General Description of Ideal Tokamak MHD Instability Ⅱ

In this subsequent study on general description of ideal tokamak MHD instability, the part II, by using a coordinate with rectified magnetic field lines, the eigenmode equations describing the low-mode-number toroidal Alfven modes (TAE and EAE) are derived through a further expansion of the shear Alfven equation of motion.

NONLINEAR MHD KELVIN-HELMHOLTZ INSTABILITY IN A PIPE

Nonlinear MHD Kelvin-Helmholtz(K-H)instability in a pipe is treated with the deriva- tive expansion method in the present paper The linear stability problem was discussed in the past by Chandrasekhar(1961)and Xu et al.(1981).Nagano(1979)discussed the nonlinear MHD K-H instability with infinite depth.He used the singular perturbation method and extrapolated the ob- tained second order modifier of amplitude vs.frequency to seek the nonlinear effect on the instability growth rate γ.However,in our view,such an extrapolation is inappropriate.Because when the instabili- ty sets in,the growth rates of higher,order terms on the right hand side of equations will exceed the cor- responding secular producing terms,so the expansion will still become meaningless even if the secular producing terms are eliminated.Mathematically speaking,it's impossible to derive formula(39) when γ_0~2 is negative in Nagano's paper.Moreover,even as early as γ_0~2→O^+,the expansion be- comes invalid because the 2nd order modifier γ_2(in his formula(56))tends to infinity.This weak- ness is removed in this paper,and the result is extended to the case of a pipe with finite depth.

Experimental study of core MHD behavior and a novel algorithm for rational surface detection based on profile reflectometry in EAST

Microwave reflectometry is a powerful diagnostic that can measure the density profile and localized turbulence with high spatial and temporal resolution and will be used in ITER,so understanding the influence of plasma perturbations on the reflect signal is important.The characteristics of the reflect signal from profile reflectometry,the time-of-flight(TOF)signal associated with the MHD instabilities,are investigated in EAST.Using a 1D full-wave simulation code by the Finite-DifferenceTime-Domain(FDTD)method,it is well validated that the local density flattening could induce the discontinuity of the simulated TOF signal and an obvious change of reflect amplitude.Experimental TOF signals under different types of MHD instabilities(sawtooth,sawtooth precursors and tearing mode)are studied in detail and show agreement with the simulation.Two new improved algorithms for detecting and localizing the radial positions of the low-order rational surface,the cross-correlation and gradient threshold(CGT)method and the 2D convolutional neural network approach(CNN)are presented for the first time.It is concluded that TOF signal analysis from profile reflectometry can provide a straightforward and localized measurement of the plasma perturbation from the edge to the core simultaneously and may be a complement or correction to the q-profile control,which will be beneficial for the advanced tokamak operation.

Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas

Magnetohydrodynamic （MHD） n=1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of βN^c=2.56 for a typical HL-2A discharge with a plasma current Ip=0.245 MA, and the scaling of βN^c -constant is confirmed.

The Effect of Equilibrium Current Profiles on MHD Instabilities in Tokamaks

A cylindrical model of linear MHD instabilities in tokamaks is presented. In the model, the cylindrical plasma is surrounded by a vacuum which is divided into inner and outer vacuum areas by a conducting wall. Linearized resistivity MHD equations with plasma viscosity are adopted to describe our model, and the equations are solved numerically as an initial value problem. Some of the results are used as benchmark tests for the code, and then a series of equilibrium current profiles are used to simulate the bootstrap current profiles in actual experiments with a bump on tail. Thus the effects of these kinds of profiles on MHD instabilities in tokamaks are revealed. From the analysis of the numerical results, it is found that more plasma can be confined when the center of the current bump is closer to the plasma surface, and a higher and narrower current bump has a better stabilizing effect on the MHD instabilities.

Observation of MHD Instabilities Driven by Energetic Electrons in the Large Helical Device

Coherent magnetic fluctuations in an acoustic range of frequency have been regularly observed in low-density（n_e〈0.2×10^（19）m^（-3））plasmas with strong second harmonic electron cyclotron resonance heating（ECRH）on the Large Helical Device.Hard X-ray measurements indicated that energetic electrons are generated in these ECRH discharges.The magnetic fluctuations are suppressed in higher density discharges where energetic electrons are not present.The ECRH power modulation experiment indicated that the observed magnetohydrodynamic（MHD）mode has an acoustic nature rather than an Alfvenic nature.

Unified Description of Tokamak Ideal MHD Instabilities(Ⅰ)

By using a coordinate system associated with magnetic surfaces, a unified eigen-mode equation for describing the tokamak ideal MHD instabilities is derived in the shear-Alfven approximation. Based on this equation having a general operator form, the eigen-mode equation governing the large-scale perturbation (such as the kink mode, the low-n ballooning mode and the Alfven mode) and small-scale perturbation (such as the high-n ballooning mode, the local mode) can be further deduced. In the first part of the present study, the small-scale perturbation is discussed in detail.

The Singular Value Decomposition as a Tool of Investigating Central MHD Instabilities in the HL-1M Tokamak

A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors. By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.

Analysis of the instability growth rate during the jet-background interaction in a magnetic field

The two-stream instability is common, responsible for many observed phe- nomena in nature, especially the interaction of jets of various origins with the back- ground plasma （e.g. extragalactic jet interacting with the cosmic background）. The dispersion relation that does not consider magnetic fields is described by the well- known Buneman relation. In 2011, Bohata, Bren and Kulhanek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches ωn（k） is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accom- panied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet - intergalactic medium in- teraction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.

Alfvén Instabilities Excited by Energetic Particles in a Parameter Regime Similar to EAST Operation

The kinetic excitation of ideal magnetohydrodynamic （MHD） Alfvén instabilities is investigated for operations at the EAST tokamak. The instabilities include α-induced toroidal Alfvén eigenmodes （αTAE; here, α =-q2 Rdβ/dr, with q being the safety factor, β the ratio between the plasma and magnetic pressures, R the major radius, and r the minor radius）, toroidicity-induced Alfvén eigenmodes （TAE）, and the energetic particle continuum mode （EPM）. The αTAE, trapped by α-induced potential wells along the magnetic field line, can be readily destabilized by energetic particles due to negligible continuum damping via wave energy tunneling. It is shown for the geometry and the parameters similar to those of the EAST equilibrium that αTAE is different not only from the EPM by the potential-well determined frequency, but also from the TAE by the broad frequency spectrum outside the toroidal frequency gap.

Identification and Analysis of Magnetic Structures on HL-2A

A method for the identification and analysis of magnetic islands is presented based on the calculation of the perturbative current and magnetic field in plasmas. A cylindrical approximation is adopted and the toroidal effect on plasma equilibrium is also included. This method has been used on the HL-2A tokamak for analysing the magnetic island structures.

Internal Magnetic Configuration Measured by ECE Imaging on EAST Tokamak

ECE imaging （electron cyclotron emission imaging） is an important diagnostic which can give 2D imaging of temperature fluctuation in the core of tokamak. A method based on ECE imaging is introduced which can give the information of the position of magnetic axis and the structure of internal magnetic surface for EAST tokamak. The EFIT equilibrium reconstruction is not reliable due to the absence of important core diagnostic at the initial phase for EAST, so the information given by ECE imaging could help to improve the accuracy of EFIT equilibrium reconstruction.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas

The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations.It is found that the radiation can reduce the pressure near the rational surface.During the nonlinear evolution,the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation.Besides,the radiation can increase the growth rate of the magnetic islands by diminishing the pressure,such that the magnetic islands do not saturate compared with that without radiation.On the other hand,with the increase of the ratio of parallel to perpendicular transport coefficientχ‖/χ⊥,the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation.Finally,the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.

Primary Results of Liquid Metal Free Surface Jet Research

The liquid metal free surface innovation concept have been considered as liquid metal devices of divertor/limiter and tile of first wall in fusion device because it can withstand over 50 MW·m^2 heating load, is easily renewed by circulation and many overcome neutron irradiation damage life time limit. There are three types of free surface in the innovation concept as film, curtain （jets or drops） and capillary. The free surface jet is played a more attention at present. But it is no so clear and only a few available data that their magneto-hydrodynamics （MHD） instabilities, interaction with plasma and exclusion of the particles （ions, Alpha particles and so on） from liquid metal, in despite of many liquid metal free surface facilities built and operated especially in US in last two years. Recently, some primary results are carried out at LMEL facility at Southwestern Institute of Physics.

Magnetic reconnection acceleration of astrophysical jets for different jet geometries

The acceleration mechanisms of relativistic jets are of great importance for understanding various astrophysical phenomena such as gamma-ray bursts, active galactic nuclei and microquasars. One of the most popular scenarios is that the jets are initially Poynting-flux dominated and succumb to magnetohydrodynamic instability leading to magnetic reconnections. We suggest that the reconnection timescale and efficiency could strongly depend on the geometry of the jet, which determines the length scale on which the orientations of the field lines change. In contrast to a usually- assumed conical jet, the acceleration of a collimated jet can be found to be more rapid and efficient （i.e. a much more highly saturated Lorentz factor can be reached） while the jets with lateral expansion show the opposite behavior. The shape of the jet could be formed due to the lateral squeezing on the jet by the stellar envelope of a collapsing massive star or the interaction of the jet with stellar winds.

Effects of helium massive gas injection level on disruption mitigation on EAST

In this study,NIMROD simulations are performed to investigate the effects of massive helium gas injection level on the induced disruption on EAST tokamak.It is demonstrated in simulations that two different scenarios of plasma cooling(complete cooling and partial cooling)take place for different amounts of injected impurities.For the impurity injection above a critical level,a single MHD activity is able to induce a complete core temperature collapse.For impurity injection below the critical level,a series of multiple minor disruptions occur before the complete thermal quench.

Stress and Thermal Analysis of the In-Vessel RMP Coils in HL-2M

A set of in-vessel resonant magnetic perturbation （RMP） coils for MHD instability suppression is proposed for the design of a HL-2M tokamak. Each coil is to be fed with a current of up to 5 kA, operated in a frequency range from DC to about I kHz. Stainless steel （SS） jacketed mineral insulated cables are proposed for the conductor of the coils. In-vessel coils must withstand large electromagnetic （EM） and thermal loads. The support, insulation and vacuum sealing in a very limited space are crucial issues for engineering design. Hence finite element calculations are performed to verify the design, optimize the support by minimizing stress caused by EM forces on the coil conductors and work out the temperature rise occurring on the coil in different working conditions, the corresponding thermal stress caused by the thermal expansion of materials is evaluated to be allowable. The techniques to develop the in-vessel RMP coils, such as support, insulation and cooling, are discussed.

Stability impacts from the current and pressure profile modifications within finite sized island

The stability(or instability)of finite sized magnetic island could play a significant role in disruption avoidance or disruption mitigation dynamics.Especially,various current and pressure profile modifications,such as the current drive and heating caused by electron cyclotron wave,or the radiative cooling and current expulsion caused by the shattered pellet injection could be applied within the island to modify its stability,thus changing the ensuing dynamics.In this study,we calculate the mode structure modification caused by such profile changes within the island using the perturbed equilibrium approach,thus obtain the change of stability criterion Δ′ and assess the corresponding quasi-linear island stability.The positive helical current perturbation is found to always stabilize the island,while the negative one is found to do the opposite,in agreement with previous results.The pressure bump or hole within the island has a more complicated stability impact.In the small island regime,its contribution is monotonic,with pressure bump that tends to stabilize the island while pressure hole destabilizes it.This effect is relatively weak,though,due to the cancellation of the pressure term’s odd parity contribution in the second derivatives of the mode structure.In the large island regime,such cancellation is broken due to the island asymmetry,and the pressure contribution to stability is manifested,which is non-monotonic.The stability analysis in this paper helps to more accurately clarify the expected island response in the presence of profile modifications caused by disruption avoidance or mitigation systems.

Corona-Support for the Entirety of High Energetic Disk

Based on results obtained from the study for MHD （magneto-hydrodynamics） of advective accretion disk, which are applied to real source showing typical values for CBS （close binary star-system）, it will investigate on self-structuring in the disk under the impact of the distribution of leading parameters （density, velocity ...）. The paper is considering the problem of development of the corona and will analyze the process of interaction of the plasma with the magnetic field in connection to support for the instabilities.