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.

Gyrokinetic simulations of nonlinear interactions between magnetic islands and microturbulence

A conservative scheme of kinetic electrons for gyrokinetic simulations in the presence of magnetic islands has been implemented and verified in the gyrokinetic toroidal code, where zonal and nonzonal components of all perturbed quantities are solved together. Using this new conservative scheme, linear simulation of kinetic ballooning mode has been successfully benchmarked with the electromagnetic hybrid model. Simulations of nonlinear interactions between magnetic islands and the ion temperature gradient(ITG) mode in a tokamak show that the islands rotate at the electron diamagnetic drift velocity. The linear ITG structure shifts from the island O-point toward the X-point due to the pressure flattening effect inside the islands, and the nonlinear ITG structure peaks along the magnetic island separatrix because of the increased pressure gradient there.

GTC Simulation of Ideal Ballooning Mode in Tokamak Plasmas

In the present paper,we first derive the eigenmode equation of the ideal ballooning mode in tokamak plasmas using a gyrokinetic equation.It is shown that the gyrokinetic eigenmode equation can be reduced to the magnetohydrodynamic（MHD） form in the long wavelength limit when kinetic effects are ignored.Then,the global gyrokinetic toroidal code（GTC） is applied for simulations of the edge-localized ideal ballooning modes.The obtained mode structures are compared with the results of ideal MHD simulations.The observed scaling of the linear growth rate with the toroidal mode number is consistent with the ideal MHD theory.The simulation results verify the GTC capability of simulating MHD processes in toroidal plasmas.

Effects of magnetic field on electron power absorption in helicon fluid simulation

In this study,a code,named Peking University Helicon Discharge(PHD),which can simulate helicon discharge processes under both a background magnetic field greater than 500 G and a pressure less than 1 Pa,is developed.In the code,two fluid equations are used.The PHD simulations led to two important findings:(1)the temporal evolution of plasma density with the background magnetic field exhibits a second rapid increase(termed as the second density jump),similar to the transition of modes in helicon plasmas;(2)in the presence of a magnetic field,the peak positions of electron power absorption appeared near the central axis,unlike in the case of no magnetic field.These results may lead to an enhanced understanding of the discharge mechanism.

Relationship of mode transitions and standing waves in helicon plasmas

Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

We investigate nonlinear phase dynamics of an ideal kink mode,induced by E×B flow.Here the phase is the cross phase(θ_(c))between perturbed stream function of velocity(f)and magnetic field(y),i.e.θ_(c)=θf−θψ.A dimensionless parameter,analogous to the R_(i)chardson number,R_(i)=16gkink w^(2)E^(2)(γkink:the normalized growth rate of the pure kink mode;wE:normalized E×B shearing rate)is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear.When R_(i)>1,θ_(c) is locked to a fixed value,corresponding to the conventional eigenmode solution.When R_(i).1,θ_(c) enters a phase slipping or oscillating state,corresponding to a nonmodal solution.The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E×B shear flow.

Nonlinear Generation of Zonal Fields by the Beta-Induced Alfven Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfven eigenmode （BAE） destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations. It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE. In the weakly driven case, the zonal fields with a strong geodesic acoustic mode （GAM） component have weak effects on the nonlinear BAE evolution. In the strongly driven case, the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.

Effects of resonant magnetic perturbations on radial electric fields in DIII-D tokamak

Gyrokinetic simulations of DIII-D tokamak equilibrium find that resonant magnetic perturbation(RMP)drives a neoclassical non-ambipolar electron particle flux,which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode(ELM).The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression(Taimourzadeh et al 2019 Nucl.Fusion59046005).Furthermore,gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.

The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code

The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code（GTC）.The ion and electron density profiles become partially flattened inside the islands.The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side,which do not move along the perturbed magnetic field lines.When the fraction of trapped particles decreases,the density profile at the low field becomes more flattened.

Test particle simulation on the ion and electron zebra stripes and their time evolution in inner radiation belt

During February 15–16, 2014, the energetic electron spectrogram for four successive inner radiation belt crossing show clearly the electron zebra structures and their time evolution which last for about 17 h. Unfortunately, the time of flight(TOF) in RBSPICE measurement is turned off below 3 RE, and the ion measurement is contaminated by electrons. Thus in this study we studied the differences between the ion and electron zebra stripe structures and their time evolution using simple theory and test particle simulation, combining the electron measurement from RBSIPICE onboard Van Allen Probes. Theoretical analysis predicts that the ion zebra stripe structures should lie at a higher energy range than the corresponding electron zebra stripe structures due to that the directions of gradient B drift and corotation E×B drift are the same for electrons while opposite for ions. Test particle simulation with the dipole magnetic field and Volland-Stern electric field model have shown that the ion and electron zebra stripe structures could be produced by the convection electric field penetrating into the inner magnetosphere in this event, with their time evolution determined by total drift velocity that are different for ions and electrons. The predicted differences between the ion and electron zebra stripe structures are partially verified through observation. The ion zebra stripe structures could have potential influence to the ring current.

Recent advances in radiation belt dynamics and wave-particle interactions in the Earth's inner magnetosphere

Radiation belt dynamics and the related wave-particle interactions in the Earth’s inner magnetosphere are a very important research field in space physics.Since the launch of Van Allen Probes on August 30,2012,many substantial advances have been achieved,and some of them are briefly reviewed in this paper.Using Van Allen Probes data soon after its launch,Baker et al.(2013)discovered a relativistic electron storage ring that was embedded in Earth’s outer Van Allen belt.