Stochastic Magnetic Field Research Articles

Inflation of universe due to nonlinear electrodynamics

A model of nonlinear electrodynamics with a dimensional parameter [Formula: see text] is considered. Electromagnetic fields are the source of the gravitation field and inflation of the universe. We imply that the universe is filled by stochastic magnetic fields. It is demonstrated that after the universe inflation the universe decelerates approaching the Minkowski space–time. We evaluate the spectral index, the tensor-to-scalar ratio, and the running of the spectral index which approximately agree with the Planck and WMAP data.

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time $t_{2}$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time $t\lesssim t_{2}$ for strong turbulence, and at $t\gtrsim t_{2}$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval $t_{2}<t\leqslant 13t_{2}$. Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form $\langle (\unicode[STIX]{x1D6FF}r)^{2}\rangle =A(z/L_{\Vert })^{p}$ ($L_{\Vert }$ is the correlation length parallel to the magnetic background field $\boldsymbol{B}_{\mathbf{0}}$, $z$ is the distance along $\boldsymbol{B}_{\mathbf{0}}$ direction), providing functional forms of the amplitude coefficient $A$ and power-law exponent $p$ as a function of the nonlinearity parameter.

Probing stochastic inter-galactic magnetic fields using blazar-induced gamma ray halo morphology

Inter-galactic magnetic fields can imprint their structure on the morphology of blazar-induced gamma ray halos. We show that the halo morphology arises through the interplay of the source's jet and a two-dimensional surface dictated by the magnetic field. Through extensive numerical simulations, we generate mock halos created by stochastic magnetic fields with and without helicity, and study the dependence of the halo features on the properties of the magnetic field. We propose a sharper version of the Q-statistics and demonstrate its sensitivity to the magnetic field strength, the coherence scale, and the handedness of the helicity. We also identify and explain a new feature of the Q-statistics that can further enhance its power.

Effect of impurity source locations on up-down asymmetry in impurity distributions in the ergodic layer of large helical device

A space-resolved spectroscopy using a 3m normal incidence vacuum ultraviolet (VUV) spectrometer was developed to measure the VUV emission profiles in wavelength range of 300–3200Å from impurities in the edge plasmas in Large Helical Device (LHD). The edge plasma of the LHD is characterized by stochastic magnetic fields with three-dimensional structure intrinsically formed by helical coils called the “ergodic layer”. The VUV spectroscopy has revealed that intensity profiles of the impurity emission from the ergodic layer have strong up-down asymmetries, namely, the emission intensities are quite different between top and bottom plasma edges. Observations of the up-down asymmetries are summarized on the following impurity line emissions: (1) CII 1335.71Å (2s-2p), CIII 977.02Å (2s-2p), and CIV 1548.20Å (2s-2p) from intrinsic carbon impurity ions sputtered from the carbon divertor plates, (2) NeVII 465.22Å (2s-2p), NeVIII 770.41Å (2s-2p), ArVII 585.75Å (3s-3p), and ArVIII 700.24Å (3s-3p) from Ne or Ar ions introduced in plasmas by gas puffing, and (3) WVI 639.68Å (5d-6p) from W ions introduced in plasmas by pellet injection.

Linear Polarization, Circular Polarization, and Depolarization of Gamma-ray Bursts: A Simple Case of Jitter Radiation

Abstract Linear and circular polarizations of gamma-ray bursts (GRBs) have been detected recently. We adopt a simplified model to investigate GRB polarization characteristics in this paper. A compressed two-dimensional turbulent slab containing stochastic magnetic fields is considered, and jitter radiation can produce the linear polarization under this special magnetic field topology. Turbulent Faraday rotation measure (RM) of this slab makes strong wavelength-dependent depolarization. The jitter photons can also scatter with those magnetic clumps inside the turbulent slab, and a nonzero variance of the Stokes parameter V can be generated. Furthermore, the linearly and circularly polarized photons in the optical and radio bands may suffer heavy absorptions from the slab. Thus we consider the polarized jitter radiation transfer processes. Finally, we compare our model results with the optical detections of GRB 091018, GRB 121024A, and GRB 131030A. We suggest simultaneous observations of GRB multi-wavelength polarization in the future.

FLiT: a field line trace code for magnetic confinement devices

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams–Moulton predictor–corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

Vertical profiles and two-dimensional distributions of carbon line emissions from C2+−C5+ ions in attached and RMP-assisted detached plasmas of large helical device

In Large Helical Device (LHD), the detached plasma is obtained without external impurity gas feed by supplying an m/n = 1/1 resonant magnetic perturbation (RMP) field to a plasma with an outwardly shifted plasma axis position of Rax = 3.90 m where the magnetic resonance exists in the stochastic magnetic field layer outside the last closed flux surface. The plasma detachment is triggered by the appearance of an m/n = 1/1 island when the density, increased using hydrogen gas feed, exceeds a threshold density. The behavior of intrinsically existing impurities, in particular, carbon originating in the graphite divertor plates, is one of the important key issues to clarify the characteristic features of the RMP-assisted plasma detachment although the particle flux still remains on some divertor plates even in the detachment phase of the discharge. For this purpose, vertical profiles and two-dimensional (2-D) distributions of edge carbon emissions of CIII to CVI have been measured at extreme ultraviolet wavelength range, and the results are compared between attached and RMP-assisted detached plasmas. It is found that the CIII and CIV emissions located in the stochastic magnetic field layer are drastically increased near the m/n = 1/1 island O-point and in the vicinity of both inboard and outboard edge separatrix X-points during the RMP-assisted detachment, while those emissions are only enhanced in the vicinity of the outboard edge X-point in attached plasmas without RMP. The result clearly indicates a change in the magnetic field lines connecting to the divertor plates, which is caused by the growth of the m/n = 1/1 edge magnetic island. In contrast, the intensity of CVI emitted radially inside the magnetic island significantly decreases during the detachment, suggesting an enhancement of the edge impurity screening. The measured carbon distribution is analyzed with a three-dimensional edge plasma transport simulation code, EMC3-EIRENE, for the attached plasmas without RMP. It is found that the narrow strip-shaped impurity trace emitted along the edge X-point and its width are sensitive to the cross-field impurity diffusion coefficient, DZ⊥. As a result, the value of DZ⊥ of C3+ ions is evaluated to be 20 times larger than that of the bulk ions in the Rax = 3.90 m configuration, while the reason is unclear at present. The measured 2-D carbon distribution is also discussed and compared to the structure of the m/n = 1/1 magnetic island, which quickly expanded during the appearance of the plasma detachment.

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.

An advection–diffusion model for cross-field runaway electron transport in perturbed magnetic fields

Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field stochasticity. Since stochasticity is naturally present in post-disruption plasma, and externally induced stochastization offers a prominent mechanism to mitigate RE avalanche, we present an advection–diffusion model that can be used to couple an orbit-following code to an orbit-averaged tool in order to capture the cross-field transport and to overcome the latter’s limitation. The transport coefficients are evaluated via a Monte Carlo method. We show that the diffusion coefficient differs significantly from the well-known Rechester–Rosenbluth result. We also demonstrate the importance of including the advection: it has a two-fold role both in modelling transport barriers created by magnetic islands and in amplifying losses in regions where the islands are not present.

Magnetic structures propagating in non-equilibrium relativistic plasma of pulsar wind nebulae

The kinetic model of highly non-equilibrium relativistic electron-positron plasma is used to study dynamical magnetic structures in pulsar wind nebulae (PWNe). The evolution equation which describes a propagation of a long-wavelength magnetosonic type perturbation of small but finite amplitude is derived. The wavelength is assumed to be longer than the scattering length of the background positrons and electrons. The rates of scattering of electrons and positrons by the stochastic magnetic field fluctuations are distinguished but the difference is supposed to be small compared with the gyrofrequencies of particles. The phase velocity, the dissipation rate and the dispersion length of the magnetic pulse are studied as the functions of plasma parameters and the scattering rates of electrons and positrons. The model being confronted to observations can help to determine the pulsar wind composition, particle distribution and non-thermal pressure in PWNe.

THE IMPLICIT CONTRIBUTION OF SLAB MODES TO THE PERPENDICULAR DIFFUSION COEFFICIENT OF PARTICLES INTERACTING WITH TWO-COMPONENT TURBULENCE

ABSTRACT We explore the transport of energetic particles in two-component turbulence in which the stochastic magnetic field is assumed to be a superposition of slab and two-dimensional modes. It is known that in magnetostatic slab turbulence, the motion of particles across the mean magnetic field is subdiffusive. If a two-dimensional component is added, diffusion is recovered. It was also shown before that in two-component turbulence, the slab modes do not explicitly contribute to the perpendicular diffusion coefficient. In the current paper, the implicit contribution of slab modes is explored and it is shown that this contribution leads to a reduction of the perpendicular diffusion coefficient. This effect improves the agreement between simulations and analytical theory. Furthermore, the obtained results are relevant for investigations of diffusive shock acceleration.

Progress in understanding disruptions triggered by massive gas injection via 3D non-linear MHD modelling with JOREK

3D non-linear MHD simulations of a D2 massive gas injection (MGI) triggered disruption in JET with the JOREK code provide results which are qualitatively consistent with experimental observations and shed light on the physics at play. In particular, it is observed that the gas destabilizes a large m/n = 2/1 tearing mode, with the island O-point coinciding with the gas deposition region, by enhancing the plasma resistivity via cooling. When the 2/1 island gets so large that its inner side reaches the q = 3/2 surface, a 3/2 tearing mode grows. Simulations suggest that this is due to a steepening of the current profile right inside q = 3/2. Magnetic field stochastization over a large fraction of the minor radius as well as the growth of higher n modes ensue rapidly, leading to the thermal quench (TQ). The role of the 1/1 internal kink mode is discussed. An Ip spike at the TQ is obtained in the simulations but with a smaller amplitude than in the experiment. Possible reasons are discussed.

Acceleration of universe by nonlinear electromagnetic fields

A new model of nonlinear electromagnetic fields possessing a dimensional parameter [Formula: see text] is proposed. Electromagnetic fields are considered as the source of the gravitation field and accelerated expansion of the universe is driven by nonlinear electromagnetic fields. We consider the magnetic universe and the stochastic magnetic field is a source of the universe acceleration. After the universe inflation and the accelerated expansion the universe decelerates. We show the causality of the model and a classical stability at the deceleration phase. The spectral index, the tensor-to-scalar ratio and the running of the spectral index were estimated that approximately fulfil the PLANCK, WMAP and BICEP2 data.

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.

Impact of magnetic topology on radial electric field profile in the scrape-off layer of the Large Helical Device

The radial electric field in the plasma edge is studied in the Large Helical Device (LHD) experiments. When magnetic field lines become stochastic or open at the plasma edge and connected to the vessel, electrons are lost faster than ions along these field lines. Then, a positive electric field appears in the plasma edge. The radial electric field profile can be used to detect the effective plasma boundary. Magnetic topology is an important issue in stellarator and tokamak research because the 3D boundary has the important role of controlling MHD edge stability with respect to ELMs, and plasma detachment. Since the stochastic magnetic field layer can be controlled in the LHD by changing the preset vacuum magnetic axis, this device is a good platform to study the properties of the radial electric field that appear with the different stochastic layer width. Two magnetic configurations with different widths of the stochastic layer as simulated in vacuum are studied for low-β discharges. It has been found that a positive electric field appeared outside of the last closed flux surface. In fact the positions of the positive electric field are found in the boundary between of the stochastic layer and the scrape-off layer. To understand where is the boundary of the stochastic layer and the scrape-off layer, the magnetic field lines are analyzed statistically. The variance of the magnetic field lines in the stochastic layer is increased outwards for both configurations. However, the skewness, which means the asymmetry of the distribution of the magnetic field line, increases for only one configuration. If the skewness is large, the connection length becomes effectively short. Since that is consistent with the experimental observation, the radial electric field can be considered as an index of the magnetic topology.

Thermal Stability Study of Tilted-Polarizer Spin Torque Nano-oscillator

The spin torque nano-oscillator (STNO) with out of film plane fixed layer magnetization, namely the tilted-polarizer spin torque nano-oscillator (TP-STNO), has the advantage of microwave generation without the help of a magnetic field, which makes it promising to be integrated into a chip. In this paper, we present a thermal stability study of TP-STNO by macrospin modeling, in which the thermal noise is induced into the H eff of the Landau-Liftshitz-Gilbert-Slonczewski equation in the form of a stochastic magnetic field. The TP-STNO with different tilted angles is studied by numerical simulations based on the macrospin model and nonlinear system theory. Depending on the analysis of Lyapunov exponents as a function of drive current density in the room temperature range, we obtain the drive current density ranges in which TP-STNO can oscillate stably in the presence of thermal noise. These quantified results are essential during the practical usage of TP-STNO.

Full particle orbit effects in regular and stochastic magnetic fields

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

Anomalous current pinch of a toroidal axisymmetric plasma with stochastic magnetic field perturbations

Anomalous current pinch, in addition to the anomalous diffusion due to stochastic magnetic perturbations, is theoretically found, which may qualitatively explain the recent DIII-D experiment on resonant magnetic field perturbation. The anomalous current pinch, which may resolve the long-standing issue of seed current in a fully bootstrapped tokamak, is also discussed for the electrostatic turbulence.

Helium transport in the core and stochastic edge layer in LHD

Radial profiles of the density ratio of helium to hydrogen ions are measured using charge exchange spectroscopy with a two-wavelength spectrometer in the large helical device. Helium transport at the last closed flux surface (LCFS) and stochastic magnetic field layer outside the LCFS as well as in the core plasma is studied for a wide range of helium fractions, i.e. from hydrogen-dominated plasmas up to helium-dominated plasmas. The helium density profile becomes more peaked and inward convection velocity increases in the hydrogen-dominant plasma, while it becomes flat or hollow and the convection velocity is in the outward direction in the helium-dominant plasmas. The density gradient of helium at the LCFS is twice that of hydrogen and becomes steeper as the hydrogen becomes more dominant.

Numerical Modeling on Heat Transport Across Stochastic Magnetic Field

AbstractThe heat diffusion across the stochastic magnetic field is studied numerically. The stochastic field is generated by the overlap of two magnetic islands. The parameter w/wc, is found tobe an important parameter in charactering the transport, where w is the magnetic island width, and wc is the critical island width for flattening the electron temperature across an island. For w/wc < 1, the enhanced radial heat diffusivity χr is proportional to the parallel heat diffusivity χ∥, and the heat transport is dominated by the additive effect of individual islands. For w/wc > 3, χr is also proportional to χ∥ and the additional degradation of the energy confinement due to stochastic magnetic field becomes apparent. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)