Trapped Modes Research Articles

Progress on physics understanding of improved confinement with fishbone instability at low q 95 < 3.5 operation regime in EAST

Improved confinement at the low q 95 < 3.5 operation regime with fishbone instability compared to sawtooth oscillation has been observed and investigated on the EAST under the dominant electron heating condition with a tungsten divertor. The formation of an internal transport barrier in the ion thermal channel strongly correlates to the excitation of the fishbone, accompanied by reduced particle outward transport in the core region identified by a central peaked density profile. Current density distribution is found to change from a monotonic shape with q 0 < 1 during sawtooth oscillation to a central flat structure, magnetic shear s ∼ 0 at ρ < 0.4, with the fishbone instability at where the higher off-axis bootstrap current fraction might play a critical role. Linear gyrokinetic simulation by NLT code was carried out to investigate the turbulent transport characteristics, which is qualitatively in good agreement with experimental measurements from CO2 laser collective scattering diagnostics. The electron-scale trapped electron mode that dominates the turbulent transport during sawtooth is found to be stabilized with the fishbone at identical heating power and plasma configurations.

Global gyrokinetic study of shaping effects on electromagnetic modes at NSTX aspect ratio with ad hoc parallel magnetic perturbation effects

Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at National Spherical Torus Experiment (NSTX) aspect ratio and high plasma β using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation, with the gyrokinetic codes GENE and GEM being used for local verification and global cross-verification. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced in a high-elongation and high-triangularity NSTX-like geometry compared to a circular NSTX-like geometry. For example, growth rates of kinetic ballooning modes at high-β are reduced to the level of that of collisionless trapped electron modes.

Global gyro-kinetic study of magnetic shaping effects on linear trapped electron mode instability in normal/reversed magnetic shear plasmas

A linear δf version of the gyro-kinetic Vlasov code GKNET (Gyro-Kinetic Numerical Experiment of Tokamak) is extended to the global cylindrical coordinates (R, φ, Z) and includes the kinetic electron response, to study the shaping effect on linear drift-wave instabilities in Tokamak plasmas. Cross-verifications are performed between three GKNET versions that use different electron models, i.e. the adiabatic electron model, hybrid electron model (only trapped electrons are calculated kinetically) and full-kinetic electron model (all electrons are calculated kinetically). A destabilizing effect of non-adiabatic passing electrons is observed in the full-kinetic case for the ion temperature gradient (ITG) mode in the short wavelength region and the trapped electron mode (TEM). The ion-to-electron mass ratio and the electron–electron collisionality have weak impacts on the destabilization of ITG/TEM. Utilizing magnetohydrodynamic equilibria designed with normal and reversed magnetic shear (NS and RS), the characteristics of linear TEMs and the corresponding impact of plasma shaping are studied based on the GKNET code with full-kinetic electrons. Due to the change in temperature/density gradient and magnetic shear either measured locally in the low field side (LFS) or averaged over the flux surface, plasma shaping shows different impacts on linear TEMs in NS and RS configurations. For the elongation κ, the increase in κ always stabilizes linear TEMs due to the reduction in the effective profile gradient over the flux surface. For the triangularity δ, in the NS case, the change in δ shows weak dependence on TEM linear growth rates due to the balance between variations of profile gradients and magnetic shear in the LFS. In the RS case, local magnetic shear in the peak gradient region is nearly zero. Thus, the variation in local profile gradient plays a dominant role on the linear growth in a plasma shaping scan. Consequently, the negative triangularity (δ < 0) has a destabilizing effect on the linear TEMs in the RS configuration mainly due to the upshift in local profile gradient in the LFS.

LC-MS/MS-MS3 for determination and quantification of Δ9-tetrahydrocannabinol and metabolites in blood samples

Due to the high prevalence of cannabinoids in forensic toxicology, it is crucial to have an efficient method that allows the use of a small sample amount and that requires a minimal sample preparation, for the determination and quantification of low concentrations. A simple, highly selective and high throughput liquid chromatography tandem mass spectrometry method (LC-MS/MS-MS3) was developed for the determination and quantification of Δ9-tetrahydrocannabinol (THC), 11-hydroxy-Δ9-THC (THC-OH) and 11-nor-Δ9-THC-9-carboxylic acid (THC-COOH) in blood samples. Chromatographic analysis was preceded by a protein precipitation of 0.1 mL of blood samples with acetonitrile, then THC, THC-OH, THC-COOH and deuterated internal standards were separated on an Acquity UPLC® HSS T3 (100 mm × 2.1 mm i.d., 1.8 mm) reversed-phase column using a gradient elution with 2 mM aqueous ammonium formate (0.1% formic acid) and methanol, at a flow rate of 0.4 mL/min, and with a run time of 10 min. For MS/MS-MS3 analysis, a SCIEX QTRAP® 6500+ linear ion trap triple quadrupole mass spectrometer was used via electrospray ionization (ESI), operated in multiple reaction mode (MRM) and linear ion trap mode (MS3). The method was validated in accordance with international accepted criteria and guidelines. The method was selective and linear between 0.5–100 ng/mL (r2 > 0.995). The lower limits of quantification (LLOQ) corresponded to the lowest concentrations used for the calibration curves. The coefficients of variation obtained for accuracy and precision were less than 15%. The mean recoveries were between 88.0–101.4% for the studied concentration levels (1 ng/mL, 5 ng/mL and 50 ng/mL). No significant interfering compounds, matrix effects or carryover were observed. The validated method provides a sensitive, efficient and robust procedure for the quantitation of cannabinoids in blood using LC–MS/MS-MS3 and a sample volume of 0.1 mL. This work is also a proof of concept for using LC-MS3 technique to determine drugs in biological samples.

Revisiting PARP2 and PARP1 trapping through quantitative live-cell imaging.

Poly (ADP-ribose) polymerase-1 (PARP1) and 2 (PARP2) are two DNA damage-induced poly (ADP-ribose) (PAR) polymerases in cells and are the targets of PARP inhibitors used for cancer therapy. Strand breaks recruit and activate PARP1 and 2, which rapidly generate PAR from NAD+. PAR promotes the recruitment of other repair factors, relaxes chromatin, and has a role in DNA repair, transcription regulation, and RNA biology. Four PARP1/2 dual inhibitors are currently used to treat BRCA-deficient breast, ovarian, prostate, and pancreatic cancers. In addition to blocking the enzymatic activity of PARP1 and 2, clinical PARP inhibitors extend the appearance of PARP1 and PARP2 on chromatin after damage, termed trapping. Loss of PARP1 confers resistance to PARP inhibitors, suggesting an essential role of trapping in cancer therapy. Yet, whether the persistent PARP1 and 2 foci at the DNA damage sites are caused by the retention of the same molecules or by the continual exchange of different molecules remains unknown. Here, we discuss recent results from quantitative live-cell imaging studies focusing on PARP1 and PARP2's distinct DNA substrate specificities and modes of recruitment and trapping with implications for cancer therapy and on-target toxicities of PARP inhibitors.

Development of an Allenyne-Alkyne [4+2] Cycloaddition and its Application to Total Synthesis of Selaginpulvilin A.

A new [4+2] cycloaddition of allenyne-alkyne is developed. The reaction is believed to proceed with forming an α,3-dehydrotoluene intermediate. This species behaves as a σπ-diradical to react with a hydrogen atom donor, whereas it displays a zwitterionic reactivity toward weak nucleophiles. The efficiency of trapping α,3-dehydrotoluene depends not only on its substituents but also the trapping agents. Notable features of the reaction are the activating role of the extra alkyne of the 1,3-diyne that reacts with the allenyne moiety and the opposite mode of trapping with oxygen and nitrogen nucleophiles. Oxygen nucleophiles result in the oxygen-end incorporation at the benzylic position of the α,3-dehydrotoluene, whereas with amine nucleophiles the nitrogen-end is incorporated into the aromatic core. Relying on the allenyne-alkyne cycloaddition as an enabling strategy, a concise total synthesis of phosphodiesterase-4 inhibitory selaginpulvilin A is realized.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

Trapped modes in a fluid with three layers topped by a rigid lid

We consider trapping of linear water waves by a submerged horizontal cylinder in a three‐layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary‐value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.

The model of particles modes. II. Transition to a fishbone-like state triggered by global synchronization and energetic particles

The interplay between kinetic aspects induced by energetic particles on turbulence is analyzed with a simplified model of ion-temperature-gradient-driven turbulence in magnetically confined plasmas. These topics are presented within an unified Hamiltonian framework in light of a new approach based on global phase synchronization between trapped particle modes and energetic particle modes. Numerical experiments have been carried out to elucidate concepts and physical processes of transition to a fishbone-like state triggered by energetic particles.

Effects of swimming environment on bacterial motility

Swimming trajectories of bacteria can be altered by environmental conditions, such as background flow and physical barriers, that limit the free swimming of bacteria. We present a comprehensive model of a bacterium that consists of a rod-shaped cell body and a flagellum which is composed of a motor, a hook, and a filament. The elastic flagellum is modeled based on the Kirchhoff rod theory, the cell body is considered to be a rigid body, and the hydrodynamic interaction of a bacterium near a wall is described by regularized Stokeslet formulation combined with the image system. We consider three environmental conditions: (1) a rigid surface is placed horizontally and there is no shear flow, (2) a shear fluid flow is present and the bacterium is near the rigid surface, and (3) while the bacterium is near the rigid surface and is under shear flow, an additional sidewall which is perpendicular to the rigid surface is placed. Each environmental state modifies the swimming behavior. For the first condition, there are two modes of motility, trap and escape, whether the bacterium stays near the surface or moves away from the surface as we vary the physical and geometrical properties of the model bacterium. For the second condition, there exists a threshold of shear rate that classifies the motion into two types of paths in which the bacterium takes either a periodic coil trajectory or a linear trajectory. For the last condition, the bacterium takes upstream motility along the sidewall for lower shear rates and downstream motility for larger shear flow rates.

Study of turbulence in the high β P discharge using only RF heating on EAST

High poloidal beta scenarios with a favorable energy confinement (, have been achieved on the Experimental Advanced Superconducting Tokamak using only radio frequency wave heating. Gyrokinetic simulations are carried out with experimental plasma parameters and tokamak equilibrium data of a typical high discharge using the gyrokinetic toroidal code. Linear simulations show that electron-temperature scale length and electron-density scale length destabilize the turbulence, collision effects stabilize the turbulence, and the instability propagates in the electron diamagnetic direction. These properties indicate that the dominant instability in the core of high plasma is a collisionless trapped electron mode. Ion thermal diffusivity, calculated by nonlinear gyrokinetic simulations, is consistent with the experimental value, in which the electron collision effects play an important role. Further analyses show that instabilities with are suppressed by collision effects and collision effects reduce the radial correlation length of turbulence, resulting in the suppression of the turbulence.

Turbulence mitigation in maximum-J stellarators with electron-density gradient

In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the density-gradient-driven branch of the ‘trapped electron mode’ (TEM) is predicted to be linearly stable if the magnetic field has the maximum-J property, as is very approximately the case in certain magnetic configurations of the Wendelstein 7-X experiment (W7-X). Here we show, using both analytical theory and simulations, that the benefits of the optimisation of W7-X also serve to mitigate ion-temperature-gradient (ITG) modes as long as an electron density gradient is present. We find that the effect indeed carries over to nonlinear numerical simulations, where W7-X has low TEM-driven transport, and reduced ITG turbulence in the presence of a density gradient, giving theoretical support for the existence of enhanced confinement regimes, in the presence of strong density gradients (e.g. hydrogen pellet or neutral beam injection).

An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency ω, but is especially efficient for high-frequency problems. It is based on a time-domain approach and consists of three steps: i) computation of a suitable incoming plane wavelet with compact support in the propagation direction; ii) solving a scattering problem in the time domain for the incoming plane wavelet; iii) reconstruction of the time-harmonic solution from the time-domain solution via a Fourier transform in time. An essential ingredient of the new method is a front-tracking mesh adaptation algorithm for solving the problem in ii). By exploiting the limited support of the wave front, this allows us to make the number of the required degrees of freedom to reach a given accuracy significantly less dependent on the frequency ω. We also present a new algorithm for computing the Fourier transform in iii) that exploits the reduced number of degrees of freedom corresponding to the adapted meshes. Numerical examples demonstrate the advantages of the proposed method and the fact that the method can also be applied with external source terms such as point sources and sound-soft scatterers. The gained efficiency, however, is limited in the presence of trapping modes.

Non-stationary oscillation of a string on the Winkler foundation subjected to a discrete mass–spring system non-uniformly moving at a sub-critical speed

We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass–spring system non-uniformly moving at a given sub-critical speed. The speed of the mass–spring system is assumed to be a slowly time-varying function. To describe a non-vanishing free oscillation we use an analytic approach based on the method of stationary phase and the method of multiple scales. The moving oscillator is characterized by a partial frequency, which can be greater or less than the cut-off frequency. Accordingly, a sub-critical uniformly accelerated motion generally has two stages. At the first stage there exists a trapped mode, and, therefore, a part of the wave energy is localized near the moving oscillator and does not propagate away. For this stage we obtain the analytic solution in a simple form describing non-vanishing free oscillation and verify it numerically. For the second stage there is no trapped mode, and all the wave energy propagate away. This stage is investigated numerically, and some unexpected results are obtained. Additionally, we consider the case of the oscillator with a destabilizing spring. The dynamics of the system in the latter case is quite different from the case of commonly used stabilizing spring, since the system loses the stability during an accelerated motion. We also take into consideration the forced oscillation caused by an external load being a superposition of harmonics with time-varying parameters (the amplitude and the frequency).

A transit through the trapping and blocking of flexural-gravity wave: Impact of two-dimensional current and in-plane compression

The combined effect of two-dimensional ocean current and compression on flexural-gravity waves trapping and blocking is investigated under the oblique incidence of the propagating mode on the floating ice sheet. The submerged horizontal cylinder has been considered to analyze the existence of trapped modes. The multipole expansion method has been used by modifying the multipoles to match the upper surface condition, including current magnitudes along the x- and y-directions. This method gives rise to a coupled system of equations having singular coefficients, which makes the problem more challenging. The occurrence of the trapped waves depends on the nature of the current, the angle of the incident wave, and the compressive force acting on the ice sheet. It has been observed that there exists a critical range of compressive force in which trapped modes show their existence, even when both the components of the current are acting in the positive direction. When the trapped mode frequency approaches the blocking frequency, a jump in the trapped wavenumber occurs due to the existence of multiple propagating modes at blocking frequency. Thus, the occurrence of frequency band of wave blocking results in a quantitative measure of trapped wave frequency under the assumption of a single propagating mode. Such a frequency band of wave blocking is shown under different choices of current type. A modified theory based on multipole expansion method that could cater to the multiple propagating modes will be required in future to obtain trapped modes within the frequency band of wave blocking.

A numerical study on the closed packed array of gold discs as an efficient dual mode plasmonic tweezers

In this report, we propose the closed pack array of gold discs on glass, as a dual mode plasmonic tweezers that benefits from two trapping modes. The first trapping mode is based on leaky surface plasmon mode (LSPM) on the gold discs with a longer penetration depth in the water and a longer spatial trapping range, so that target nanoparticles with a radius of 100 nm can be attracted toward the gold surface from a vertical distance of about 2 µm. This trapping mode can help to overcome the inherent short range trapping challenge in the plasmonic tweezers. The second trapping mode is based on the dimer surface plasmonic mode (DSPM) in the nano-slits between the neighboring gold discs, leading to isolated and strong trapping sites for nanoparticles smaller than 34 nm. The proposed plasmonic tweezers can be excited in both LSPM and DSPM modes by switching the incident wavelength, resulting in promising and complementary functionalities. In the proposed plasmonic tweezers, we can attract the target particles towards the gold surface by LSPM gradient force, and trap them within a wide half widthhalfmaximum (HWHM) that allows studying the interactions between the trapped particles, due to their spatial proximity. Then, by switching to the DSPM trapping mode, we can rearrange the particles in a periodic pattern of isolated and stiff traps. The proposed plasmonic structure and the presented study opens a new insight for realizing efficient, dual-mode tweezers with complementary characteristics, suitable for manipulation of nanoparticles. Our thermal simulations demonstrate that the thermal-induced forces does not interefe with the proposed plasmonic tweezing.

Integrable modulation, curl forces and parametric Kapitza equation with trapping and escaping

In this present communication, the integrable modulation problem has been applied to study parametric extension of the Kapitza rotating shaft problem, which is a prototypical example of curl force as formulated by Berry and Shukla in (JPA 45:305201, 2012) associated with simple saddle potential. The integrable modulation problems yield parametric time-dependent integrable systems. The Hamiltonian and first integrals of the linear and nonlinear parametric Kapitza equation (PKE) associated with simple and monkey saddle potentials have been given. The construction has been illustrated by choosing $$ \omega (t)=a +b\cos t$$ and that maps to Mathieu-type equations, which yield Mathieu extension of PKE. We study the dynamics of these equations. The most interesting finding is the mixed mode of particle trapping and escaping via the heteroclinic orbits depicted with the parametric Mathieu–Kapitza equation, which are absent in the case of nonparametric cases.

Symmetry-protected, zero-energy disclination modes and their observation in an acoustic lattice

Building upon the bulk-boundary correspondence in topological phases, disclinations-crystalline topological defects that induce a curvature singularity in a lattice-have been harnessed for trapping modes within the bulk of synthetic lattices. These trapped modes are useful in photonic and sonic crystals because the bulk surrounding a defect generates a bandgap that isolates the mode from the gapless free space. However, in current realizations, these modes are not protected from delocalization because so far, experimentally realized mode-trapping disclinations have broken chiral symmetry. As such, their modes do not lie at mid-gap and can hybridize with bulk modes to form resonances, losing their confinement. Here, we devise a fundamentally new paradigm that allows the protection of modes bound to disclinations that preserve chiral symmetry. These disclination modes are consequently pinned at the mid-gap, which in turn result in their protected maximal confinement. By presenting a protection mechanism that rests on the interplay between the topology of the lattice and the point group symmetry of defects and by experimentally probing these modes in judiciously designed chiral-symmetric acoustic lattices, our work demonstrates the existence of protected modes within the bulk of synthetic lattices.

The propagation and decay of a coastal vortex on a shelf

A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simple shelf geometry, we determine analytic expressions for the wave wake and the leading-order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self-similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure.

High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells.

We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of controlled ejection of solitons with significantly high speeds. At the outset, we describe the scattering setup and characterize the soliton ejection in terms of the different parameters of the system. Then, we formulate a theoretical model revealing the underlying physics of soliton ejection. The model is based on energy and norm exchange between the incident soliton and a stable trapped mode corresponding to an exact solution of the governing nonlinear Schrödinger equation. Remarkably, stationary solitons can lead to high-speed soliton ejection where part of the nonlinear interaction energy transforms to translational kinetic energy of the ejected soliton. Our investigation shows that soliton ejection always occurs whenever the incident soliton norm is greater than that of the trapped mode whereas their energy is almost the same. Once the incident soliton is trapped, the excess in norm turns to an ejected soliton in addition to a small amount of radiation that share translational kinetic energy. We found that higher ejection speeds are obtained with multinode trapped modes that have higher binding energy. Simultaneous two-soliton ejection has been also induced by two solitons scattering with the potential from both of its sides. An ejection speed almost twice as that of single soliton ejection was obtained. Ejection outcome and ejection speed turn out to be sensitive to the relative phase between the two incoming solitons, which suggests a tool for soliton phase interferometry.