Nonadiabatic Response Research Articles

Scheme for Measuring Topological Transitions in a Continuous Variable System

AbstractA scheme for measuring topological properties in a two‐photon‐driven Kerr‐nonlinear (KNR) resonator subjected to a single‐photon modulation is proposed. The topological properties are revealed through the observation of the Berry curvature and hence the first Chern number, as a nonadiabatic response of the physical observable to the change rate of the control parameter of the modulated drive. The parameter manifold, constructed from the system's Hamiltonian that determines its dynamics constrained in the state space spanned by the even and odd cat states as two basis states, is adjusted so that the degeneracy crossing the manifold indicates a topological transition. The scheme, with such continuous variable states in mesoscopic systems, provides a new perspective for exploration of the geometry and the related topology with complex systems.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in [Porcelli F et al 1994 Phys. Plasmas 1 470] is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic (MHD). Here, we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency large-scale MHD in a low-beta plasma. The obtained perturbed Lagrangian is consistent with Chen’s gyrokinetic theory [Chen L and Zonca F 2016 Rev. Mod. Phys. 88 015008], where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible. As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications, this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

A modified model for thermoelastic stress analysis under low frequency fatigue loading

Thermoelastic stress analysis (TSA) can be used to determine the stress field of structures or materials under cyclic loadings through temperature under adiabatic conditions. So high-frequency cyclic loadings are considered as a fundamental condition. However, loading frequencies in many practical applications do not meet the adiabatic conditions. In order to improve the accuracy of TSA under low-frequency fatigue loadings, the non-adiabatic response in TSA was derived by combining the classical thermoelastic equation and heat conduction equation. This response was used to create a modified model that accounted for heat transfer and temperature distribution under low-frequency loading conditions. Otherwise, fatigue test and finite element method were used to evaluate the correctness of the modified model using epoxy resin material. The results showed that the temperature change obtained from the modified model were in good agreement with the experiment results. The modified model can effectively evaluate the structural stress under low-frequency fatigue loadings.

Global simulations of energetic electron excitation of beta-induced Alfvén eigenmodes

The energetic electron (EE) excitation of beta-induced Alfvén eigenmodes is investigated by using the newly developed global eigenvalue code MAS, which is based on a hybrid model that consists of Landau fluid bulk plasma and drift kinetic EE. Specifically, the bulk plasma kinetic effects such as finite Larmor radius, diamagnetic drifts and Landau dampings, and the EE adiabatic fluid response of convection and non-adiabatic kinetic response of precessional drift resonance are incorporated in the simulations. The global eigenmode equation is solved for e-BAE mode structure and linear dispersion relation in tokamak non-perturbatively. The radial width of e-BAE mode structure becomes narrower as the toroidal mode number increases, which can be explained by the change of Alfvén continuous spectra that interact with kinetic Alfvén waves for corresponding eigenmode formation. The e-BAE growth rate exhibits a non-monotonic variation with toroidal mode number for precessional drift resonance destabilization, while the e-BAE real frequency is close to the continuum accumulation point that almost remains the same. The parametric dependence of e-BAE stability on EE density and that on temperature are analyzed by MAS non-perturbative simulations, which shows that the EE density can affect e-BAE real frequency and thus changes the resonance condition, resulting in e-BAE stabilization in the strong EE drive regime. Further, the EE non-perturbative effect on the symmetry breaking of e-BAE mode structure is reported. The poloidal symmetry breaking characterized by the ‘boomerang’ shape two-dimensional (2D) structure can be greatly enhanced by increasing EE temperature, together with the large radial variation of the poloidal phase angle of dominant principal poloidal harmonic. The radial symmetry breaking of e-BAE mode structure arises when EE density/temperature drive is not symmetric with respect to corresponding rational surface, which can lead to a net volume-averaged value of e-BAE parallel wave number which drives plasma intrinsic rotation. These results are helpful in understanding the e-BAE dynamics observed in recent experiments.

Probing quantum many-body correlations by universal ramping dynamics

Ramping a physical parameter is one of the most common experimental protocols in studying a quantum system, and ramping dynamics has been widely used in preparing a quantum state and probing physical properties. Here, we present a novel method of probing quantum many-body correlation by ramping dynamics. We ramp a Hamiltonian parameter to the same target value from different initial values and with different velocities, and we show that the first-order correction on the finite ramping velocity is universal and path-independent, revealing a novel quantum many-body correlation function of the equilibrium phases at the target values. We term this method as the non-adiabatic linear response since this is the leading order correction beyond the adiabatic limit. We demonstrate this method experimentally by studying the Bose-Hubbard model with ultracold atoms in three-dimensional optical lattices. Unlike the conventional linear response that reveals whether the quasi-particle dispersion of a quantum phase is gapped or gapless, this probe is more sensitive to whether the quasi-particle lifetime is long enough such that the quantum phase possesses a well-defined quasi-particle description. In the Bose-Hubbard model, this non-adiabatic linear response is significant in the quantum critical regime where well-defined quasi-particles are absent. And in contrast, this response is vanishingly small in both superfluid and Mott insulators which possess well-defined quasi-particles. Because our proposal uses the most common experimental protocol, we envision that our method can find broad applications in probing various quantum systems.

Influence of adiabatic response of passing energetic ions on high-frequency fishbone

Adiabatic response effects on high-frequency fishbone instability driven by passing energetic ions are studied. With finite orbit width effects, the adiabatic contribution is derived analytically for purely passing energetic ions. By approximating the adiabatic contribution to the first order of the reverse aspect ratio we derive one of its analytic expressions, which is expected to be more accurate than that in a previous work (Graves J P 2004 Phys. Rev. Lett. 92 185003). For high-frequency fishbone instability, nonadiabatic response is usually dominant over adiabatic response, but under certain circumstances the latter plays an important role, comparable to the former. With a more generalized distribution function by introducing Gaussian-type factors representing their pitch and radial dependences and using a slowing-down equilibrium distribution for the energy of energetic ions, numerical analysis indicates that the adiabatic contribution is conducive to stabilization of the mode and causes a decrease in mode frequency. In addition, we find that the adiabatic contribution has a weak stabilizing effect on the fishbone instability when the finite orbit width effect is taken into account. We further analyze the dependence of the adiabatic contribution on the characteristic parameters of the distribution function. When the neutral beam has either a larger deviation from the plasma axis or a larger radial profile, the adiabatic contribution has a more evident effect on the fishbone instability. When the neutral beam has a relatively small critical energy, the adiabatic contribution has a greater effect on the mode instability.

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Due to the small electron-to-ion mass ratio and the large electron transit frequency, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes. However, in gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal magnetic fields, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations in narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, in axisymmetric toroidal magnetic geometry, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating parallels in structure and physical processes to neoclassical transport theory. By examining initial-value simulations of the fastest-growing eigenmodes, the predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insight from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

Effect of collisions on non-adiabatic electron dynamics in ITG-driven microturbulence

Non-adiabatic electron response leads to significant changes in ion temperature gradient (ITG) eigenmodes, leading, in particular, to fine-structures that are significantly extended along the magnetic field lines at corresponding mode rational surfaces (MRSs). These eigenmodes can nonlinearly interact with themselves to drive zonal flows via the so-called self-interaction mechanism. In this paper, the effect of collisions on these processes are studied. In the presence of non-adiabatic electrons, the linear growth rate of ITG eigenmodes decreases with the increasing collisionality. Detailed velocity space analysis of the distribution function shows that this results from collisions leading to a more adiabatic-like response of electrons away from MRSs. In linear simulations, collisions are furthermore found to broaden the radial width of the fine-structures, which translates to narrower tails of the eigenmode in extended ballooning space. The characteristic parallel scale length associated with these tails is shown to scale with the mean free path of electrons. In nonlinear turbulence simulations accounting for physically relevant values of collisionality, the fine-structures located at MRSs, together with the associated drive of zonal flows via self-interaction, are shown to persist and play a significant role.

Non-adiabatic Response and Counterdiabatic Driving of Coherent States

Quantum state preparation has drawn great attention to physical community. In order to solve this challenge, the protocol of counterdiabatic driving was put forward. In this paper, the idea was applied to two important models, Coherent states and Spin coherent states, which had played important roles in the development of quantum optic and atomic physics. If their parameters vary slowly, the evolution can be studied by the adiabatic perturbation theory. Furthermore, their non-adiabatic response are investigated respectively. Specifically, we build the relationship between the generalized force and Berry curvature of coherent states and spin coherent states. And the leading corrections to energy are also been researched, which lead to the mass and moment of inertia renormalization respectively. In addition, we also calculate the broadening of the energy distribution (energy variance), which determined by the metric tensor. Finally, in order to suppress transition and speed up the evolution, the counterdiabatic Hamiltonians are designed, which would have potential use in the field of quantum manipulation.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Analysis of the multielectron dynamics in intense laser-induced ionization of CO by the time-dependent effective potentials for natural orbitals

We simulated the multielectron dynamics of a CO molecule irradiated by near-IR λ = 760 nm two-cycle pulses with different carrier envelope phases by using the multiconfiguration time-dependent (TD) Hartree–Fock (MCTDHF) method. The ionization rate estimated from the simulations is higher when the laser electric field ɛ(t) points from C to O than in the opposite case, in agreement with the results of two-color experiments. The mechanism of the directional anisotropy in tunnel ionization of CO was examined by converting the obtained multielectron dynamics to the representation in terms of TD natural orbitals {ϕj(t)}. Within the framework of MCTDHF, we derived the equations of motion for {ϕj(t)}. From the derived equations, we defined the TD effective potentials that govern the dynamics of ϕj(t). consists of the one-body part v1(t) including the interaction with ɛ(t) and the two-body part v2,j(t) originating from electron–electron interaction. In for the 5σ HOMO, a narrow hump associated with the increase in v2,5σ(t) is surmounted on the field-distorted barrier of v1(t) + v2,5σ(0) near the nucleus C when ɛ(t) points from C to O, which results in the anisotropic ionization of CO. For 4σ, a high barrier that suppresses ionization is formed in when ɛ(t) points from C to O, which suggests that dynamical correlation exists between 4σ and 5σ electrons on route to ionization. For the opposite phase, becomes barrierless, enhancing high-harmonic generation through 4σ. We also simulated the dynamics for a λ = 380 nm pulse to investigate how reflects the nonadiabatic electronic response to the pulse. We found that the height of the hump in v1(0) + v2,5σ(t) is nearly proportional to the induced dipole moment of ϕ5σ(t), irrespective of whether the response is adiabatic or not. The for LiH is also presented to demonstrate the ubiquity of hump structures.

Reversal of Simple Hydrogenic Isotope Scaling Laws in Tokamak Edge Turbulence.

The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio dependence of turbulent ion and electron energy fluxes. The mass-ratio dependence arises from the nonadiabatic response associated with fast electron parallel motion and plays a key role in altering-and in the case of the DIII-D edge, favorably reversing-the naive gyro-Bohm scaling behavior. In the reversed regime hydrogen energy fluxes are larger than deuterium fluxes, which is the opposite of the naive prediction.

Hybrid-kinetic simulation of resonant interaction between energetic-ions and tearing modes in a tokamak plasma

The effect of energetic-ions on magnetohydrodynamic instabilities is pivotal in the basic physics that will be vital in burning plasma experiments. Recently, it has been found in the HL-2A tokamak that an m/n = 2/1 unstable tearing mode (TM) interacts with energetic-ions, resulting in amplitude-bursting and frequency-chirping fishbone-like activities, and it is numerically identified that the co-passing energetic-ions play a dominant role in the wave-particle resonances (Chen et al 2019 Nucl. Fusion 59 096037). Motivated by fully and deeply understanding such a resonant interaction between energetic-ions and TM, a more detailed study of global nonlinear hybrid kinetic-MHD simulations with M3D-K code is performed in the present work. The kinetic effect of co-passing energetic-ions from non-adiabatic response is interestingly found to be strongly destabilizing, while the net effect with both adiabatic and non-adiabatic contributions is weakly destabilizing. For passing energetic-ions, the m/n = 2/1 TM is found to be most unstable in the case of , where q0 is the central safety factor. Effects of energetic-ion beta and pinch angle determining different energetic-ion fractions on the resonance features, such as the growth rate, frequency chirping and mode structure, are discussed in detail. The relevant simulation results are consistent with the observations on HL-2A. Furthermore, the effects of both counter-passing and trapped energetic-ions on the TM have also been explored, but the corresponding resonance phase space is found to be very narrow in the plane. In addition, the redistribution and loss induced by the resonant interaction between TM and energetic-ions are analyzed in multiple-mode simulations. Significant redistribution and loss are clearly observed, and the scaling of energetic-ion loss fraction with the fluctuation amplitude is found to be , indicating that the loss is convective. These discoveries are conducive to understanding the mechanisms of TM-induced energetic-ion loss through the resonant interaction.

Intrinsic current driven by electromagnetic electron drift wave turbulence in the tokamak pedestal region

The local intrinsic parallel current density driven by electron drift wave (DW) turbulence including electromagnetic (EM) effects is analytically studied. The scalings of the ratios of intrinsic current density driven by residual turbulent flux and by a turbulent source to the bootstrap (BS) current density with electron density and temperature are predicted to be and respectively. Based on the typical parameters in the DIII-D pedestal region, the local intrinsic current density driven by both the residual turbulent flux and the turbulent source is negligible. However, despite the negligible turbulent source driven current, the residual turbulent flux driven local intrinsic current density by EM DW turbulence can reach about 66% of the BS current density for International Thermonuclear Experimental Reactor (ITER) pedestal parameters due to much lower collisionality in ITER than in DIII-D. Moreover, the contributions from adiabatic ES parts, non-adiabatic ES parts, and non-adiabatic EM parts of the plasma response to EM fluctuations are analyzed. It is found that there is a strong cancellation between the non-adiabatic ES response and the non-adiabatic EM response for the ITER pedestal case, and thus the kinetic stress contributed by the adiabatic ES response of parallel electron pressure dominates the intrinsic current drive. This is different from the ES electron DW case. Therefore, the EM effects on turbulence driven intrinsic current density should be carefully considered in the future reactor with a high ratio of electron pressure to the magnetic pressure and steep pressure profile.

Edge turbulence evolution and intermittency development near the density limit on the HL-2A tokamak

The development of intermittent non-Gaussian processes is studied in the edge turbulence of ohmically heated HL-2A discharges approaching the density limit. As the density limit is approached, the E×B shear flow at the last closed flux surface (LCFS) weakens, a strong positive skewness develops in the scrape-off layer (SOL), and negative skewness develops inside the LCFS of turbulent density fluctuations. A conditional averaging analysis confirms more frequent increased amplitude positive (negative) going density fluctuation activity in the SOL (inside the LCFS) as the density limit is approached. The measured turbulent stress across the edge, LCFS, and SOL region is decomposed into diffusive and residual stress components, and the nonlinear exchange of kinetic energy between the turbulence and the low-frequency E×B shear flow is determined. Residual stress acts to amplify the E×B flow at the LCFS, while the diffusive stress acts to dissipate the flow just inside this region, at the interface between the core plasma and the LCFS. The relative strength of the flow drive associated with the residual stress weakens as the density limit is approached, while the turbulent viscosity associated with the diffusive stress increases at high density. The adiabatic parameter, kz2vth2/ωνe, drops significantly to about 0.5 in the SOL when the density limit is approached, indicating a transition from the adiabatic regime to the hydrodynamic regime due to increased collisionality. Such changes enhance the particle transport through the nonadiabatic electron response and hence should result in a stronger edge cooling at fixed edge plasma heat flux.

Reversal of turbulent gyroBohm isotope scaling due to nonadiabatic electron drive

The influence of kinetic electrons on the isotope scaling of gyrokinetic turbulent energy flux is assessed. A simple framework is used to study the transition from ion-dominated turbulence regimes to regimes where electron and ion transport levels are comparable. In the ion-dominated regime, the turbulent ion energy flux increases as the ion mass increases, in agreement with simple gyroBohm scaling arguments. Conversely, in the latter regime for which the influence of electrons is significant, a strong reversal of the gyroBohm scaling is observed which cannot be captured by mixing length estimates. In this reversed regime, the turbulent ion energy flux decreases as ion mass increases. The reversal is controlled by the finite electron-to-ion mass-ratio dependence of the nonadiabatic electron response. This mass-ratio dependence is dominated by the parallel motion terms in the electron gyrokinetic equation and provides a correction to the bounce-averaged-electron limit which is independent of the mass ratio. The finite-mass correction is larger for light ions and explains the observed gyroBohm reversal for hydrogen plasmas. An implication is that isotope scaling may not be properly described by simplified fluid or bounce-averaged electron equations.

Analytical finite-Lamor-radius and finite-orbit-width model for the LIGKA code and its application to KGAM and shear Alfvén physics

In this paper, a finite Larmor radius (FLR) and finite orbit width (FOW) model within the LIGKA [1] framework is derived and its implementation in LIGKA is verified against analytical theory. The model is based on an expansion in k ⊥ ϱi and thus valid for low and intermediate mode numbers. Assuming Maxwellian distribution functions and considering circulating ions only, analytical expressions for the non-adiabatic response in the quasi-neutrality (QN) and the gyrokinetic moment equation (GKM) are derived. It is shown how these expressions, also valid for n ≠ 0 can be connected to results in the literature for n = 0. Verification tests with analytical literature [2] are carried out for mode frequency, damping and radial mode propagation. A set of parameters is chosen that is based on recent experiments at ASDEX Upgrade [3] featuring strong EGAM (energetic particle induced geodesic acoustic mode) and BAE (beta-induced Alfvén eigenmode) activity. For finite n, the model can be used to determine the local radiative damping consistently, which is needed for the fast evaluation of linear AE (Alfvén eigenmode) stability boundaries that are typically required by energetic particle transport models.

Neoclassical and turbulent E × B flows in flux-driven gyrokinetic simulations of Ohmic tokamak plasmas

The interplay of flows and turbulence in Ohmic FT-2 tokamak plasmas is analysed via gyrokinetic simulations with the flux-driven ELMFIRE code. The simulation predictions agree qualitatively with analytical estimates for the scaling of the neoclassical radial electric field as a function of collisionality for ad hoc parameters. For the experimental parameters, the global full-f modeling agrees well with the analytical estimates in a neoclassical setting, while including kinetic electrons and impurities has a small impact. Allowing turbulence to develop modifies the flow profile through relaxation of profiles caused by turbulent transport, non-adiabatic response of passing electrons around rational surfaces, and turbulent flow drive. Geodesic acoustic mode (GAM) is the main zonal flow component in the simulations, and its frequency and amplitude agree with theoretical predictions and experimental measurements. In the simulations, the non-linear energy transfer from the turbulence to the flows through the Reynolds force is balanced by the collisional flow dissipation. Temporal relationship between the oscillating flow, Reynolds force, and turbulent particle flux is consistent with the fundamental physics picture of GAM modulating turbulent transport on the time scale of the mode. Experimental evidence also suggests anti-correlation of GAM amplitude and turbulent fluctuations.

Modelling and measurement of the electrostatic potential perturbation in consideration of the non-adiabatic electron response to trace tungsten concentration in a tokamak

Trace tungsten ions are almost unavoidable in tokamaks with the tungsten as the first wall material. In high performance plasma, tungsten ions are easily concentrated in the core with a finite gradient along the radius. Prevention of the concentration is an important task for long-pulse H-mode operations. In this paper, it is shown that the tungsten concentration generates electrostatic perturbations due to the bulk electron drift with dissipation. That leads to a phase difference between the electron and the tungsten ion density perturbations. The resultant electrostatic potential extends away from the resonant surface of an internal mode which is characterized by the mode frequency chirping down. This work indicates that the electrostatic potential is mainly determined by the electron kinetics as well as the tungsten-bulk ion collisions, and that the impurity ion dynamics is efficiently influenced by the electron perturbations. Modification of the electron kinetics is a candidate to control the tungsten transport in experiments.

TDDFT investigation of excitation of water tetramer under femtosecond laser pulse irradiation

We study the static properties of water tetramer in ground state, the optical absorption spectra and ultrafast nonadiabatic dynamical response of water tetramer to short and intense laser pulses with different intensities by a real-space, real-time implementation of time-dependent density functional theory coupled to molecular dynamics (TDDFT–MD) nonadiabatically. The calculated results are in good agreement with available values in literature. Four typical irradiated scenarios of water tetramer in laser field, which are “normal vibration,” “break and reorganization,” “fragmentation and new formation” and “pure fragmentation”, are explored by discussing the ionization, the bond lengths of OH bonds and hydrogen bonds and the kinetic energy of ions. The dynamic simulation shows that the reaction channel of water tetramer can really be controlled by choosing appropriate laser parameters referring to the optical absorption spectra and hydrogen ions play an important role in the reaction channel. Furthermore, it is found that the laser intensity affects the kinetic energy of ejected protons more than that of the remaining fragments and all dynamic processes are somehow directly related to the velocity of departing protons.