Three-dimensional Magnetic Configurations Research Articles

Mitigation of large amplitude edge-localized modes by resonant magnetic perturbations on LHD

In the Large Helical Device (LHD), H-mode plasmas are produced, having large amplitude edge-localized modes (ELMs) which are induced by resistive interchange modes (RICs) at the ι/2π = 1 rational surface near the foot of the edge transport barrier (ETB). These large ELMs expel a large fraction of plasma stored energy, up to 20% of the stored energy (Wp). The ETB and the ι/2π = 1 surface are thought to be in the stochastic field region (SFR) generated intrinsically in three-dimensional magnetic configuration on LHD, because plasma shielding effects for such stochastic fields are not significant due to low electrical conductivity σ and moderate angular frequency of plasma rotation ω in the ETB and the field penetration depth is estimated to be comparable to the ETB width. Even if the ETB is in such intrinsic SFR where electron mean free path is much shorter than the connection length, large amplitude ELMs are excited. Such ELMs were mitigated by externally applied m = 1/n = 1 resonant magnetic perturbations (RMPs), for the first time, in a stellarator/helical plasma, where m and n are the poloidal and toroidal mode numbers, respectively. The RMPs reduce the amplitude, enhancing the repetition frequency significantly. The energy loss fraction ΔWp/Wp is reduced less than ∼5% by the mitigation. This mitigation is realized without terminating the H-mode and large penalty to global energy confinement. The RMPs preferentially decrease electron density in ETB indicating enhanced particle transport, while electron and ion temperature profiles are nearly unchanged. Plasma shielding effects for the applied RMPs is also not significant because of low σ and moderate ω in ETB. Noticeable decrease in the gradients of electron density and pressure in the ETB and also at the ι/2π = 1 surface is induced by the penetration of the applied RMPs. Enhanced ELM frequency indicates that MHD stability of ETB for RICs is degraded by RMPs. Potential mechanisms of ELM mitigation on LHD are discussed.

Time evolution of the plasma spatial structure during the formation of a current sheet in argon according to holographic interferometry

The spatiotemporal dynamics of plasma sheets formed in argon plasma in two- and three-dimensional magnetic configurations with an X-type singular line was studied using holographic interferometry. An analogy is revealed between the development of plasma sheets and the time evolution of the current sheet structure, which was previously studied using magnetic measurements. In the late stage of the sheet evolution, a change in the rotation direction of plasma sheets formed in 3D magnetic configurations was observed. Apparently, this is caused by a change in the direction of the Hall currents at the side edges of the current sheet.

VECTOR TOMOGRAPHY FOR THE CORONAL MAGNETIC FIELD. II. HANLE EFFECT MEASUREMENTS

In this paper, we investigate the feasibility of saturated coronal Hanle effect vector tomography or the application of vector tomographic inversion techniques to reconstruct the three-dimensional magnetic field configuration of the solar corona using linear polarization measurements of coronal emission lines. We applied Hanle effect vector tomographic inversion to artificial data produced from analytical coronal magnetic field models with equatorial and meridional currents and global coronal magnetic field models constructed by extrapolation of real photospheric magnetic field measurements. We tested tomographic inversion with only Stokes Q, U, electron density, and temperature inputs to simulate observations over large limb distances where the Stokes I parameters are difficult to obtain with ground-based coronagraphs. We synthesized the coronal linear polarization maps by inputting realistic noise appropriate for ground-based observations over a period of two weeks into the inversion algorithm. We found that our Hanle effect vector tomographic inversion can partially recover the coronal field with a poloidal field configuration, but that it is insensitive to a corona with a toroidal field. This result demonstrates that Hanle effect vector tomography is an effective tool for studying the solar corona and that it is complementary to Zeeman effect vector tomography for the reconstruction of the coronal magnetic field.

Plasma acceleration in current sheets formed in helium in two- and three-dimensional magnetic configurations

The processes of heating and acceleration of plasma in current sheets formed in 2D and 3D magnetic configurations with an X-line in helium plasma have been investigated using spectroscopic methods. It is found that, in 2D magnetic configurations, plasma flows with energies of 400–1000 eV, which are substantially higher than the ion thermal energy, are generated and propagate along the width (the larger transverse dimension) of the sheet. In 3D configurations, the influence of the longitudinal (directed along the X-line) component of the magnetic field on the plasma parameters in the current sheet has been studied. It is shown that plasma acceleration caused by the Ampere force can be spatially inhomogeneous in the direction perpendicular to the sheet surface, which should lead to sheared plasma flows in the sheet.

Evolution of heliospheric magnetized configurations via topological invariants

The analogy between magnetohydrodynamics (MHD) and knot theory is utilized in presenting a new method for an analysis of stability and evolution of complex magnetic heliospheric flux tubes. Planar projection of a three-dimensional magnetic configuration depicts the structure as a two-dimensional diagram with crossings, to which one may assign mathematical operations leading to robust topological invariants. These invariants enrich the topological information of magnetic configurations beyond helicity. It is conjectured that the field which emerges from the solar photosphere is structured as one of the simplest knots—unknot or prime knot—and these flux ropes are then stretched while carried by the solar wind into the interplanetary medium. Preservation of invariants for small diffusivity and large cross section of the emerging magnetic flux makes them impervious to large scale reconnection, allowing us to predict the observed structures at 1AU as elongated prime knots. Similar structures may be observed in magnetic clouds which got disconnected from their footpoints and in ion drop-out configurations from a compact flare source in solar impulsive solar events. Observation of small scale magnetic features consistent with prime knots may indicate spatial intermittency and non-Gaussian statistics in the turbulent cascade process. For flux tubes with higher resistivity, magnetic energy decay rate should decrease with increased knot complexity as the invariants are then harder to be violated. These observations could be confirmed if adjacent satellites happen to measure distinctly oriented magnetic fields with directionally varying suprathermal particle fluxes.

Development of Integrated Transport Code, TASK3D, and Its Applications to LHD Experiment

The integrated transport code for helical plasmas, TASK3D, has been developed both by modifying modules in TASK to be applicable to three-dimensional magnetic configurations, and by adding new modules for stellarator-heliotron specific physics and incorporating three-dimensional equilibria. In this paper, these module developments so far are collectively introduced, and recent progress on the applications of TASK3D to heat transport analyses of LHD plasmas is introduced.

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.

Destruction of hyperbolic magnetic axes in steady three-dimensional toroidal magnetic structures

A study is made of the boundary regions of magnetic structures formed either near the last closed flux surface of the main magnetic configuration in a stellarator or near magnetic islands in more general toroidal confinement systems with topologically equivalent sheared magnetic configurations. With a relatively simple approximate analytic model based on the perturbation method, it was possible not only to reproduce earlier results on the destruction of hyperbolic magnetic axes in the three-dimensional toroidal magnetic configurations under consideration but also to obtain some new results, in particular, to analytically estimate the sizes of the separatrix regions of stochastic magnetic fields that arise in the main stellarator configuration and also near the inner chains of magnetic islands in any magnetic configuration under consideration. It is notable that the boundary region of the main stellarator magnetic configuration is a multiply connected structure, the outer part of which is largely governed by the current distribution in the magnetic system creating this configuration.

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1, 2]. The concept of a quasi-separatrix layer[3, 4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor[3-5] and the electrostatic potential difference used in kinematic reconnection studies[6, 7]. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like behavior in line-tied modes. [1] G. L. Delzanno and J. M. Finn. Physics of Plasmas, 15(3):032904, 2008. [2] Y.-M. Huang and E. G. Zweibel. Physics of Plasmas, 16(4):042102, 2009. [3] E. R. Priest and P. D\'emoulin. J. Geophys. Res., 100(A12):23443-23463, 1995. [4] P. D\'emoulin, J. C. Henoux, E. R. Priest, and C. H. Mandrini. Astron. Astrophys., 308:643-655, Apr. 1996. [5] V. S. Titov and G. Hornig. Advances in Space Research, 29(7):1087-1092, 2002. [6] Y. Lau and J. M. Finn. The Astrophysical Journal, 350:672-691, Feb. 1990. [7] Y. Lau and J. M. Finn. The Astrophysical Journal, 366:577-591, 1991.

Suprathermal plasma flows in current sheets formed in two- and three-dimensional magnetic configurations

Dynamics of the thermal and directed motions of argon plasma ions in current sheets formed in various magnetic configurations was investigated experimentally Measurements in three-dimensional magnetic configurations with an X line were carried out for the first time. The results of these measurements were compared with the data obtained in experiments with two-dimensional magnetic configurations. The ion temperature and the energies and velocities of directed plasma flows within the current sheet were determined by analyzing the shapes of argon ion spectral lines broadened due to the Doppler effect. It is found that, under the given experimental conditions, the axial magnetic field does not affect the ion temperature and plasma acceleration in the sheet.

SLIP-SQUASHING FACTORS AS A MEASURE OF THREE-DIMENSIONAL MAGNETIC RECONNECTION

A general method for describing magnetic reconnection in arbitrary three-dimensional magnetic configurations is proposed. The method is based on the field-line mapping technique previously used only for the analysis of magnetic structure at a given time. This technique is extended here so as to analyze the evolution of magnetic structure. Such a generalization is made with the help of new dimensionless quantities called "slip-squashing factors". Their large values define the surfaces that border the reconnected or to-be-reconnected magnetic flux tubes for a given period of time during the magnetic evolution. The proposed method is universal, since it assumes only that the time sequence of evolving magnetic field and the tangential boundary flows are known. The application of the method is illustrated for simple examples, one of which was considered previously by Hesse and coworkers in the framework of the general magnetic reconnection theory. The examples help us to compare these two approaches; they reveal also that, just as for magnetic null points, hyperbolic and cusp minimum points of a magnetic field may serve as favorable sites for magnetic reconnection. The new method admits a straightforward numerical implementation and provides a powerful tool for the diagnostics of magnetic reconnection in numerical models of solar-flare-like phenomena in space and laboratory plasmas.

Enhancement of the guide field during the current sheet formation in the three-dimensional magnetic configuration with an X line

Results are presented from studies of the formation of current sheets during exciting a current aligned with the X line of the 3D magnetic configuration, in the CS-3D device. Enhancement of the guide field (parallel to the X line) was directly observed for the first time, on the basis of magnetic measurements. After the current sheet formation, the guide field inside the sheet exceeds its initial value, as well as the field outside. It is convincingly demonstrated that an enhancement of the guide field is due to its transportation by plasma flows on the early stage of the sheet formation. The in-plane plasma currents, which produce the excess guide field, are comparable to the total current along the X line that initiates the sheet itself.

Spectroscopic measurements of the electron and ion temperatures and effective ion charge in current sheets formed in two- and three-dimensional magnetic configurations

The spatial distributions of the electron temperature and density, the effective and average ion charges, and the thermal and directed ion velocities in current sheets formed in two-dimensional magnetic fields and three-dimensional magnetic configurations with an X line were studied using spectroscopic and interference holographic methods. The main attention was paid to studying the time evolution of the intensities of spectral lines of the working-gas (argon) and impurity ions under different conditions. Using these data, the electron temperature was calculated with the help of an original mathematical code based on a collisional-radiative plasma model incorporating the processes of ionization and excitation, as well as MHD plasma flows generated in the stage of the current-sheet formation. It is shown that the electron temperature depends on the longitudinal magnetic field, whereas the ion temperature is independent of it. The effective ion charge of the current-sheet plasma was determined for the first time.

Large-Scale Synthesis of Single-Crystalline Iron Oxide Magnetic Nanorings

We present an innovative approach to the production of single-crystal iron oxide nanorings employing a solution-based route. Single-crystal hematite (alpha-Fe2O3) nanorings were synthesized using a double anion-assisted hydrothermal method (involving phosphate and sulfate ions), which can be divided into two stages: (1) formation of capsule-shaped alpha-Fe2O3 nanoparticles and (2) preferential dissolution along the long dimension of the elongated nanoparticles (the c axis of alpha-Fe2O3) to form nanorings. The shape of the nanorings is mainly regulated by the adsorption of phosphate ions on faces parallel to c axis of alpha-Fe2O3 during the nanocrystal growth, and the hollow structure is given by the preferential dissolution of the alpha-Fe2O3 along the c axis due to the strong coordination of the sulfate ions. By varying the ratios of phosphate and sulfate ions to ferric ions, we were able to control the size, morphology, and surface architecture to produce a variety of three-dimensional hollow nanostructures. These can then be converted to magnetite (Fe3O4) and maghemite (gamma-Fe2O3) by a reduction or reduction-oxidation process while preserving the same morphology. The structures and magnetic properties of these single-crystal alpha-Fe2O3, Fe3O4, and gamma-Fe2O3 nanorings were characterized by various analytical techniques. Employing off-axis electron holography, we observed the classical single-vortex magnetic state in the thin magnetite nanorings, while the thicker rings displayed an intriguing three-dimensional magnetic configuration. This work provides an easily scaled-up method for preparing tailor-made iron oxide nanorings that could meet the demands of a variety of applications ranging from medicine to magnetoelectronics.

Efficient Heating at the Third-Harmonic Electron Cyclotron Resonance in the Large Helical Device

Efficient heating at the third-harmonic electron cyclotron resonance was attained by injection of millimeterwave power with 84 GHz frequency range at the magnetic field strength of 1 T in LHD. The electron temperature at the plasma center clearly increased, and the increment in the temperature reached 0.2-0.3 keV. The dependence of the power absorption rate on the antenna focal position was investigated experimentally, showing that the optimum position was located in the slightly high-field side of the resonance layer. Ray-tracing calculation was performed in the realistic three-dimensional magnetic configuration, and its results are compared with the experimental results.

Holographic interferometry study of two-fluid properties of the plasma in current sheets formed in heavy noble gases

Two-exposure holographic interferometry was used to study the structure of current sheets formed in three-dimensional magnetic configurations with a singular X line in heavy noble gases (Ar, Kr, and Xe). It is found that, in the presence of a longitudinal magnetic field BZ directed along the X line, plasma sheets take on an unusual shape: they are titled and asymmetric. Their asymmetry becomes more pronounced as the mass of a plasma ion increases—a manifestation of the two-fluid properties of the plasma. The observed effects can be attributed to additional forces arising due to the interaction of the longitudinal magnetic field BZ with Hall currents excited in a plane perpendicular to the X line. A qualitative model describing plasma dynamics with allowance for the Hall effect and accounting for most of the experimentally observed effects is proposed.

Poloidal trapping of the high-frequency Alfvén continuum and eigenmodes in stellarators

Alfvén oscillations in three-dimensional toroidal magnetic configurations (stellarators) are considered. It is shown that the wave functions of the Alfvén continuum can be trapped in certain ‘waveguides’ when there are sufficiently large harmonics with sufficiently close periods along the magnetic field lines in the Fourier spectrum of the magnetic configuration. Such trapping is typical in the frequency range of the helicity-induced continuum gaps, in which case the wave functions are typically trapped at the inner circumference of the magnetic flux surface. Trapping also takes place near the crossings of continuum gaps, the localization of the wave becoming stronger on approaching the crossing point. At the crossing point, the continuum wave functions are localized at single field lines, which is shown to result in the ‘annihilation’ of the gaps (the width of the joint gap is the difference in the widths that the two gaps would have had if they were alone). It is shown with the use of the ballooning formalism that the Alfvén eigenmodes (AEs) associated with the trapped continua are also trapped in the regions of the same shape. Experimental observations on the stellarator Wendelstein 7-AS are reported, which indicate that trapping of AEs at the inner circumference of the plasma indeed takes place.

Properties of Ballooning Modes in the Planar Axis Heliotron Configurations with a Large Shafranov Shift

In the three-dimensional magnetic confinement configurations, the results of local mode analyses of the ballooning modes in the covering space (quasi modes) cannot be directly connected by superposition to the global mode analyses of the ballooning modes in the configuration space (physical modes) because of the lack of symmetry. However, a qualitative relation has been established to connect the quasi modes to physical modes in planar axis heliotron configurations with a large Shafranov shift. This relation is based on the topological structure of the level surfaces of the eigenvalues of the quasi modes. High-beta magnetohydrodynamic equilibria in the inward-shifted Large Helical Device configuration are examined. It is shown that the core plasma stays in the second stability, and the peripheral plasma stays near the marginally stable state against ballooning modes.

Study of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by holographic interferometry

Results are presented from studies of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by means of holographic interferometry. It is found that the efficiency of plasma compression into the sheet is reduced as the longitudinal magnetic field B z , directed along the X line, increases. This effect is attributed to the enhancement of the longitudinal component of the magnetic field within the sheet and to the corresponding increase in the magnetic pressure. It is shown that the formation of a plasma sheet lags behind the beginning of the plasma current pulse, the delay time being close to the characteristic Alfven time.

Prominence Formation by Thermal Nonequilibrium in the Sheared‐Arcade Model

The existence of solar prominences—cool, dense, filamented plasma suspended in the corona above magnetic neutral lines—has long been an outstanding problem in solar physics. In earlier numerical studies we identified a mechanism, thermal nonequilibrium, by which cool condensations can form in long coronal flux tubes heated locally above their footpoints. To understand the physics of this process, we began by modeling idealized symmetric flux tubes with uniform cross-sectional area and a simplified radiative-loss function. The present work demonstrates that condensations also form under more realistic conditions, in a typical flux tube taken from our three-dimensional MHD simulation of prominence magnetic structure produced by the sheared arcade mechanism. We compare these results with simulations of an otherwise identical flux tube with uniform cross-sectional area, to determine the influence of the overall three-dimensional magnetic configuration on the condensation process. We also show that updating the optically thin radiative loss function yields more rapidly varying, dynamic behavior in better agreement with the latest prominence observations than our earlier studies. These developments bring us substantially closer to a fully self-consistent, three-dimensional model of both magnetic field and plasma in prominences.