Stochastic Magnetic Field Lines Research Articles

Lagrangian Perspectives on the Small-scale Structure of Alfvénic Turbulence and Stochastic Models for the Dispersion of Fluid Particles and Magnetic Field Lines in the Solar Wind

Lagrangian perspectives on the small-scale structure of anisotropic Alfvénic turbulence are adopted. We are interested in relating the statistical properties of the Eulerian field increments evaluated along the fluid particle trajectories, in the direction perpendicular to the guiding magnetic field and along the magnetic field lines. We establish the basis for a unified multifractal phenomenology of Eulerian and Lagrangian Alfvénic turbulence. The critical balance condition is generalized to structure functions of an order different than 2. A Lagrangian perspective is not only useful for investigating the small-scale structure of Alfvénic turbulence, it is also tailored to the modeling of large-scale turbulent transport. Therefore, we develop Lagrangian stochastic models for the dispersion of fluid particles and magnetic field lines in the solar wind. The transport models are based on the integrated Ornstein–Uhlenbeck process that is not Markov, yielding smooth stochastic fluid particle trajectories and magnetic field lines. Brownian diffusion is recovered by tending the integral scale parameter to zero while keeping the diffusivity finite.

Nonlinear MHD modeling of soft β limits in W7-AS

An important question for the outlook of stellarator reactors is their robustness against pressure driven modes, and the underlying mechanism behind experimentally observed soft β limits. Towards building a robust answer to these questions, simulation studies are presented using a recently derived reduced nonlinear MHD model. First, the initial model implementation is extended to capture fluid compression by including the influence of parallel flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite β, net-zero current carrying stellarator with low magnetic shear are then used to demonstrate the modeling capabilities. Finally, a validation study is conducted on experimental reconstructions of finite β W7-AS discharges. In agreement with past experimental analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft β limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low n MHD activity is observed at intermediate β values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is mild, explaining the soft β limit, because the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. For the assumed transport parameters, the enhanced perpendicular transport along stochastic magnetic field lines can be overcome with the experimental heating power. The limitations in the current modeling are described, alongside an outlook for characterizing the quasi-steady state operational limit in W7-AS and other devices in more detail in future work.

Tailoring resonant magnetic perturbation to optimize fast-ion confinement during ELM control in KSTAR

3D resonant magnetic perturbation (RMP) is one promising way to control edge localized modes that can cause excessive material erosion of tokamak first walls. However, RMP can lead to undesired degradation of plasma confinement, including fast-particle losses, which can impact the performance and safety of the reactor. This work investigates the optimization of the poloidal spectrum of the 3D field to optimize fast ion confinement during edge localized mode (ELM) suppression. In the initial step, the validity of the modeling framework is tested against experimental data. Simulations successfully replicate an increase in poloidal limiter temperature with different poloidal spectra. Then, the simulation shows improvement of fast ion confinement with a reduction of core resonant response, while edge resonant magnetic fields are maintained above the threshold to sustain the ELM suppression. Reduction of the core resonant fields keeps the Kolmogorov–Arnold–Moser surface and reduces the fast particle losses due to the stochastic magnetic field lines. The results highlight the potential of edge localization of the resonant fields to enhance the performance of fusion reactors, but further investigation is needed to improve the validation of this approach.

The 3D magnetic topology and plasma dynamics in open stochastic magnetic field lines

The thermal quench triggered by locked modes is known to be mainly due to open stochastic magnetic field lines connected to the wall boundary. It is essential to understand the 3D structure of open stochastic field lines since it determines the overall plasma dynamics in the system. In this study, we analyze the 3D magnetic topology for two key concepts, the connection length Lc and the effective magnetic mirror ratio Meff, and present a comprehensive picture of electron and ion dynamics related to the magnetic topology. The connection length determines the 3D structure of the ambipolar potential, and a sharp potential drop across distinct Lc regions induces the E × B transport and mixing across the field line. The confinement of electrons and ions along the field line is determined by the ambipolar potential and Meff configuration. Electron and ion temperatures in magnetic hills (Meff<1) are lower than in magnetic wells (Meff>1) because particles in magnetic hills are more likely to escape toward the wall boundary along the field line. The mixing between the magnetic wells and hills by E × B and magnetic drift motions results in collisionless detrapping of electrons and ions, which reduces their temperature efficiently. Numerical simulations of two different magnetic configurations demonstrate the importance of the collisionless detrapping mechanism, which could be the main cause of plasma temperature drop during the thermal quench.

Collisionless plasma transport mechanisms in stochastic open magnetic field lines in tokamaks

The collisionless plasma transport in stochastic magnetic fields connecting to wall boundary has been studied to understand the underlying mechanisms of thermal quench physics in tokamak disruption. In this study, we present a comprehensive understanding of the plasma dynamics in three-dimensional stochastic open magnetic field lines, taking into account the consistent coupling of electron and ion dynamics through the ambipolar electric field. The open stochastic field lines act as a 3D magnetic mirror consisting of the magnetic well and hill regions. It was found that the magnetic hill regions play a critical role in enhancing electron thermal transport. When the plasma collapses to the wall, the 3D ambipolar potential arises in the stochastic layer to maintain the quasi-neutrality of the plasma. The E × B vortices induced by the 3D ambipolar potential mix the plasma across stochastic field lines and enhance the radial transport. Particularly, the E × B mixing between the magnetic well and hill regions provides a collisionless detrapping mechanism that plays a major role in the loss of high-energy trapped electrons. As a result, the electron temperature steadily decreases at a rate of about −0.5 keV ms−1, comparable to the rate observed in thermal quench experiments.

The three-dimensional equilibrium with magnetic islands and MHD instabilities in the CFQS quasi-axisymmetric stellarator

The equilibrium of the Chinese first quasi-axisymmetric stellarator (CFQS) has been investigated by the HINT code. It is found that the stochastization of magnetic field lines expands with the increase in the volume-averaged beta value 〈β〉 in the plasma boundary. In the high-β regime, the generation of large magnetic islands at rational surfaces not only leads to an effective shrinkage of the plasma confinement region but also increases the outward shift of the magnetic axis. With bootstrap current effects, the low-order islands spread over the whole plasma area, leading to a stochastization of magnetic field lines due to island chain overlapping. However, for a flat pressure profile, the magnetic islands are significantly suppressed so that the magnetic surfaces can be fairly maintained. Moreover, the magnetohydrodynamic (MHD) instabilities in the optimized CFQS configurations have been simulated by the MEGA code. The linear properties of unstable resistive MHD modes are studied. The results show that in the CFQS the main MHD behaviour is dominated by the resistive ballooning modes with strong mode coupling. The mode structure and resistivity scaling are consistent with related theories.

Gyrokinetic study of collisional resonant magnetic perturbation (RMP)-driven plasma density and heat transport in tokamak edge plasma using a magnetohydrodynamic screened RMP field

The total-f gyrokinetic particle-in-cell code XGC is applied to study various aspects of collisional transport in the tokamak edge pedestal in the presence of resonant magnetic perturbations (RMPs) calculated with M3D-C1. Simulations including the separatrix and scrape-off layer are exercised for a model DIII-D H-mode plasma. Neutral particle recycling is modeled by means of ionization and charge exchange with the plasma. A fully nonlinear Fokker–Planck collision operator is utilized to account for non-Maxwellian edge plasma. The study yields kinetic evidence that (i) neglecting the non-axisymmetric component of the RMP-generated electrostatic potential perturbation could yield a fictitiously high particle pump-out rate in the edge pedestal; that (ii) the experimental level of particle pump-out from the pedestal cannot be provided by collisional transport across Kolmogorov–Arnold–Moser surfaces except across the magnetic separatrix where stochastic magnetic field lines exist; that (iii) the H-mode type electron heat barrier is retained in the steep slope area under the M3D-C1 calculated RMPs; and that (iv) the stochastic electron heat-transport rate around the magnetic separatrix surface is much lower than the prediction by Rechester–Rosenbluth (1978 Phys. Rev. Lett. 40 38–41) and is qualitatively consistent with the experimentally observed rate. Detailed kinetic physics analysis on how the transport fluxes, electrostatic potential perturbation, and -well structure respond to onset of RMPs is also reported.

Diffusion of stochastic magnetic field lines with average poloidal magnetic component

We study the diffusion of stochastic isotropic and anisotropic magnetic field lines in turbulence with average poloidal magnetic field component. In the current work we employ the so-called DeCorrelation Trajectory method in order to compute the running and asymptotic diffusion coefficients of stochastic magnetic field lines with average poloidal magnetic field component. A modification of the diffusion coefficients is caused by the average magnetic field component parameter in the presence of trajectory trapping. We calculate the field line diffusion coefficients Dxx and Dyy for different values of the magnetic Kubo number K, the average magnetic field component parameter Kav and the anisotropy parameter Λ. Furthermore we compare our new findings with those already obtained in papers dealing with the calculus of the diffusion coefficients for a stochastic sheared magnetic field.

Magnetic surface loss and electron runaway

The exponentiation of a small seed of energetic electrons into a strong current of relativistic electrons during disruptions is a major threat to the ITER mission; the adequacy of the plan for the protection of ITER remains far from clear. The hope that issues involving relativistic electrons can be resolved in the non-nuclear phase of ITER operations has a fundamental flaw. In the nuclear phase two mechanisms exist for producing seed electrons: remnant and steady production. In the non-nuclear phase only the more easily avoidable remnant source exists. Whether the plasma current in ITER must be severely constrained to avoid unacceptable machine damage rests on issues discussed in this paper. An adequate understanding of fast magnetic reconnection is one of these issues. The loss of poloidal field energy during a disruption occurs through two distinct processes: (1) a quasi-ideal fast magnetic reconnection, which conserves magnetic helicity and accounts for large and sudden drops in the internal inductance, and (2) the resistive dissipation, which dissipates the helicity and is required to quench the current. To correctly separate these two processes requires spatial and temporal resolutions far beyond those of existing simulations. The assumption that stochastic magnetic field lines have a diffusive radial motion allows simple simulations of existing experiments and predictions for ITER that go far beyond existing analyses.

Characterization of the 20 kHz transient MHD burst at the fast U-3M confinement modification stage

In the URAGAN-3M (U-3M) torsatron the low-frequency transient 20–30 kHz mode is observed during the plasma confinement transition that occurs at a plasma current value of about 1 kA. The burst of this mode is always accompanied by the fast jump of the Alfvén eigenmode frequency. The transient 20–30 kHz mode contains two parts. The non-rotating part of the mode has higher amplitude and is localized in the stochastic region of the plasma. It is observed only in the vicinity of the radio-frequency antenna used for plasma production and does not propagate along the torus because of fast losses. Its high amplitude indicates that the major part of the 20–30 kHz mode is excited in the stochastic region near the antenna. In contrast, the second rotating part of the mode is localized everywhere along the torus near the plasma edge (ρ = 0.8–1). This is the n/m = 1/2 mode that rotates in the electron diamagnetic direction. It is observed in different toroidal cross-sections by various diagnostics (magnetic probe array, optics, Langmuir probe). Appearance of the 1/2 rational surface at the stochastic magnetic field line region near the plasma edge at 1 kA plasma current stage can be responsible for the mode generation. Modification of electron component gradients in the mode generation region near the antenna and the drop of the fast ion concentration (above 1 keV) in this region are observed simultaneously with the mode generation. The mode can be exited by the strong transient plasma gradients generated in the vicinity of the rational surface by the antenna.

Stochastic field-line wandering in magnetic turbulence with shear. II. Decorrelation trajectory method

We study the diffusion of magnetic field lines in turbulence with magnetic shear. In the first part of the series, we developed a quasi-linear theory for this type of scenario. In this article, we employ the so-called DeCorrelation Trajectory method in order to compute the diffusion coefficients of stochastic magnetic field lines. The magnetic field configuration used here contains fluctuating terms which are described by the dimensionless functions bi(X, Y, Z), i = (x, y) and they are assumed to be Gaussian processes and are perpendicular with respect to the main magnetic field B0. Furthermore, there is also a z-component of the magnetic field depending on radial coordinate x (representing the gradient of the magnetic field) and a poloidal average component. We calculate the diffusion coefficients for magnetic field lines for different values of the magnetic Kubo number K, the dimensionless inhomogeneous magnetic parallel and perpendicular Kubo numbers KB∥, KB⊥, as well as Kav=byavKB∥/KB⊥.

Evidence and relevance of spatially chaotic magnetic field lines in MCF devices

Numerical evidence for the existence of spatially chaotic magnetic field lines about the collapse phase of tokamak sawteeth with incomplete reconnection is presented. This uses the results of extensive test particle simulations in different sets of electromagnetic perturbations tested against experimental JET measurements. In tokamak sawteeth, that form a laboratory prototype of magnetic reconnection, the relative magnetic perturbation may reach a few percents. This does not apply to tokamak operating regimes dominated by turbulence where is usually not larger than . However, this small magnetic perturbation being sustained by a large spectrum of modes is shown to be sufficient to ensure the existence of stochastic magnetic field lines. This has important consequences for magnetic confinement fusion where electrons are dominantly governed by the magnetic force. Indeed some overlap between magnetic resonances can locally induce chaotic magnetic field lines enabling the spatial redistribution of the electron population and of its thermal content. As they are the swiftest plasma particles, electrons feed back the most rapid perturbations of the magnetic field.

THREE-DIMENSIONAL SPONTANEOUS MAGNETIC RECONNECTION

ABSTRACT Magnetic reconnection is best known from observations of the Sun where it causes solar flares. Observations estimate the reconnection rate as a small, but non-negligible fraction of the Alfvén speed, so-called fast reconnection. Until recently, the prevailing pictures of reconnection were either of resistivity or plasma microscopic effects, which was contradictory to the observed rates. Alternative pictures were either of reconnection due to the stochasticity of magnetic field lines in turbulence or the tearing instability of the thin current sheet. In this paper we simulate long-term three-dimensional nonlinear evolution of a thin, planar current sheet subject to a fast oblique tearing instability using direct numerical simulations of resistive-viscous magnetohydrodynamics. The late-time evolution resembles generic turbulence with a −5/3 power spectrum and scale-dependent anisotropy, so we conclude that the tearing-driven reconnection becomes turbulent reconnection. The turbulence is local in scale, so microscopic diffusivity should not affect large-scale quantities. This is confirmed by convergence of the reconnection rate toward with increasing Lundquist number. In this spontaneous reconnection, with mean field and without driving, the dissipation rate per unit area also converges to , and the dimensionless constants 0.015 and 0.006 are governed only by self-driven nonlinear dynamics of the sheared magnetic field. Remarkably, this also means that a thin current sheet has a universal fluid resistance depending only on its length to width ratio and to .

Loss of relativistic electrons when magnetic surfaces are broken

Relativistic runaway electrons in ITER could be confined in a broad annulus of stochastic magnetic field lines bounded by an annulus of magnetic surfaces. The outer confining annulus can be broken by either an evolution of the magnetic field or by the drift of the plasma into the walls. Both possibilities are studied, and in both cases, the relativistic electrons in the stochastic region are lost to the walls in a short pulse of length τℓ along a narrow tube, which carries a flux fψst, where f∼10−3 and ψst is the toroidal flux in stochastic annulus. Both τℓ and f are determined by two parameters: the time it takes for a toroidal transit of a relativistic electron τt=2πR/c, which is approximately 0.1 μs in ITER, and the evolution time τev, which is of order 100 ms in most conditions of interest for ITER. The concept of turnstiles in Hamiltonian mechanics is used to obtain the relation between τℓ and f and τt and τev. The turnstile concept is also important in the theory of divertors for stellarators.

Microtearing turbulence: Magnetic braiding and disruption limit

A realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation in the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of δB/B above which stochasticity is no longer benign yet, leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence δB/B has been measured to grow with the plasma electron density, this would also be a density limit.

Investigation of radial electric field in the edge region and magnetic field structure in the Large Helical Device

In the Large Helical Device experiments, a significant pressure gradient is observed in the edge region where the three-dimensional magnetohydrodynamics equilibrium analysis predicts the stochastization of magnetic field lines. Therefore, experimental investigation of this edge plasma behavior is attracting much interest to identify either the plasma response to stochastic magnetic fields or the topological change of magnetic fields due to the plasma. In this study, we have investigated the relation of the stochastization of magnetic field lines to the radial electric field, Er. When magnetic field lines become stochastic or open and connected to the vessel, electrons are lost along these field lines while ions are trapped. Then, a strong Er shear from negative to positive appears at the boundary. Two magnetic configurations with different widths of the stochastic layer in the vacuum are studied for low-β discharges. It has been found that the position of a strong Er shear appears outside of the last closed flux surface. When comparing the vacuum magnetic field, the positions of strong Er shear are observed in the edge of the stochastic layer. In the stochastic region, the scatter of stochastic field lines is studied. The position of a strong Er shear appears in the region where the outward scatter of the field lines increases. In that region, stochastic field lines intersect the regions with long and short connection lengths. Although the connection length is longer than the electron mean free path, the scatter of stochastic field lines with short connection lengths appear in the regions with positive Er. These results are compared with moderate-β discharges, where a large plasma response is expected. The prediction of the vacuum magnetic field qualitatively agree with the experimental observations but quantitative differences are found.

A test electron model for the study of three dimensional magnetic reconnection effects

Understanding the mechanisms that enable the conversion of the explosive release of magnetic energy into the electron energization that is experimentally observed in space and laboratory plasmas represents a long-standing question in the study of magnetic reconnection.We present a test particle model able to follow the dynamics of the electron guiding centers in the presence of the electromagnetic fields characterizing a non-steady-state, three-dimensional magnetohydrodynamic (3D-MHD) description of magnetic reconnection. The resulting electron equations, based on a relativistic Hamiltonian formulation of the particle dynamics, have been implemented in a code that evolves the spatial position and the velocity of the electrons according to the fields obtained by the numerical solutions of a two-fluid reconnection model. By the calculation of the electron distribution function in the phase space, the electron kinetic moments can be obtained with a δf technique particularly suitable during the early stages of the reconnection process, which can be replaced by a full-f approach in the nonlinear reconnection phase. Thanks to its capability to reproduce the electron response in a quite realistic reconnection configuration, this numerical tool represents a new instrument for the investigation of the nonlinear electron dynamics in particularly complex reconnection regions, such as those characterized by magnetic field line stochasticity.

ASYMMETRIC DIFFUSION OF MAGNETIC FIELD LINES

Stochasticity of magnetic field lines is important for particle transport properties. Magnetic field lines separate faster than diffusively in turbulent plasma, which is called superdiffusion. We discovered that this superdiffusion is pronouncedly asymmetric, so that the separation of field lines along the magnetic field direction is different from the separation in the opposite direction. While the symmetry of the flow is broken by the so-called imbalance or cross-helicity, the difference between forward and backward diffusion is not directly due to imbalance, but a non-trivial consequence of both imbalance and non-reversibility of turbulence. The asymmetric diffusion perpendicular to the mean magnetic field entails a variety of new physical phenomena, such as the production of parallel particle streaming in the presence of perpendicular particle gradients. Such streaming and associated instabilities could be significant for particle transport in laboratory, space and astrophysical plasmas.

Two-Dimensional Distribution of Electron Temperature in Ergodic Layer of LHD Measured from Line Intensity Ratio of CIV and NeVIII

Two-dimensional distribution of impurity lines emitted from ergodic layer with stochastic magnetic field lines in Large Helical Device (LHD) has been observed using a space-resolved extreme ultraviolet (EUV) spectrometer. The two-dimensional electron temperature distribution in the ergodic layer is successfully measured using the line intensity ratio of Li-like NeVIII 2s-3p ( 2 S1/2- 2 P3/2: 88.09 A, 2 S1/2- 2 P1/2: 88.13 A) to 2p-3s ( 2 P1/22 S1/2: 102.91 A, 2 P3/2- 2 S1/2: 103.09 A) transitions emitted from radial location near Last Closed Flux Surface (LCFS). The intensity ratio analyzed with ADAS code shows no dependence on the electron density below 10 14 cm −3 . The result indicates a little higher temperature, i.e., 220 eV, in the poloidal location at high-field side near helical coils called O-point compared to the temperature near X-point, i.e., 170 eV. The electron temperature profile is also measured at the edge boundary of ergodic layer using the line intensity ratio of Li-like CIV 2p-3d ( 2 P1/2- 2 D3/2: 384.03 A, 2 P3/2- 2 D5/2: 384.18 A) to 2p-3s ( 2 P1/2- 2 S1/2: 419.53 A, 2 P3/2- 2 S1/2: 419.71 A) transitions. The intensity ratios analyzed with CHIANTI, ADAS and T.Kawachi codes show a slightly higher temperature near O-point, i.e., 25 eV for CHIANTI, 21 eV for ADAS and 11 eV for T.Kawachi’s codes, compared to the temperature at X-point, i.e., 15 - 21 eV for CHIANTI, 9 - 15 eV for ADAS and 6 - 9 eV for T.Kawachi codes. It suggests that the transport coefficient in the ergodic layer is varied with three-dimensional structure.

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure

Analysis Method for the Low-Order Resistive Interchange Instability in LHD with Stochastic Magnetic Field Line Structure