factors. The effect of momentum conservation is very important for OKCD and on-axis EC current drive (ECCD), but this effect is not important for off-axis ECCD. The results from this study show that the effects of electron trapping and the collision between resonant passing electrons and trapped electrons are responsible for the decrease in off-axis ECCD efficiency.

Large deflections of inextensible cantilevers: modeling, theory, and simulation

A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam’sinextensibility– local arc length preservation – rather than traditional extensible effects attributed to fully restricted boundary conditions. Enforcing inextensibility leads to:nonlinear stiffnessterms, which appear as quasilinear and semilinear effects, as well asnonlinear inertiaeffects, appearing as nonlocal terms that make the beam implicit in the acceleration. In this paper we discuss the derivation of the equations of motionviaHamilton’s principle with a Lagrange multiplier to enforce theeffective inextensibility constraint. We then provide the functional framework for weak and strong solutions before presenting novel results on the existence and uniqueness of strong solutions. A distinguishing feature is that the two types of nonlinear terms present independent challenges: the quasilinear nature of the stiffness forces higher topologies for solutions, while the nonlocal inertia requires the consideration of Kelvin-Voigt type damping to close estimates. Finally, a modal approach is used to produce mathematically-oriented numerical simulations that provide insight into the features and limitations of the inextensible model.

Toroidal modeling of resonant magnetic perturbations in preparation for the initial phase of ITER operation

A systematic and comprehensive numerical investigation is carried out in order to understand linear and quasi-linear effects of the applied resonant magnetic perturbations (RMPs) on the plasma, during the initial phase of ITER operation at 5 MA plasma current and 1.8 T toroidal field, assuming a limited number of available power supplies (PSs) for controlling the type-I edge localized modes (ELMs) and taking into account uncertainties associated with predicting the plasma toroidal rotation in ITER. Utilizing the plasma surface displacement near the X-point as a proxy for the ELM control capability by RMPs, the coil phasing optimization finds optima that are not sensitive to the variation of the assumed plasma toroidal flow, nor to the choice of toroidal waveform of the coil current distribution. Several assumptions regarding the number of PSs available in this initial phase have been explored, comprising 9 and 13 for current waveforms with n = 3 symmetry: using the equatorial coil row alone, upper and lower rows of coils and the three rows of ELM control coils. The resulting effects on ELM control (through the X-point displacement proxy) and core and edge torques have been evaluated. Optimization and comparison for the three ELM control coil configurations—all three rows, upper and lower rows, and equatorial row—reveal a strong coupling between the core and edge plasma response—both linear and quasi-linear—for these ITER plasma conditions. The equatorial ELM control coil row has the strongest effects on core and edge plasma response, but provides no flexibility in its optimization; this can only be achieved by optimizing the current waveform with the upper and lower rows. A quantitative comparison of the achievable optimization of ELM control and core plasma response with the three configurations of coils has been performed, assuming that nine PSs will be available in the initial ITER operation.

Mechanism of memory effect of paste which dominates desiccation crack patterns.

When a densely packed colloidal suspension, called a paste, behaves as plastic fluid, it can remember the direction of its motion it has experienced, such as vibrational motion and flow. These memories kept in paste can be visualized as the morphology of crack patterns that appear when the paste is dried. For example, when a paste remembers the direction of vibrational motion, all primary desiccation cracks propagate in the direction perpendicular to the direction of the vibrational motion that the paste has experienced. On the other hand, when a paste remembers the direction of flow motion, all primary cracks propagate along the flow direction. To find out the mechanism of memory effect of vibration, we perform experiments to rewrite memory in paste by applying additional vibration to the paste along a different direction before the paste is dried. By investigating the process of rewriting memory in paste, we find the competitive phenomena between quasi-linear effect and nonlinear effect, which were studied in each theoretical model based on residual tension theories. That is, at the initial stage of the memory-imprinting process of the vibrational motion, the mechanism predicted by the quasi-linear analysis based on residual tension theory holds, but, as the paste is vibrated repeatedly, the mechanism shown by the nonlinear analysis gradually come to play a dominant role in the memory effect.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

The effects of kinetic instabilities on the electron cyclotron emission from runaway electrons

In this paper we show that the kinetic instabilities associated with runaway electron beams play an essential role for the production of high-level non-thermal electron–cyclotron-emission (ECE) radiation. Most of the non-thermal ECE comes from runaway electrons in the low-energy regime with large pitch angle, which are strongly scattered by the excited whistler waves. The power of ECE from runaway electrons is obtained using a synthetic diagnostic model based on the reciprocity method. The electron distribution function is calculated using a kinetic simulation model including the whistler wave instabilities and the quasilinear diffusion effects. Simulations based on DIII-D low-density discharge reproduces the rapid growth of the ECE signals observed in DIII-D experiments. Unlike the thermal ECE where radiation for a certain frequency is strongly localized inside the resonance region, the non-thermal ECE radiation from runaway electrons is nonlocal, and the emission-absorption ratio is higher than that of thermal electrons. The runaway electron tail is more significant for ECE with higher frequencies, and the ECE spectrum becomes flatter as RE population grows. The nonlinear behavior of the kinetic instabilities is illustrated in the oscillations of the ECE waves. The good agreement with the DIII-D experimental observations after including the kinetic instabilities clearly illustrate the significance of the scattering effects from wave-particle interactions, which can also be important for runaway electrons produced in disruptions.

The environment and host haloes of the brightest z ∼ 6 Lyman-break galaxies

By studying the large-scale structure of the bright high-redshift Lyman-break galaxy (LBG) population it is possible to gain an insight into the role of environment in galaxy formation physics in the early Universe. We measure the clustering of a sample of bright (-22.7<M_UV<-21.125) LBGs at z~6 and use a halo occupation distribution (HOD) model to measure their typical halo masses. We find that the clustering amplitude and corresponding HOD fits suggests that these sources are highly biased (b~8) objects in the densest regions of the high-redshift Universe. Coupled with the observed rapid evolution of the number density of these objects, our results suggest that the shape of high luminosity end of the luminosity function is related to feedback processes or dust obscuration in the early Universe - as opposed to a scenario where these sources are predominantly rare instances of the much more numerous M_UV ~ -19 population of galaxies caught in a particularly vigorous period of star formation. There is a slight tension between the number densities and clustering measurements, which we interpret this as a signal that a refinement of the model halo bias relation at high redshifts or the incorporation of quasi-linear effects may be needed for future attempts at modelling the clustering and number counts. Finally, the difference in number density between the fields (UltraVISTA has a surface density ~1.8 times greater than UDS) is shown to be consistent with the cosmic variance implied by the clustering measurements.

Assessment of quasi-linear effect of RF power spectrum for enabling lower hybrid current drive in reactor plasmas

The main research on the energy from thermonuclear fusion uses deuterium plasmas magnetically trapped in toroidal devices. To suppress the turbulent eddies that impair thermal insulation and pressure tight of the plasma, current drive (CD) is necessary, but tools envisaged so far are unable accomplishing this task while efficiently and flexibly matching the natural current profiles self-generated at large radii of the plasma column [1–5]. The lower hybrid current drive (LHCD) [6] can satisfy this important need of a reactor [1], but the LHCD system has been unexpectedly mothballed on JET. The problematic extrapolation of the LHCD tool at reactor graded high values of, respectively, density and temperatures of plasma has been now solved. The high density problem is solved by the FTU (Frascati Tokamak Upgrade) method [7], and solution of the high temperature one is presented here. Model results based on quasi-linear (QL) theory evidence the capability, w.r.t linear theory, of suitable operating parameters of reducing the wave damping in hot reactor plasmas. Namely, using higher RF power densities [8], or a narrower antenna power spectrum in refractive index [9,10], the obstacle for LHCD represented by too high temperature of reactor plasmas should be overcome. The former method cannot be used for routinely, safe antenna operations, Thus, only the latter key is really exploitable in a reactor. The proposed solutions are ultimately necessary for viability of an economic reactor.

Modeling of high harmonic fast wave current drive on EAST tokamak

High harmonic fast waves (HHFW) are among the candidates for non-inductive current drive (CD), which is essential for long-pulse or steady-state operation of tokamaks. Current driven with HHFW in EAST tokamak plasmas is numerically studied. The HHFW CD efficiency is found to increase non-monotonically with the wave frequency, and this phenomenon is attributed to the multi-pass absorption of HHFW. The sensitivity of CD efficiency to the value of the parallel refraction index of the launched wave is confirmed. The quasilinear effects, assessed as significant in HHFW current drive with the GENRAY/CQL3D package, cause a significant increase in CD efficiency as RF power is increased, which is very different from helicon current drive. Simulations for a range of toroidal dc electric fields, in combination with a range of fast wave powers, are also presented and indicate that the presence of the DC field can also enhance the CD efficiency.

Numerical studies of electron cyclotron wave current drive on HL-2A tokamak

The electron cyclotron wave (ECW) current drive (CD) for the HL-2A tokamak is investigated numerically with a new ray-tracing and Fokker-Planck code. The code is benchmarked with other well-tested linear and quasilinear codes and is then used to study the electron cyclotron current drive on the HL-2A tokamak. The wave propagation, power deposition, and driven-current profiles are presented. The effect of electron trapping is also assessed. It is found that quasilinear effects are negligible at the present ECW power levels and that when both waves are injected at an angle of 20° on the plasma equatorial plane, the CD efficiency for the HL-2A saturates at ∼0.029 × 1020 A/W/m2 and ∼0.020 × 1020 A/W/m2 for the 0.5 MW/68 GHz first harmonic ordinary (O1) and 1 MW/140 GHz second harmonic extraordinary (X2) modes, respectively. The effects of the plasma density, temperature, and wave-launching position on the driven current are also investigated analytically and numerically.

Electrooptic properties of one-dimensional photonic crystals based on organic ferroelectric and dye

We present the results of our study of the electrooptic properties of a one-dimensional photonic crystal created from alternating thin layers of two organic compounds, a ferroelectric and a dye. We show that the ferroelectric subsystem of molecular layers in such a heterostructure can be polarized by an external electric field, leading to a linear electrooptic effect and bistability of the electrooptic response in the spectral region of the photonic stop band. On the other hand, a quasi-linear electrooptic effect attributable to the quadratic Stark effect and the built-in spatially periodic static electric field is observed in the spectral region of the absorption of dye molecules. The emergence of this built-in field is explained in terms of the continuity of the electric displacement vector in a spatially periodic dielectric heterostructure with a macroscopically polarized subsystem of ferroelectric layers.

Larger π-extended anti-/syn-aroylenediimidazole polyaromatic compounds: synthesis, physical properties, self-assembly, and quasi-linear conjugation effect

Four polyaromatic compounds with 11- or 13-fused rings have been synthesized and their physical properties have been studied.

Comment on “Undamped electrostatic plasma waves” [Phys. Plasmas 19, 092103 (2012)

The relevance of linear “corner modes” for the description of coherent electrostatic structures, as proposed by Valentini et al. [Phys. Plasmas 19, 092103 (2012)], is questioned. Coherency in their on-dispersion simulation is instead found to be caused by particle trapping in agreement with Schamel's nonlinear wave model [Phys. Plasmas 19, 020501 (2012)]. The revealed small amplitude structures are hence of cnoidal electron hole type exhibiting vortices in phase space. They are ruled by trapping nonlinearity rather than by linearity or quasi-linear effects, as commonly assumed. Arguments are presented, which give preference to these cnoidal hole modes over Bernstein-Greene-Kruskal modes. To fully account for a realistic theoretical scenario, however, at least four ingredients are mandatory. Several corrections of the conventional body of thought about the proper kinetic wave description are proposed. They may prove useful for the general acceptance of this “new” nonlinear wave concept concerning structure formation, updating several prevailing concepts such as the general validity of a linear wave Ansatz for small amplitudes, as assumed in their paper. It is conjectured that this nonlinear trapping model can be generalized to the vortex structures of similar type found in the more general setting of driven turbulence of magnetized plasmas. They appear as eddies in both, the phase and the position spaces, embedded intermittently on the Debye length scale.

Plasma equilibrium in a semiclassical plasma due to non-resonant wave particle interactions

A nonresonant perturbative approach has been utilized to probe the modification of the equilibrium plasma distribution function due to plasma interaction with externally launched high-frequency large-amplitude RF waves in the presence of quantum effects. The quantum distribution function from the complete Wigner equation has been obtained for a high-frequency wave with constant amplitude. For waves with weak spatial or temporal modulation, the equilibrium distribution function has been obtained by solving the Wigner equation as an initial or boundary-value problem and retaining only lowest-order quantum effects. In the dipole approximation, a higher order diffusion has been identified in addition to quantum modified ponderomotive and quasilinear diffusion effects. Additional terms of the Wigner equation give the impression of higher order diffusion effects in the system.