Stochastic Layer Research Articles

Defect generation and propagation mechanism during additive manufacturing by selective beam melting

During powder bed based additive manufacturing processes a component is fabricated by locally melting of powder layers with a laser or an electron beam. The fast melting process of the stochastic powder bed induces vigorous melt pool movements which sometimes lead to faults acting as starting points for larger defects such as channels bridging many layers. Since the formation of these defects cannot be understood in the framework of a homogenized numerical approach we have developed a mesoscopic numerical model based on the Lattice Boltzmann Method for the local melting process which considers individual powder particles. The model takes into account full hydrodynamics including capillary and wetting effects. It is shown that these effects combined with the stochastic powder layer are the origin of fault formation. The numerical results are compared with experiments in order to demonstrate the predictive value of our model.

Analysis of tilted multilayer Laue lens with stochastic layer thickness error

The propagation of X-rays in tilted multilayer Laue lenses (MLLs) with stochastic layer thickness error is analyzed by using the beam propagation method (BPM). The accuracy of BPM is studied by comparing wave fields calculated by BPM and the Takagi–Taupin description (TTD) of X-ray dynamical diffraction theory. Influences of the stochastic layer thickness error on the focusing performance are evaluated. This study shows that, because of the stochastic layer thickness error, the zone plate law could be broken locally, which would lead to undesired foci around the principal focus. Simulation results suggest that for a typical tilted MLL, the root mean square (RMS) value of the stochastic layer thickness error should be smaller than about 1.5% in order to keep the MLL׳s performance. It is demonstrated that BPM can serve as an efficient tool for the analysis of tilted MLLs with imperfections.

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.

Reservoir Geological Model of Reef-Bank Carbonate Rocks of Ordavician in Tazhong Area, Tarim Basin, NW China

The reservoir of Lianglitage formaton mainly distribute in the Liang 1~Liang 2 section, and slight amount distribute in Liang 3 section. The microfacies are abundant and, and they apparently affect the development of the reservoir. Based on the geologic feature, we propound the concept:"microfacies combination". It is composed by two or several microfacies, and each microfacies have similar reservoir conditions. Using the seismic facies interpretation, combining the methods of deterministic modeling and stochastic modeling, the "microfacies combination" model is established. Appling the method that "microfacies combination" controls the modeling course, taking the wave impedance which has good corresponding relationship with reservoir as secondary variable, small layer application of stochastic modeling method based on the porosity model is finally established through the stochastic modeling method layer and layer. Considering the crack influence on permeability, the first step is establishing the fracture distribution model, then the permeability model is established taking the fracture distribution as secondary variable, which improves the practicability of permeability model.

Control of 3D edge radiation structure with resonant magnetic perturbation fields applied to the stochastic layer and stabilization of radiative divertor plasma in LHD

It is found that resonant magnetic perturbation (RMP) fields have a stabilizing effect on the radiating edge plasma, realizing stable sustainment of radiative divertor (RD) operation in the Large Helical Device (LHD). Without RMP, thermal instability leads to radiative collapse. Divertor power load is reduced by a factor of 3–10 during the RMP-assisted RD phase, while maintaining relatively good core plasma confinement with confinement enhancement factor . It has also been demonstrated that the RMP field itself can initiate transition to RD operation by increasing perturbation strength, while keeping constant density and injection power. The results show a possibility of a new control knob for divertor power load in a 3D magnetic field configuration. It is also found that after the transition to RD, the energy confinement enhancement factor based on ISS04 scaling increases by a factor of 1.4 compared with the attached phase. The operation range of the RMP-assisted RD is identified in terms of RMP strength and radial location of the resonance layer of the RMP. A 3D edge radiation structure is analysed using the edge transport code EMC3-EIRENE and the results are compared with experiments. The comparison indicates that the application of RMP modulates the 3D edge radiation structure such that an intense radiation appears around the X-point of the m/n = 1/1 island in the case with RMP, while it is located at the inboard side without RMP.

Magnetospheric convection and magnetopause shadowing effects in ULF wave‐driven energetic electron transport

Magnetospheric radiation belt electron transport in the presence of ULF waves and a convection electric field is investigated using a model that includes a nightside plasma sheet source and electron losses by magnetopause shadowing. Narrow‐band ULF waves launched from a prescribed dayside magnetopause source are shown to interact with trapped and untrapped equatorially mirroring electrons within the magnetosphere. For magnetic moments less than 8 keV/nT and a strong convection electric field (in the order of 5 mV/m), we find that a limb of untrapped plasma sheet electrons extending across the dayside magnetosphere into the afternoon sector provides a phase space density (PSD) source for injection to lower L‐shells by ULF waves, causing a rapid enhancement in PSD. However, the same ULF wave activity gives rise to a rapid dropout in PSD for electrons with a higher magnetic moment or in the presence of a weaker convection electric field, since in this case the plasma sheet electrons escape through the magnetopause before they reach the afternoon sector. In their place, a lack of PSD, or PSD “holes” can be periodically injected from the magnetopause to lower L‐shells by ULF waves, leading to the rapid depletion in average PSD. In each case, the magnitude and extent in L‐shell of the PSD enhancement or depletion is strongly dependent on the amplitude of ULF waves in the afternoon sector, and is significantly augmented by the overlap of drift‐resonant islands and an associated stochastic transport layer.

Stochastic dynamics of electric dipole in external electric fields: A perturbed nonlinear pendulum approach

The motion of a dipole in external electric fields is considered in the framework of nonlinear pendulum dynamics. A stochastic layer is formed near the separatrix of the dipole pendulum in a restoring static electric field under the periodic perturbation by plane-polarized electric fields. The width of the stochastic layer depends on the direction of the forcing field variation, and this width can be evaluated as a function of perturbation frequency, amplitude, and duration. A numerical simulation of the approximate stochastic layer width of a perturbed pendulum yields a multi-peak frequency spectrum. It is described well enough at high perturbation amplitudes by an analytical estimation based on the separatrix map with an introduced expression of the most effective perturbation phase. The difference in the fractal dimensions of the phase spaces calculated geometrically and using the time-delay reconstruction is attributed to the predominant development of periodic and chaotic orbits, respectively. The correlation of the stochastic layer width with the phase space fractal dimensions is discussed.

Edge impurity transport study in the stochastic layer of LHD and the scrape-off layer of HL-2A

Edge impurity transport has been investigated in the stochastic layer of the Large Helical Device (LHD) and the scrape-off layer (SOL) of the Huan Liuqi-2A (HL-2A) tokamak, as a comparative analysis based on the three-dimensional (3D) edge transport code EMC3–EIRENE and on the carbon emission profile measurement. The 3D simulation predicts not only an impurity screening effect in both devices, but also different impurity behaviour against collisionality and impurity source location between the two devices. The difference is caused by geometrical structures of the magnetic field lines in the stochastic layer and X-point poloidal divertor SOL, i.e. the number of poloidal turns of flux tubes affecting the poloidal distribution of plasma parameters and the impact of perpendicular transport on parallel pressure conservation and energy transport. These processes have an influence on the impurity screening efficiency at upstream and downstream positions of field lines. The carbon emission measured in the stochastic layer of LHD clearly indicates the screening effect in the high-density region. The result can be qualitatively interpreted by the present modelling, although the modelling shows a slight difference in the quantitative behaviour of carbon ions in the stochastic layer of LHD. On the other hand, a comparison of the carbon emission profile from HL-2A with the modelling is not straightforward. It is found that the impurity distribution in the HL-2A SOL is very sensitive to the impurity source location. In order to interpret the experimental observation a further study is necessary, in particular, on the impurity source distribution in the divertor plate and the first wall.

Three-vortex quasi-geostrophic dynamics in a two-layer fluid. Part 2. Regular and chaotic advection around the perturbed steady states

AbstractWe study fluid-particle motion in the velocity field induced by a quasi-stationary point vortex structure consisting of one upper-layer vortex and two identical vortices in the bottom layer of a rotating two-layer fluid. The regular regimes are investigated, and the possibility of chaotic regimes (chaotic advection) under the effect of quite small non-stationary disturbances of stationary configurations has been shown. Examples of different scenarios are given for the origin and development of chaos. We analyse the role played by the stochastic layer in the processes of mixing and in the capture of fluid particles within a vortex area. We also study the influence of stratification on these effects. It is shown that regular and chaotic advection situations exhibit significant differences in the two layers.

Edge and divertor plasma measurements with ion sensitive and Mach probes in LHD

Abstract Spatial profiles of plasma flow and Mach number in the stochastic magnetic boundary layer as well as ion temperature ( T i ) and electron temperature ( T e ) in the divertor region in Large Helical Device (LHD) have been studied by a movable multiple functions probe, which consists of Mach probes and an ion sensitive probe. The results of ion saturation current measurements indicated plasma flow direction is alternated in the stochastic magnetic boundary. Mach number profiles for different plasma densities have been evaluated experimentally which compared with 3-D transport code. T i and T e in the divertor region measured by the ion sensitive probe decreased with increasing line-averaged density. Although T i was higher than T e in the low density plasma, both temperatures became almost the same at higher density.

Publisher's Note: “Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions” [Rev. Sci. Instrum. 83, 10E509 (2012)

Publisher's Note: “Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions” [Rev. Sci. Instrum. 83, 10E509 (2012)

Radial profile measurement of electron temperature in edge stochastic magnetic field layer of LHD using intensity ratio of extreme ultraviolet line emissions

Vertical profile of neon line emissions in 30-650 Å wavelength range has been observed in horizontally elongated plasma cross section of Large Helical Device (LHD). Intensity ratio between the neon line emissions is studied to measure the radial profile of electron temperature in the edge stochastic magnetic field layer of LHD. The edge temperature profile successfully obtained from the line ratio of NeVIII 2s-3p to 2p-3s transitions is compared with the simulation based on three-dimensional edge transport code. The result shows a reasonably good agreement with the edge temperature profile analyzed from atomic data and analysis structure code. The electron temperature at last closed flux surface measured from the intensity ratio is also in good agreement with that measured from Thomson scattering.

The Effect of Externally Applied Resonant Magnetic Perturbations on Fusion Product Dynamics in Toroidal Plasmas: Numerical Simulation

The suppression of edge-localized modes by means of externally induced resonant magnetic perturbations (RMPs) has been investigated extensively on present-day tokamaks. In this paper we examine the modification of the loss of fusion born α-particles as effected by the application of RMPs in tokamak plasmas. This study was performed by means of test-particle simulations. To simplify the calculations we use a toroidal magnetic field model with circular magnetic flux surfaces. The transport properties of energetic α-particles are investigated during a 3 s time interval by tracing the test-particle ensemble with each particle trajectory following by integration of the full orbit equation. Three regimes of particle losses are identified during the evolution of the particle ensemble. A natural consequence of RMP excitation is the formation of magnetic islands together with stochastic magnetic layers at the plasma edge. The formation of these resonant magnetic field structures are associated with irregularities of the energetic α-particle orbits, which can substantially increase the loss of slowing down α-particles from the plasma periphery. At the same time the first orbit losses of fusion alphas are practically unaffected by RMPs.

Magnetic barriers and their q95 dependence at DIII-D

It is well known that externally generated resonant magnetic perturbations (RMPs) can form islands in the plasma edge. In turn, large overlapping islands generate stochastic fields, which are believed to play a role in the avoidance and suppression of edge localized modes (ELMs) at DIII-D. However, large coalescing islands can also generate, in the middle of these stochastic regions, KAM surfaces effectively acting as ‘barriers’ against field-line dispersion and, indirectly, particle diffusion. It was predicted in Ali and Punjabi (2007 Plasma Phys. Control. Fusion 49 1565–82) that such magnetic barriers can form in piecewise analytic DIII-D plasma equilibria. In this work, the formation of magnetic barriers at DIII-D is corroborated by field-line tracing calculations using experimentally constrained EFIT (Lao et al 1985 Nucl. Fusion 25 1611) DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. According to these calculations, the occurrence and location of magnetic barriers depend on the edge safety factor q95. It was thus suggested that magnetic barriers might contribute to narrowing the edge stochastic layer and play an indirect role in the RMPs failing to control ELMs for certain values of q95. The analysis of DIII-D discharges where q95 was varied, however, does not show anti-correlation between barrier formation and ELM suppression.

Resonant features of energy and particle transport during application of resonant magnetic perturbation fields at TEXTOR and DIII-D**This is the paper of the IAEA contribution by Schmitz O. et al 2010 Key results from the DIII-D/TEXTOR Collaboration on the Physics of Stochastic Boundaries projected to ELM control at ITER, EXD/P3-30.

In this paper, results of a direct comparison of TEXTOR and DIII-D experiments with resonant magnetic perturbation (RMP) fields are presented. This comparison of resistive L-mode plasmas at TEXTOR with highly conductive H-mode plasmas at DIII-D is useful to identify generic physics mechanisms during application of RMP fields with a strong field line pitch angle alignment in the plasma edge.A reduction in the pedestal electron pressure pe with increasing extension of the vacuum modelled stochastic layer and pe recovery with decreasing layer width is found caused by a q95 resonant reduction in the edge (0.8 < ΨN < 0.95) electron temperature Te(q95) on both devices. For RMP edge-localized mode (ELM) suppressed H-mode plasmas at DIII-D, the gradients ∇Te and nominal values of Te are reduced in this edge region while increasing in the pedestal (0.95 < ΨN < 1.0) with RMP field applied and both are highly dependent on q95. In contrast, an increase in the central ion temperature with strong steepening of the ion temperature profile at mid-radius is found—again being highly dependent on q95. However, these resonant thermal transport effects are only seen in high triangularity plasmas revealing a strong shape dependence of the thermal transport. In contrast to the highly q95 dependent thermal transport features, the reduction of ne—known as density pump out—shows a much weaker dependence on q95. We show the potential to reduce the RMP induced particle pump out by fine tuning of the RMP spectral properties. At low resonant field amplitudes enhanced particle confinement is seen in high-field side limited L-mode discharges on both devices while higher resonant field amplitudes yield particle pumps out.

Passive scalar advection in the vicinity of two point vortices in a deformation flow

The dynamics of passive fluid particles in the vicinity of two point vortices with arbitrary intensities, embedded in a steady external deformation flow, is studied. The motion of passive fluid particles is described by a nonintegrable 1.5 degrees of freedom dynamical system. Though the external flow is stationary, the additional half degree of freedom appears because the vortices’ motion about their stationary positions is periodic. Then, this periodic motion plays the role of a periodic perturbation for the system describing the passive particle dynamics. Therefore, chaotic advection of passive fluid particles in the vicinity of these two vortices can occur. If the vortices, however, are situated at their stationary positions, they become motionless, and the dynamical system describing the passive particles’ dynamics is also stationary. In the case of motionless vortices, a classification of the phase portraits of the passive particle motion is conducted by analyzing the number of critical points. When the vortices do not lie at their stationary position, the system becomes nonstationary. In this case, the existence of impenetrable transport barriers for chaotic advection is shown. These barriers are destroyed when stochastic layers merge; these layers widen as the deviation of the vortex position from the stationary points, increases. The efficiency of chaotization is analyzed by means of Poincaré sections and accumulated Lyapunov exponents.

Convective and diffusive ULF wave driven radiation belt electron transport

[1] The process of magnetospheric radiation belt electron transport driven by ULF waves is studied using a 2-D ideal MHD model for ULF waves in the equatorial plane including day/night asymmetry and a magnetopause boundary, and a test kinetic model for equatorially mirroring electrons. We find that ULF wave disturbances originating along the magnetopause flanks in the afternoon sector can act to periodically inject phase space density from these regions into the magnetosphere. Closely spaced drift-resonant surfaces for electrons with a given magnetic moment in the presence of the ULF waves create a layer of stochastic dynamics for L-shells above 6.5–7 in the cases examined, extending to the magnetopause. The phase decorrelation time scale for the stochastic region is estimated by the relaxation time for the diffusion coefficient to reach a steady value. This is found to be of the order of 10–15 wave periods, which is commensurate with the typical duration of observed ULF wave packets in the magnetosphere. For L-shells earthward of the stochastic layer, transport is limited to isolated drift-resonant islands in the case of narrowband ULF waves. We examine the effect of increasing the bandwidth of the ULF wave driver by summing together wave components produced by a set of independent runs of the ULF wave model. The wave source spectrum is given a flat-top amplitude of variable width (adjusted for constant power) and random phase. We find that increasing bandwidth can significantly enhance convective transport earthward of the stochastic layer and extend the stochastic layer to lower L-shells.

Asymptotic properties of wall-induced chaotic mixing in point vortex pairs

The purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or “wall”), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. An asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. A Melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair (and rotating with it) do not survive when a wall is present. The thickness of the resulting inner stochastic layer is estimated by using the separatrix map method and is shown to scale like the inverse of the squared distance to the wall. This estimation provides a lower-bound to the numerical thickness measured from either Poincaré sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. In addition, it is shown that the outer homoclinic cycle, separating the vortices from the external (open) flow, is also perturbed from inside by the rotation of the vortex pair. As a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. However, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough.

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the finite time Lyapunov exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian coherent structures (LCS) that act as barriers for the transport of field lines.

Barriers in the transition to global chaos in collisionless magnetic reconnection. II. Field line spectroscopy

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.