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.

Experimental observation of reverse-sheared Alfvén eigenmodes(RSAEs) in ELMy H-mode plasma on the EAST tokamak

Reverse-sheared Alfv6n eigenmodes （RSAEs） have been observed by using an interferometer and ECE diagnostics in NBI heated ELMy H-mode plasma on EAST tokamak. A typical feature of these modes is a fast frequency sweeping upward from -80 kHz to -110 kHz in hundred milliseconds during which the plasma temperature, density and rotation keeps no change. Only core channels of the interferometer can observe these modes, implying a core localized mode. The ECE measurement further showed that these modes located at about ρ = 0.37-0.46, just around the position of qmin with ρ -0.4. These core localized modes are very weak in the magnetic fluctuations measured by mirnov probes mounted at the machine vacuum vessel. A multiple frequency fluctuation component, seemingly the so-called ＇grand cascades＇, was also clearly observed on the ECE signal at ρ = 0.46. During the phase, a transient internal transport barrier （ITB） in ion temperature and toroidal rotation was observed and the ITB foot was just close to the position of qmin. A modulation of RSAE frequency by ELM event was observed and this modulation could be attributed to rotation decrease or qmin increase due to ELM. Further study of these modes in EAST can provide valuable constraints for the q profile measurement and will be important for the long pulse operation.

Discrete Alfvn eigenmodes in international thermonuclear experimental reactor operations with negative magnetic shear

Discrete Alfven eigenmodes in steady-state operation scenarios with negative magnetic shear in the international thermonuclear experimental reactor are investigated in this paper. These magnetohydrodynamic eigenmodes are trapped by the s-induced potential wells along the magnetic field line. Here α = -q2Rdβ/dr with q being the safety factor, the ratio between plasma and magnetic pressures, and R the major radius, and r the minor radius. Due to negligible continuum damping via wave energy tunneling, these Alfven eigenmodes could be readily destabilized by energetic particles.

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.

Ion Heating from Nonlinear Landau Damping of High Mode Number Toroidal Alfvén Eigenmodes

Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes （TAEs） is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spectral transfer rate to more stable modes, but relatively insensitive to the details of linear damping mechanisms.

Magnetic Configuration Effects on Fast Ion Losses Induced by Fast Ion Driven Toroidal Alfvén Eigenmodes in the Large Helical Device

Beam-ion losses induced by fast-ion-driven toroidal Alfven eigenmodes （TAE） were measured with a scintillator-based lost fast-ion probe （SLIP） in the large helical device （LHD）. The SLIP gave simultaneously the energy E and the pitch angle X=arccos（v///v） distribution of the lost fast ions. The loss fluxes were investigated for three typical magnetic configurations of Rax-vac=3.60 m, 3.75 m. and 3.90 m, where Rax-vac is the magnetic axis position of the vacuum field. Dominant losses induced by TAEs in these three configurations were observed in the E/X regions of 50-190 keV/40°, 40-170 keV/25°, and 30-190 keV/30°, respectively. Lost-ion fluxes induced by TAEs depend clearly on the amplitude of TAE magnetic fluctuations, Rax-vac and the toroidal field strength Bt. The increment of the loss fluxes has the dependence of （bTAE/Bt）s. The power s increases from s = 1 to 3 with the increase of the magnetic axis position in finite beta plasmas.

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.

MHD Instabilities and Their Effects on Plasma Confinement in Large Helical Device Plasmas with Intense Neutral Beam Injection

MHD stability of the Large Helical Device (LHD) plasmas produced with intenseneutral beam injection is experimentally studied. When the steep pressure gradient near the edge isproduced through L-H transition or linear density ramp experiment, interchange-like MHD modes whoserational surface is located very close to the last closed flux surface are strongly excited in acertain discharge condition and affect the plasma transport appreciably. In NBI-heated plasmasproduced at low toroidal field, various Alfven eigenmodes are often excited. Bursting toroidalAlfven egenmodes excited by the presence of energetic ions induce appreciable amount of energeticion loss, but also trigger the formation of internal and edge transport barriers.

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.

Contribution of the Large Helical Device Plasmas to Alfvén Eigenmode Physics in Toroidal Plasmas

In the large helical device （LHD） having three dimensional configuration, Alfven eigenmodes （AEs） destabilized by energetic ions are widely investigated using neutral beam heated plasmas with monotonic and non-monotonic rotational transform （l/2π） profiles. In a plasma with monotonic l/2π-profile, core-localized toroidicity-induced Alfven eigenmode （TAE） as well as global one are often observed. With the increase in the averaged toroidal beta value, defined as the ratio of total plasma pressure to toroidal magnetic pressure, core-localized TAE with low toroidal mode number becomes global. In a relatively high beta plasma with monotonic l/2π-profile, two TAEs with different toroidal mode number often interact nonlinearly and generate another modes through three wave coupling. In a plasma with non-monotonic l/2π-profile generated by intense counter neutral beam current drive, reversed shear Alfven eigenmode （RSAE） and geodesic acoustic mode （CAM） excited by energetic ions were observed for the first time in a helical plasma. Nonlinear coupling was also observed between RSAE and GAM.

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].

Effects of Boundary Current on Electromagnetic Dispersion Characteristics for a Relativistic Electron Beam

With betatron oscillation characteristics of the electron beam and ion channel effect taken into account,dispersion characteristics of electrostatic modes and TM modes for a relativistic electron beam guided by ion channel are studied.Dispersion relations are derived and solved numerically to investigate the dependence of the dispersion characteristics for electrostatic modes and TM modes on the betatron oscillation frequency and the ratio of the relativistic electron beam radius to the waveguide radius.The effects of the boundary current on the dispersion characteristic of the TM modes and the interaction between the betatron modes and TM modes are analyzed.When considering the boundary current,for a strong ion channel,a new low-frequency branch of the TM modes arises and the interaction frequency between the betatron modes and the TM01modes is increased with the same parameters.

Relationship between group velocity and symmetry of photonic crystals

Group velocity （GV） of eigenmode is a crucial parameter to explain the extraordinary phenomena about light propagation in photonic crystals （PhCs）. To study relationships between group velocity and symmetry of PhCs, a new general expression of CV in PhCs made up of non-dispersive material is introduced. Based on this, the CVs of eigenmodes of PhCs, especially those of degenerate eigenmodes at highly symmetric points in the first Brillouin zone, are discussed. Some interesting results are obtained. For example, the summation of degenerate eigenmodes＇ CVs is invariant under the operations of wave vector K-group MK. In addition, some numerical results are presented to verify them.