Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.

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.

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.

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.

Simulations of Reversed Shear Configuration in EAST

The reversed shear （RS） mode is one of the advanced configurations being considered in EAST. Predictive simulations of EAST reversed shear configuration are carried out using an 1.5D equilibrium evolution code. In order to have the desired monotonic q-profile during a tokamak discharge, a successful preparation phase is required. In our simulation, the plasma current is ramped up from 100 kA to a fiat-top maximum of 1.0 MA for four seconds. An ICRH power of 1 MW is applied until the plasma shape is formed at the moment of 4 s, and then the power is raised to 3 MW. A LHCD power of 3.5 MW is applied from ls to optimize the plasma current density profile. A series of simulations are performed to study the influence of the time of applying the auxiliary heating on the plasma parameters. Based on these simulations, a scheme is proposed and tested for the control of the safety factor profile, which is very useful in real time profile control in tokamak experiments.

Stability of Tokamak Equilibrium with Internal Transport Barrier against High-n MHD Ballooning Mode

A new eigen-mode equation for the tokamak high-n （the toroidal mode number） ideal magnetohydrodynamic （MHD） ballooning mode in tokamak plasmas is derived to include the toroidal effects that are significant for stability of configurations with internal transport barriers （ITBs）, Fot tokamak equilibria of shift circular flux surfaces, these toroidal effects basically are the finite inverse aspect ratio and the Shafranov shift. The former yields the averaged favorable curvature stabilization while the latter further strengthens this effect, leading to a low shear stable channel connecting the first and second stability regions, and to the shrinkage of unstable region in the （8,α） diagram. The dependence of the critical shear, below which the plasma is stable, on these effects is given. These results are important for understanding the ITB physics to some regards.

Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode(DTM)are numerically investigated through the three-dimensional,toroidal,nonlinear resistive-MHD code(CLT).We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations,which are similar to those driven by the kink mode.The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations.With a high perpendicular thermal conductivity,the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow.However,with a low perpendicular thermal conductivity,the system tends to exhibit sawtooth-like oscillations.With a sufficiently high or low heating rate,the system exhibits sawtooth-like oscillations,while with an intermediate heating rate,the system quickly evolves into a steady state.At the steady state,there exist the non-axisymmetric magnetic field and strong radial flow,and both are with helicity of m/n=2/1.Like the steady state with m/n=1/1 radial flow,which is beneficial for preventing the helium ash accumulation in the core,the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady state operations in future fusion reactors.We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry,which implies that the steady state with saturated m/n=2/1 islands might exist in different tokamaks.

A Simulation of the Effect of Collisional Dissipation of Fast Electrons on the Radial Profiles of the Current Driven by Lower-Hybrid-Waves on the HT-7 Tokamak

For the effect of the collisional dissipation of fast electrons driven by the lower-hybrid waves, a predictive simulation is made for the HT-7 plasma. The simulation results show that the dissipation of fast electrons counteracts the effect of radial diffusion to some extent, thereby making the lower-hybrid driven current profile closer to the power deposition profile. So, in the case of an off-axis lower-hybrid wave power launching, the dissipation is helpful in maintaining a center-hollowed current profile in lower hybrid current drive （LHCD） plasmas, and thus possibly maintains the desired reversed magnetic shear.

Reversibility of the structure and dewaterability of anaerobic digested sludge

The reversibility of the structure and dewaterability of broken anaerobic digested sludge（ADS）is important to ensure the efficiency of sludge treatment or management processes.This study investigated the effect of continuous strong shear（CSS）and multipulse shear（MPS）on the zeta potential,size（median size,d（50））,mass fractal dimension（DF）,and capillary suction time（CST）of ADS aggregates.Moreover,the self-regrowth（SR）of broken ADS aggregates during slow mixing was also analyzed.The results show that raw ADS with d（50） of 56.5μm was insensitive to CSS–SR or MPS–SR,though the size slightly decreased after the breakage phase.For conditioned ADS with d（50） larger than 600μm,the breakage in small-scale surface erosion changed to large-scale fragmentation as the CSS strength increased.In most cases,after CSS or MPS,the broken ADS had a relatively more compact structure than before and d（50） is at least 200μm.The CST of the broken fragments from optimally dosed ADS increased,whereas that corresponding to overdosed ADS decreased.MPS treatment resulted in larger and more compact broken ADS fragments with a lower CST value than CSS.During the subsequent slow mixing,the broken ADS aggregates did not recover their charge,size,and dewaterability to the initial values before breakage.In addition,less than 15%self-regrowth in terms of percentage of the regrowth factor was observed in broken ADS after CSS at average velocity gradient no less than 1905.6 sec^（-1）.