MHD Perturbations Research Articles

Mitigation and prediction of disruption on the HL-2A Tokamak

Injection of high-Z impurities into plasma has been proved to be able to reduce the localized thermal load and mechanical forces on the in-vessel components and the vacuum vessel, caused by disruptions in Tokamaks. An advanced prediction and mitigation system of disruption is implemented in HL-2A to safely shut down plasmas by using the laser ablation of high-Z impurities with a perturbation real-time measuring and processing system. The injection is usually triggered by the amplitude and frequency of the MHD perturbation field which is detected with a Mirnov coil and leads to the onset of a mitigated disruption within a few milliseconds. It could be a simple and potential approach to significantly reducing the plasma thermal energy and magnetic energy before a disruption, thereby achieving safe plasma termination. The plasma response to impurity injection, a mechanism for improving plasma thermal and current quench in major disruptions, the design of the disruption prediction warner, and an evaluation of the mitigation success rate are discussed in the present paper.

Finite frequency zonal flows in multi-scale plasma turbulence including resistive MHD and drift wave instabilities

The evolution of multi-scale plasma turbulence including resistive MHD and micro-instabilities is studied based on a 5-field slab gyrofluid simulation aiming to understand complex nonlinear interactions and turbulent transport. It is observed that the spatial structure of the mixed-scale electromagnetic turbulence is characterized by a power-law scaling spectrum typical of MHD perturbations, but the spectral amplitude is enhanced by the micro-instability at all scales. A robust oscillatory zonal flow (ZF) with finite frequency is created in slab geometry for the first time due to the multi-scale interaction so that the ion heat transport is not efficiently suppressed. It is identified that the finite frequency ZF results from a net oscillatory electromagnetic torque, which is sustained by micro-instability through multi-scale nonlinear interaction.

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.

MHD stability condition of an anisotropic-pressure plasma in axially symmetric confinement systems formed by a poloidal field

A set of integrodifferential (over the longitudinal coordinate) equations for the transverse components of the plasma displacement minimizing the Kruskal-Oberman functional of the potential energy of MHD perturbations is derived. The stability condition corresponds to the absence of negative eigenvalues of this set for any magnetic surface in plasma.

MHD stability of a finite-pressure plasma in axisymmetric configurations of the poloidal magnetic field

A set of linear integrodifferential equations is presented for the plasma displacement components that minimize the Kruskal-Oberman functional of the potential energy of an MHD perturbation. Marginal stability results when the smallest eigenvalue of this set of equations is zero.

Stability of Alfvén modes in a collisionless anisotropic plasma confined by a highly curved magnetic field

The stability of Alfven modes in a collisionless plasma with an anisotropic pressure in a highly curved magnetic field is studied. A linearized equation for describing longitudinally nonuniform MHD perturbations with frequencies below the bounce frequency is derived. In this equation, the perturbations of longitudinal and transverse pressures are calculated using a collisionless kinetic equation. It is shown that longitudinal fluxes of the transverse and longitudinal plasma energies give rise to pressure perturbations different from those in the Chew-Goldberger-Low collisionless hydrodynamics. The corresponding energy principle is constructed. A stability criterion for Alfven modes is obtained and is found to be more stringent than that in the Chew-Gold-berger-Low model.

Fast-Ion Losses due to High-Frequency MHD Perturbations in the ASDEX Upgrade Tokamak

Time-resolved energy and pitch angle measurements of fast-ion losses correlated in frequency and phase with high-frequency magnetohydrodynamic perturbations have been obtained for the first time in a magnetic fusion device and are presented here. A detailed analysis of fast-ion losses due to toroidal Alfvén eigenmodes has revealed the existence of a new core-localized magnetohydrodynamic perturbation, the sierpes mode. The sierpes mode is a non-Alfvénic instability which dominates the losses of fast ions in ion cyclotron resonance heated discharges, and it is named for its footprint in the spectrograms ("sierpes" means "snake" in Spanish). The sierpes mode has been reconstructed by means of highly resolved multichord soft-x-ray measurements.

Spatio-temporal investigations on the triggering of pellet induced ELMs

Pellets injected into type-I ELMy H-mode discharges are known to trigger edge-localized modes (ELMs). In order to understand the underlying processes the triggering mechanism was investigated in this paper. The major questions of the investigations to be answered were: at which magnetic surface was the ELM initiated and what was the corresponding perturbation caused by the ablating pellet? During the investigations the natural ELM cycle was probed by injecting pellets from the high field side of the ASDEX Upgrade tokamak with significantly lower frequency than the natural ELM frequency. To determine the location of the seed perturbation of the ablating pellet triggering an ELM, the dynamics of the triggered ELMs was linked to the time history of the pellet position in the plasma. The ELM onset was determined by analysing magnetic pick-up coil signals and its delay relative to the time when the pellet crossed the separatrix was measured as a function of the pellet velocity. Supposing that to trigger an ELM a pellet has to reach a certain magnetic surface of the plasma independently of its mass and velocity, the most probable location of the seed perturbation was found to be at the middle of the pedestal—at the high plasma pressure gradient region. The onset of the MHD signature of the ELMs was detected about 50 µs after the pellet reached the seed position. According to our observations ELMs can be triggered either by the cooling of the pedestal region causing sudden increase of the pedestal plasma pressure gradient driving the plasma to the unstable region of the ballooning mode or by the strong MHD perturbation triggering an instability developing into an ELM.

On the nature of dark spots arising in a tokamak plasma during a disruption

The sudden appearance of bright and dark spots against the background lithium emission from the central regions of the plasma column was observed during major plasma disruptions in the T-11M tokamak with a lithium limiter. The measurements were performed with the help of an AXUV photodiode array operating in the energy range 1–5000 eV. Such spots in the plasma core arise in the fast transient stage of a major disruption (during the onset of the positive pulse of the plasma current) and are rather narrowly localized over r (in particular, over the vertical axis). It is supposed that the observed dark spots are related to the development of magnetic islands induced in the plasma core by an outer MHD perturbation. This effect can be used as a tool for studying specific forms of MHD resonance.

Generation of dense multicharged ion flows from an ECR plasma confined in a quasi-gas-dynamic magnetic cusp trap

The possibility of generating dense multicharged ion beams with a current density as high as ∼1 A/cm2 from an ECR plasma confined in a quasi-gas-dynamic cusp trap is studied both theoretically and experimentally. The most important advantages of this type of ion source are that the plasma in the cusp is stabile against MHD perturbations and that a trap intended to operate at fairly high pump-field frequencies (above 30 GHz) is relatively inexpensive. A theoretical model of confinement of a high-density nonequilibrium ECR plasma (Te ≫ Ti) in an open magnetic trap is proposed and results are presented from model experiments with an ∼30-cm-long cusp trap (here, by the cusp length is meant the volume of a paraxial magnetic tube divided by the area of its cross sections in magnetic mirrors) pumped by a pulsed microwave field with a frequency of 37.5 GHz and power of 100 kW. The possibility of achieving a quasi-gas-dynamic regime of plasma confinement of an ECR plasma in a cusp trap is demonstrated. Ion beams with a average ion charge number of 2–4 (depending on the sort of working gas) and current densities unprecedented for ECR sources are obtained. Good agreement between theoretical and experimental results makes it possible to reliably predict the ion beam parameters that can be achieved at even higher microwave frequencies.

Diagnostics of MHD instability in the Globus-M spherical tokamak

The paper describes a diagnostic system for studying MHD plasma perturbations in the Globus-M spherical tokamak (a major radius of 0.36 m, a minor radius of 0.24 m, and an aspect ratio of 1.5). The system includes a poloidal and a toroidal array consisting of 28 and 16 Mirnov probes, respectively, as well as a 32-channel proportional soft X-ray detector. Methods are described for calculating the poloidal and toroidal numbers of the dominant helical perturbations by using data from probe measurements. Results are presented of processing the experimental data from some tokamak discharges with a plasma current of 150–250 kA, an average electron density of up to 1020 m−3, and a toroidal magnetic field of 0.4 T. Specific features of MHD perturbations and their influence on the parameters of the plasma column in different stages of a discharge are briefly discussed.

High current ECR source of multicharged ion beams

Great demand for multicharged ion (MCI) sources stimulated investigation of new methods of producing plasma by means of ECR gas discharge in magnetic traps. The authors of this research propose a new type of pulsed sources of MCI, namely, a quasi-gasdynamic ECR source. Its main difference from the classical ECR MCI sources is a different, quasi-gasdynamic regime of plasma confinement in a magnetic trap. A zero-dimensional model describing gas breakdown, formation of charge state distribution in a plasma, and plasma flux through the plugs of the trap was constructed. A wide spectrum of model experimental studies was covered. Plasma was produced and heated by a pulsed (1ms) gyrotron at the frequency of 37.5GHz and power of 100kW in a cusp magnetic trap. Such a trap has axisymmetric configuration and allows one to realize a quasi-gasdynamic regime of confinement with reliable stabilization of MHD perturbations. It was demonstrated that with such a confinement regime it is possible to generate multicharged ions and create intense (more than 1A/cm2) ion fluxes through the trap plugs. Comparison of results of calculations and data of experiments shows that they are in a good agreement, which allows us to predict with a high degree of certainty creation of an ECR source of a new generation. The data obtained were used to design a pulsed quasi-gasdynamic ECR MCI source with pumping at the frequency of 100GHz, effective trap size 1m, average ion charge in plasma comparable with that in the best classical MCI ECR sources but with an order of magnitude higher flux density and absolute magnitude of plasma flux from a trap. Creation of intense plasma fluxes allows one to extract high-current MCI beams of high brightness. Transverse homogeneity of a plasma flux makes it possible to use a multi-aperture extraction system for formation of broad intense MCI beams.

Gasdynamic ECR source of multicharged ions based on a cusp magnetic trap

One of the modern trends in the development of electron cyclotron resonance (ECR) sources of multicharged ions is enhancement of the power and frequency of microwave pumping. Therefore, gyrotrons—powerful sources of radiation in the millimetre wavelength range—are now used for the creation and heating of plasma. These generators of microwave radiation are capable of producing and confining plasma of very high density (1013 cm−3 and higher), thus providing conditions for a substantial increase in the extracted ion beam current. Most ECR sources use for plasma confinement mirror magnetic traps with ‘min B’ configuration, which suppress MHD plasma instabilities. However, it is extremely difficult to construct such systems for pumping frequencies higher than 30 GHz because strong magnetic fields of complicated configuration are needed. All this makes the search for simpler axisymmetric MHD-stable systems for plasma confinement very topical.A cusp trap produced by two coils with opposite currents is the simplest MHD-stable magnetic trap. Magnetic lines at any point of plasma in such a trap have a curvature that suppresses MHD perturbation in the plasma. In the present work the possibility of creation of an effective ECR source of multicharged ions based on a cusp magnetic trap was investigated numerically and in experiments. The pioneer result is the realization of the quasi-gasdynamic regime of plasma confinement in the trap of the multicharged ion ECR source of multicharged ions with cusp configuration of the magnetic field. Experiments were made with a small cusp trap which was designed for plasma creation by 37.5 GHz gyrotron radiation under ECR conditions. The total current and ion charge state distribution in the extracted ion beam were studied. The results of experiments with the simplest kind of cusp trap have demonstrated good correspondence with theoretical calculations, and therefore the adequacy of the developed approach and the possibility to build more effective source on this basis. Two ways of possible evolution of ECR ion sources based on a cusp magnetic trap are proposed.

Scale-free thin discs with an isopedic magnetic field

Global stationary configurations of both aligned and logarithmic spiral MHD perturbations are constructed analytically within an axisymmetric background ofrazor-thin scale-free gas disc, which is embedded in an axisymmetric gravitational potential of a dark matter halo and involves an isopedic magnetic field almost vertically threaded through the disc plane. The scale-free index $\beta$ of the disc rotation speed $v_{\theta}\propto R^{-\beta}$ falls in the rangeof $(-1/2 , 1/2)$ where $R$ is the cylindrical radius. With the holding-back of a deep background dark matter halo potential, the isopedic magnetic field may be strong enough to allow for the magnetic tension force overtaking the disc self-gravity, which can significantly influence global stationary MHD perturbation configurations and stability properties of the scale-free disc system. Only for stationary logarithmic spiral MHD perturbations with a perturbation scale-free index $\beta_1=1/4$ or for aligned stationary MHD perturbations, can the MHD disc maintain a constant radial flux of angularmomentum. The variable radial flux of angular momentum in the radial direction corresponds to a complex dispersion relation. The marginal instabilities foraxisymmetric MHD disturbances are also examined for a special case as an example. When the magnetic tension force overtakes the disc self-gravity, the scale-free disc can be completely stable against axisymmetric MHD disturbances of all wavelengths. We predict the possible existence of an isopedicallymagnetized gas disc system in rotation primarily confined by a massive dark matter halo potential.

Axisymmetric stability criteria for a composite system of stellar and magnetized gaseous singular isothermal discs

Using the fluid-magnetofluid formalism, we obtain axisymmetric stability criteria for a composite disc system consisting of stellar and gaseous magnetized singular isothermal discs (MSIDs). Lou & Zou recently constructed exact global stationary configurations for both axisymmetric and nonaxisymmetric coplanar MHD perturbations in such a composite MSID system and proposed the MHD $D_s-$criteria for axisymmetric stability by the hydrodynamic analogy. In a different perspective, we derive and analyze here the time-dependent WKBJ dispersion relation in the low-frequency and tight-winding regime to examine axisymmetric stability properties. By introducing a rotational Mach number $D_s$ for the ratio of the stellar rotation speed $V_s$ to the stellar velocity dispersion $a_s$, one readily determines the stable range of $D_s^2$ numerically to establish the $D_s-$criteria for axisymmetric MSID stability. Those MSID systems rotating either too fast (ring ragmentation) or too slow (Jeans collapse) are unstable. Our WKBJ results of (M)SID instability provide physically compelling explanations for the stationary analysis of Lou & Zou. We further introduce an effective MHD $Q$ parameter for a composite MSID system and compare with the earlier work of Elmegreen, Jog and Shen & Lou. As expected, an axisymmetric dark matter halo enhances the stability against axisymmetric disturbances in a composite partial MSID system.

A van der Pol coupled-oscillator model as a basis for developing a system for suppressing MHD instabilities in a tokamak

The main parameters of tokamak discharges are known to be limited by large-scale MHD instabilities. Sometimes, the instabilities lead to a rapid (on time scales of tens of microseconds) disruption of the discharge current and to the release of all the energy stored in the plasma column at the discharge chamber wall. This process, which is called the disruptive instability, may have irreversible catastrophic consequences for the operation of a fusion reactor. In the present paper, a study is made of the dynamics of self-oscillations in systems of two and six van der Pol coupled oscillators. A van der Pol coupled-oscillator model is used to develop a multivariable feedback controller based on the combined principle of compensating for internal cross feedbacks within the object and introducing damping feedbacks in each control channel. By using mathematical simulation methods, it is shown that the controller designed guarantees the suppression of self-oscillations in a system of van der Pol oscillators over a fairly broad range of parameters of the object under control (and thereby provides the structural stability of the object). The nonlinear control system model makes it possible to suppress coupled MHD perturbations developing in a tokamak plasma.

Differential rotation in weakly magnetized neutron star atmospheres

The atmospheres of weakly magnetized neutron stars expand hydrostatically and rotate differentially during thermonuclear X-ray bursts. Differential rotation is probably related to the frequency drifts of millisecond-burst oscillations exhibited by about a dozen nuclear-powered X-ray pulsars. Here, we analyse the linear stability of this differential rotation with respect to local, axisymmetric, multidiffusive MHD perturbations, at various heights in the neutron star atmosphere. Unstable magnetorotational modes are identified from within to well above the burning layers. Properties of the fastest growing modes depend sensitively on the local magnetic field geometry. Linear estimates suggest that momentum transport due to magnetorotational instabilities can affect atmospheric rotation profiles on time-scales relevant to burst oscillations. This transport would likely strengthen the coherence of burst oscillations and contribute to their drifts.

The Sun as the Source of Nonlinear MHD Perturbations of the Solar Corona and the Heliosphere

The extended discussion of the Nonlinear MHD Perturbations of the Solar Corona and the Heliosphere has been exposed. To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

An MHD model for a heliospheric current sheet

A numerical solution of the full set of MHD equations shows the generation of a heliospheric current sheet during the thermal expansion of the corona. Calculations were performed for a compressible plasma taking into account dissipative terms and anisotropy of the thermal conductivity of the magnetized plasma. It is shown that the current sheet is not magnetically neutral. The sheet contains a normal component of the magnetic field, which plays a fundamental role during the formation of the sheet and in the stationary state. The sheet is stable against MHD perturbations, which are apparently carried away by the plasma flow. For the numerical scheme chosen, the minimum sheet thickness is determined by the length of the spatial integration step. The PERESVET code was used for the calculations.

Empirical mode decomposition method for investigating the structure of large-scale MHD instabilities in a tokamak

A new approach to the processing of experimental data from MHD diagnostics is developed for the purpose of investigating the spatial structure of large-scale MHD instabilities in a tokamak. The empirical mode decomposition method is applied to expand a multimode MHD perturbation in individual modes, which are then identified by constructing a spatial analytic signal with the help of the Hilbert transform. The method can be used to analyze the structure of the tearing instability and of the resistive wall modes.