Basis functions for shallow-water temperature profiles based on the internal-wave eigenmodes

The shallow-water temperature profile is typically parameterized using a few empirical orthogonal function(EOF)coefficients.However,when the experimental area is poorly known or highly variable,the adaptability of the EOFs will be significantly reduced.In this study,a new set of basis functions,generated by combining the internal-wave eigenmodes with the average temperature gradient,is developed for characterizing the temperature perturbations.Temperature profiles recorded by a thermistor chain in the South China Sea in 2015 are processed and analyzed.Compared to the EOFs,the new set of basis functions has higher reconstruction accuracy and adaptability;it is also more stable in ocean regions that have internal waves.

Numerical simulation of the multiple reversed shear Alfvén eigenmodes associated with the triangularity Alfvén gap

It was found that there are multiplicity of low shear toroidicity-induced Alfv′en eigenmodes in a zero beta limit if the inverse aspect ratio is larger than the magnetic shear at the mode location(Candy 1996 Phys. Lett. A 215 299). Because the reversed shear Alfv′en eigenmode(RSAE) and even the RSAE associated with the non-circular triangularity-induced Alfv′en eigenmode(NAE) gap(NAE–RSAE) usually reside near the shear-reversal point, the condition that the inverse aspect ratio is larger than the magnetic shear is naturally satisfied. For this reason, we numerically investigate the existence of multiplicity of core-localized NAE–RSAEs and mode characteristics in the present work. We firstly verify the existence of the multiplicity for zero beta plasma by using a D-shaped equilibrium. It is pointed out that, for a given toroidal mode number, the Alfv′en cascade spectrum accommodates down-sweeping and up-sweeping modes above and below the NAE range of frequencies. An analytical model for the existence of multiple RSAE modes is in good agreement with the simulation results. One notices that the triangularity has a greater effect on the odd-type modes than that on the even-type modes: the odd-type modes come into existence because of the plasma triangularity.

Linear gyrokinetic simulations of reversed shear Alfvén eigenmodes and ion temperature gradient modes in DIII-D tokamak

Global linear gyrokinetic simulations using realistic DIII-D tokamak geometry and plasma profiles find co-existence of unstable reversed shear Alfvén eigenmodes(RSAE)with low toroidal mode number n and electromagnetic ion temperature gradient(ITG)instabilities with higher toroidal mode number n.For intermediate n?=?[10,12],RSAE and ITG co-exist and overlap weakly in the radial domain with similar growth rates but different real frequencies.Both RSAE and ITG growth rates decrease less than 5%when compressible magnetic perturbations are neglected in the simulations.The ITG growth rates increase less than 7%when fast ions are not included in the simulations.Finally,the effects of trapped electrons on the RSAE are negligible.

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

Nonlinear evolution of multiple toroidal Alfvén eigenmodes(TAEs)driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas.To clearly identify the effect of nonlinear coupling on the beam ion loss,simulations over single-n modes are also carried out and compared with those over multiple-n modes,and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail.It is found that in the multiple-n case,the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case.Moreover,increasing fast ion betaβh can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases.For example,the loss level in the multiple-n case forβh=6.0%can even reach 13%of the beam ions and is 44%higher than the sum loss level calculated from all individual single-n modes in the single-n case.On the other hand,when the closely spaced resonance overlap occurs in the multiple-n case,the release of mode energy is increased so that the widely spaced resonances can also take place.In addition,phase space characterization is obtained in both single-n and multiple-n cases.

Stability analysis of Alfvén eigenmodes in China Fusion Engineering Test Reactor fully non-inductive and hybrid mode scenarios

In this paper, NOVA/NOVA-K codes are used to investigate the stability of Alfvén eigenmodes(AEs) in the China Fusion Engineering Test Reactor(CFETR). Firstly, the stability of AEs excited by energetic alpha particles is investigated. For the fully non-inductive scenario, it is found that all AEs are stable, and the least stable toroidal mode number is n= 8. However, for the hybrid mode scenario, it is found that many AEs are unstable, and the least stable toroidal mode numbers are n= 7, 8. Secondly, the effect of energetic alpha-particle parameters and beam ions on AE stability is also presented. The threshold of the least stable AE is about βcrit,α = 1.12%,crit,less than the value of alpha-particle beta(βα=1.34%). The result demonstrates that the AEs excited by alpha particles are weakly unstable. The effect of the beam ions on AE stability is found to be very weak in CFETR.

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

In this work,the gyrokinetic eigenvalue code LIGKA,the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of reversed shear Alfvén eigenmodes(RSAEs).Using the parameters from an ASDEXUpgrade plasma,a benchmark with the three different physical models for RSAE without and with energetic particles(EPs)is carried out.Reasonable agreement has been found for the mode frequency and the growth rate.Mode structure symmetry breaking(MSSB)is observed when EPs are included,due to the EPs’non-perturbative effects.It is found that the MSSB properties are featured by a finite radial wave phase velocity,and the linear mode structure can be well described by an analytical complex Gaussian expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number with opposite signs is generated.The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport.The parallel velocity of EPs is generated in opposite directions,due to different values of the average radial wave number,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.

Influences of the Shape of Rods in Two Dimension Photonic Crystals on Their Defect Eigenmodes

The cross section of photonic crystal fiber (PCF) is a two dimensional photonic crystal. The rods formed in PCF are not exact cylinders, the shape of rods will affect the eigenmode formed in two dimensional photonic crystals around a defect. Based on the relations between the defect eigenmodes and the radius of dielectric cylinders, the defect eigenmodes in photonic crystals in which the ellipse rods take the place of cylinders are studied by numerical calculation. The analysis of the relation between the eigenfrequency and the minor axis radius of ellipse rods show that the defect eigenfrequency is controlled by the cross section area of rods and the distribution of electromagnetic field around the defect is also affected by the cross section shape of rods. It provides a better way to modify the distribution of electromagnetic fields in photonic crystal and keeps the eigenfrequency unchanged.

Self-polarization emission based on coherent combination of intracavity eigenmodes in Nd:YAG/Cr^(4+):YAG lasers

The behavior of self-polarization emission in Nd∶Y_(3)Al_(5)O_(12)(YAG)=Cr^(4+)∶YAG lasers has been proved in some cases.However,the degree and direction of polarization were often sensitive and unstable.We experimentally observed different beam profiles versus the angle of the polarizer relative to the polarization direction of the laser.In order to explore the polarization mechanism,the dynamics of intracavity polarized eigenmodes was analyzed theoretically.Simulative results were well consistent with our experimental observations.It indicated that the linear self-polarization emission was a composite state rather than an intrinsic state.This study contributed to the improvement of the polarization stability in Nd∶YAG=Cr^(4+)∶YAG passively Q-switched lasers.

Runaway electron dynamics in Experimental Advanced Superconducting Tokamak helium plasmas

The generation of runaway electrons(REs)is observed during the low-density helium ohmic plasma discharge in the Experimental Advanced Superconducting Tokamak(EAST).The growth rate of hard x-ray(HXR)is inversely proportional to the line-average density.Besides,the RE generation in helium plasma is higher than that in deuterium plasma at the same density,which is obtained by comparing the growth rate of HXR with the same discharge conditions.The potential reason is the higher electron temperature of helium plasma in the same current and electron density plateau.Furthermore,two Alfvén eigenmodes driven by REs have been observed.The frequency evolution of the mode is not fully satisfied with the Alfvén scaling and when extension of the Alfvén frequency is towards 0,the high frequency branch is~50 kHz.The different spatial position of the two modes and the evolution of the helium concentration could be used to understand deviation between theoretical and experimental observation.

Alfvén eigenmode stability analysis and energetic particle transport prediction for CFETR hybrid scenario

The hybrid scenario is a projection for CFETR operation with high plasma current and density.Therefore, the energetic particles(EPs) generated by fusion reactions can destabilize Alfvén eigenmodes(AEs), which could result in significant EPs loss and redistribution. Both the eigenvalue code NOVA-K and the wrapped local stability code TGLFEP are used to analyze AE stability. The simulation indicates the beta-induced Alfvén eigenmodes with n?>?5 in the core region are the most unstable. The NOVA-K code is used to benchmark the critical density gradient calculated by TGLFEP. In addition, the EPtran code is employed to predict EP transport induced by unstable AEs and turbulence, which reduce EP density in the core and drive approximately 30% EP transport from the core to the edge, thus the EP density profile flattens and EPs with lower energy deposit near the edge.

Electromagnetic dispersion characteristics of a high energy electron beam guided with an ion channel

Taking self-fields into consideration,dispersion properties of two types of electromagnetic modes for a high energy electron beam guided with an ion channel are investigated by using the linear perturbation theory.The dependences of the dispersion frequencies of electromagnetic waves on the electron beam radius,betatron frequency and boundary current are revealed.It is found that the electron beam radius and betatron frequency have different influences on the electromagnetic waves dispersion behavior by compared with the previous works.As the boundary current is taken into account,the TM modes will have two branches and a lowfrequency branch emerged as the new branch in strong ion channel case.This new branch has similar dispersion behavior to the betatron modes.For TE modes,there are two branches and they have different dispersion behaviors in strong ion channel case.However,in weak ion channel case,the dispersion behaviors for both of the low frequency and high frequency branches are similar.

The AK Transform

In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded distribution functions such as in Q machines/plasma diodes or in the scrap-off layer of Tokamak fusion plasmas. The results are valid for functions of function spaces—Lebesgue spaces, which are defined using a natural generalization of the p-norm for finite-dimensional vector spaces, where is the real set, σs is the σ-algebra of Lebesgue measurable sets, and the μ Lebesgue measure. , so that . Note that, using a simpler notation, more natural/known to engineers, f could be considered any piecewise continuous function, that is: Here is a Euclidian space with the usual norm (inner product: ) given by: [1].

Transition from fishbone mode toβ-induced Alfvén eigenmode on HL-2A tokamak

In the presence of energetic particles(EPs)from auxiliary heating and burning plasmas,fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes.Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code,we have identified such a transition between the fishbone instability and theβ-induced Alfvén eigenmode(BAE)for the NBI heated plasmas on HL-2 A.When the safety factor at magnetic axis is well below one,typical kink-fishbone transition occurs as the EP fraction increases.When q0 is raised to approaching one,the fishbone mode is replaced with BAE for sufficient amount of EPs.When q0 is slightly above one,the toroidicity-induced Alfvén eigenmode dominates at lower EP pressure,whereas BAE dominates at higher EP pressure.

CONTACT FRICTION ANALYSIS AND STRESS OSCILLATION SUPPRESSION WITH A SIMPLE INTERFACE ELEMENT

A simple interface element for analyzing contact friction problems is developed.Taking nodaldisplacements and contact stresses as unknowns,this element can simulate frictional slippage,decouplingand re-bonding of two bodies initially mating or having gaps at a common interface.The method is based onthe Finite Element Method and load incremental theory.The geometric and static constraint conditions oncontact surfaces are treated as additional conditions and are included in stiffness equations.This simple ele-ment has the advantages of easy implementation into stan ’dard finite element programs and fast speed for conv-ergence as well as high accuracy for stress distribution in interface.Undesirable stress oscillations are also in-vestigated whenever large stress gradients exist over the contact surfaces.Exact integration or the convention-al Gauss integration scheme used to evaluate the interpolation function matrix of the interface element is foundto be the source of the oscillations.Eigenmode analysis demonstrates that the stress behavior of an interfaceelement can be improved by using the Newton-Cotes integration scheme.Finally,the test example of a stripfooting problem is presented.

Preliminary computation of the gap eigenmode of shear Alfvén waves on the LAPD

Characterizing the gap eigenmode of shear Alfv′en waves(SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on the on Large Plasma Device(LAPD)(Zhang et al. 2008 Phys. Plasmas 15 012103), a linear large plasma device(Gekelman et al. 1991 Rev. Sci. Instrum. 62 2875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions(Chang 2014 Ph.D Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAWs using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it clearer. Such a spectral gap is obtained for the magnetic field of B_0(z) = 1.2 + 0.6 cos[2π(z-33.68)/3.63] with 7.74-m magnetic beach. By introducing two types of local defects(corresponding to E_θ(z_0) = 0 and E'_θ(z_0) = 0 respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of B_0(z) = 0.2 + 0.1 cos[2π(z-33.68)/3.63] and with only four magnetic mirrors, which are achievable by the LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAWs on the LAPD and other linear plasma devices.

Influence of number and depth of magnetic mirror on Alfvnic gap eigenmode

Alfvnic gap eigenmode(AGE) can eject energetic particles from confinement and thereby threaten the success of magnetically controlled fusion. A low-temperature plasma cylinder is a promising candidate to study this eigenmode, due to easy diagnostic access and simple geometry, and the idea is to arrange a periodic array of magnetic mirrors along the plasma cylinder and introduce a local defect to break the field periodicity. The present work validates this idea by reproducing a clear AGE inside a spectral gap, and more importantly details the influence of the number and depth(or modulation factor)of magnetic mirror on the characteristics of AGE. Results show that AGE is suppressed by other modes inside the spectral gap when the number of magnetic mirrors is below a certain value, which leads to a weakened Bragg's effect. The structure and frequency of AGE remain unchanged for a decreased number of magnetic mirrors, as long as this number is enough for the AGE formation. The width of spectral gap and decay constant(inverse of decay length) of AGE are linearly proportional to the depth of magnetic mirror, implying easier observation of AGE through a bigger mirror depth. The frequency of AGE shifts to a lower range with the depth increased, possibly due to the unfrozen plasma with field line and the invalidity of small-perturbation analysis. Nevertheless, it is exciting to find that the depth of field modulation can be increased to form AGE for a very limited number of magnetic mirrors. This is of particular interest for the experimental implementation of AGE on a low-temperature plasma cylinder with limited length.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

Robust structured light in atmospheric turbulence

Structured light is routinely used in free-space optical communication channels,both classical and quantum,where information is encoded in the spatial structure of the mode for increased bandwidth.Both real-world and experimentally simulated turbulence conditions have revealed that free-space structured light modes are perturbed in some manner by turbulence,resulting in both amplitude and phase distortions,and consequently,much attention has focused on whether one mode type is more robust than another,but with seemingly inconclusive and contradictory results.We present complex forms of structured light that are invariant under propagation through the atmosphere:the true eigenmodes of atmospheric turbulence.We provide a theoretical procedure for obtaining these eigenmodes and confirm their invariance both numerically and experimentally.Although we have demonstrated the approach on atmospheric turbulence,its generality allows it to be extended to other channels too,such as aberrated paths,underwater,and in optical fiber.

Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters

Spatial modes have received substantial attention over the last decades and are used in optical communication applications.In fiber-optic communications,the employed linearly polarized modes and phase vortex modes carrying orbital angular momentum can be synthesized by fiber vector eigenmodes.To improve the transmission capacity and miniaturize the communication system,straightforward fiber vector eigenmode multiplexing and generation of fiber-eigenmode-like polarization vortices(vector vortex modes)using photonic integrated devices are of substantial interest.Here,we propose and demonstrate direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters.By exploiting vector vortex modes(radially and azimuthally polarized beams)generated from silicon microring resonators etched with angular gratings,we report data-carrying fiber vector eigenmode multiplexing transmission through a 2-km large-core fiber,showing low-level mode crosstalk and favorable link performance.These demonstrations may open up added capacity scaling opportunities by directly accessing multiple vector eigenmodes in the fiber and provide compact solutions to replace bulky diffractive optical elements for generating various optical vector beams.

Comparative first-principles study of elastic constants of covalent and ionic materials with LDA,GGA,and meta-GGA functionals and the prediction of mechanical hardness

Accurate prediction of single-crystal elastic constants is critical for materials design and for understanding phase transition and elastic interactions in materials.In this work,the accuracy of elastic constants calculated with three density functional approximations has been compared,including the local density approximation(LDA),the generalized gradient approximation(GGA),and the recently developed strongly constrained and appropriately normed(SCAN)meta-GGA.The results show that SCAN and PBE describe elastic constants better than LDA.The strong correlation between the mechanical hardness and the stiffness of the softest eigenmode(SSE)has been given for above three density functionals.The correlation is capable of predicting accurately the hardness of covalent,ionic,and mixed covalent-ionic crystals,and providing us a convenient indicator for the discovery of hard or superhard materials.