Perpendicular Diffusion Research Articles

Evaluation of local erosion and deposition on the W-monoblock of JA-DEMO divertor

We developed and performed a 3D Monte-Carlo simulation on local erosion and deposition in outer divertor target of JA-DEMO. The local erosion and deposition were evaluated considering the divertor plasma parameters and the roof shape of W-monoblocks. First, for local erosion simulation, the trajectories of D ions and impurity (He and Ar) ions were traced before irradiating the monoblock surface. The physical sputtering was calculated by these ions irradiation, considering their charge states, incident-energies and -angles. The highest sputtering flux was produced by multiply-charged Ar ions (Ar3+–Ar5+). The sputtering flux strongly depended on the poloidal positions along the divertor target. Although almost no erosion (sputtering) was obtained in low-temperature zone (∼1 eV), the erosion occurred in mid- (∼10 eV) and high-temperature (>10 eV) zone. Second, for local deposition simulation, the trajectories of W atoms emitted from the monoblock surface were traced. After transport (including ionization and recombination) in the plasma, W atoms and ions were deposited on the monoblock surface. The deposition occurred even on the area where plasmas did not irradiate (shadow). This was due to perpendicular diffusion to magnetic field lines, gyro-orbit effects for W ions and straight-line motion for neutral W atoms. The poloidal distribution of the deposition fluxes was similar to that of the sputtering fluxes. In low-temperature zone, no deposition flux occurred due to very low sputtering flux. The deposition flux in mid-temperature zone increased significantly and that in high-temperature zone remained high.

Fully Kinetic Simulations of Proton-beam-driven Instabilities from Parker Solar Probe Observations

The expanding solar wind plasma ubiquitously exhibits anisotropic nonthermal particle velocity distributions. Typically, proton velocity distribution functions (VDFs) show the presence of a core and a field-aligned beam. Novel observations made by the Parker Solar Probe (PSP) in the innermost heliosphere have revealed new complex features in the proton VDFs, namely anisotropic beams that sometimes experience perpendicular diffusion. In this study, we use a 2.5D fully kinetic simulation to investigate the stability of proton VDFs with anisotropic beams observed by PSP. Our setup consists of a core and an anisotropic beam population that drift with respect to each other. This configuration triggers a proton beam instability from which nearly parallel fast magnetosonic modes develop. Our results demonstrate that before this instability reaches saturation, the waves resonantly interact with the beam protons, causing perpendicular heating at the expense of the parallel temperature.

Application of preoperative advanced diffusion magnetic resonance imaging in evaluating the postoperative recurrence of lower grade gliomas

BackgroundRecurrence of lower grade glioma (LrGG) appeared to be unavoidable despite considerable research performed in last decades. Thus, we evaluated the postoperative recurrence within two years after the surgery in patients with LrGG by preoperative advanced diffusion magnetic resonance imaging (dMRI).Materials and methods48 patients with lower-grade gliomas (23 recurrence, 25 nonrecurrence) were recruited into this study. Different models of dMRI were reconstructed, including apparent fiber density (AFD), white matter tract integrity (WMTI), diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), neurite orientation dispersion and density imaging (NODDI), Bingham NODDI and standard model imaging (SMI). Orthogonal Partial Least Squares-Discriminant Analysis (OPLS-DA) was used to construct a multiparametric prediction model for the diagnosis of postoperative recurrence.ResultsThe parameters derived from each dMRI model, including AFD, axon water fraction (AWF), mean diffusivity (MD), mean kurtosis (MK), fractional anisotropy (FA), intracellular volume fraction (ICVF), extra-axonal perpendicular diffusivity (De⊥), extra-axonal parallel diffusivity (De∥) and free water fraction (fw), showed significant differences between nonrecurrence group and recurrence group. The extra-axonal perpendicular diffusivity (De⊥) had the highest area under curve (AUC = 0.885), which was significantly higher than others. The variable importance for the projection (VIP) value of De⊥ was also the highest. The AUC value of the multiparametric prediction model merging AFD, WMTI, DTI, DKI, NODDI, Bingham NODDI and SMI was up to 0.96.ConclusionPreoperative advanced dMRI showed great efficacy in evaluating postoperative recurrence of LrGG and De⊥ of SMI might be a valuable marker.

$\mathcal{R}^2$ curvature-squared corrections on Langevin diffusion coefficients

Abstract The effect of finite coupling corrections to the Langevin diffusion coefficients on a moving heavy quark in the Super Yang-Mills plasma is investigated. 
These corrections are related to curvature squared corrections in the corresponding gravity sector. 
We compare the results of both longitudinal and perpendicular Langevin diffusion coefficients with those in $\mathcal{N}$=4 Super Yang-Mills plasma. It is observed that the curvature-squared corrections influence the Langevin diffusion coefficients, and the corrections for both Langevin diffusion coefficients demonstrate the dependence on the velocity of the moving heavy quark and the specifics of the higher derivative correction.
In addition, we conduct calculations for the Langevin diffusion coefficients of a moving heavy quark within the Gauss-Bonnet background. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios χ∥/χ⊥⋙1 (with χ∥, χ⊥ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. The implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ∼(NΔt)1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios (χ∥/χ⊥=1010).

Boron powder injection experiments in WEST with a fully actively cooled, ITER grade, tungsten divertor

Reactor relevant fusion devices will use tungsten (W) for their plasma facing components (PFCs) due to its thermomechanical properties and low tritium retention. However, W introduces high-Z impurities into the plasma, degrading its performance. Different wall conditioning methods have been developed to address this issue, including coating of W PFCs with layers of low-Z material. Wall conditioning by boron (B) powder injection using an impurity powder dropper (IPD) is being studied in WEST. Two series of experiments were conducted since the installation of the new ITER grade full W divertor. During the first series in 2023 ∼ 1 g of B powder was injected in total at a maximum rate of ∼ 58 mg/s, both of which are three times greater than respective values in the initial WEST powder injection experiments. The second series of experiments included injection of B and BN powders for comparison of their effects on plasma performance. The presence of an instantaneous conditioning effect is suggested by visible spectroscopy measurements of low-Z impurity lines and a rollover of total radiated power past an injection rate of ∼ 20 mg/s was observed. Presence of B coating layer formation is supported by the evolution of the average radiance of visible lines of B, W and oxygen (O). To understand B transport, an interpretative modeling workflow is employed, utilizing the SOLEDGE-EIRENE fluid boundary plasma code and the Dust Injection Simulator (DIS) code. Parameters like B perpendicular diffusivity and recycling coefficients are varied to match experimental results to see if the initial assumption of B sticking to the PFCs immediately after the contact with the wall is adequate for correctly modelling its distribution on the PFCs.

Numerical Simulation of Equal Ratio Relations for the Peak Intensities of >10 MeV Energetic Protons

Previous studies have highlighted the significance of perpendicular diffusion in the decay phase of particle intensities for >10 MeV energetic protons. Recently, an observational study has indicated that the peak intensity ratios across different energy channels (13−64 MeV protons) remain almost constant as the spacecraft location varies in many solar proton events. This interesting phenomenon is referred to as equal ratio relations. These findings suggest that perpendicular diffusion not only affects particle intensity during the decay phase but also throughout the rising phase. In this study, we perform numerical simulations of >10 MeV energetic proton events observed by STEREO A, STEREO B, and the Solar and Heliospheric Observatory. Our findings demonstrate that perpendicular diffusion strongly affects the entire time profile of particle intensity for spacecraft not magnetically connected to the source region. The numerical simulation results indicate that in order to reproduce observations, we need to include perpendicular diffusion near the source region and in interplanetary space. Perpendicular diffusion leads to nearly uniform peak ratios at different locations and contributes to the formation of the reservoir phenomenon during the decay phase. Consequently, these numerical results support the significant role of perpendicular diffusion in the formation of the longitudinal distribution of >10 MeV proton events.

Plasma dynamics and collisional magnetic presheath structure in unmagnetized divertor plasma in fusion devices

A model of strongly ionized plasma dynamics in a slightly inclined magnetic field with ions, unmagnetized with respect to ion–ion collisions, typical for detached regimes, is presented. It is demonstrated that far from the material surface, the parallel dynamics remains almost the same as in the magnetized plasma. In the wall vicinity, parallel plasma motion is transformed into perpendicular classical diffusion originating from electron–ion collisions, forming a diffusive layer. At a distance of few ion gyroradii from the material surface, a collisional magnetic presheath is formed, where ions move toward the surface with the velocity of the order of the sound speed, in spite of the fact that an ion exhibits many collisions before reaching the surface. For typical inclination angles of magnetic field of the order of few degrees, the electrostatic potential in the diffusive layer and in the presheath deviates considerably from the Boltzmann potential for electrons, which is typical for collisionless magnetic presheath. Moreover, the normal electric field in some regions is directed away from the surface, which is important for impurities to interact with the surface.

Transport of energetic particles in turbulent space plasmas: pitch-angle scattering, telegraph, and diffusion equations

Introduction: In this article, we revisit the pitch-angle scattering equation describing the propagation of energetic particles through magnetized plasma. In this case, solar energetic particles and cosmic rays interact with magnetohydrodynamic turbulence and experience stochastic changes in the pitch-angle. Since this happens over an extended period of time, a pitch-angle isotropization process occurs, leading to parallel spatial diffusion. This process is described well by the pitch-angle scattering equation. However, the latter equation is difficult to solve analytically even when considering special cases for the scattering coefficient.Methods: In the past, a so-called subspace approximation was proposed, which has important applications in the theory of perpendicular diffusion. Alternatively, an approach based on the telegraph equation (also known as telegrapher’s equation) has been developed. We show that two-dimensional subspace approximation and the description based on the telegraph equation are equivalent. However, it is also shown that the obtained distribution functions contain artifacts and inaccuracies that cannot be found in the numerical solution to the problem. Therefore, an N-dimensional subspace approximation is proposed corresponding to a semi-analytical/semi-numerical approach. This is a useful alternative compared to standard numerical solvers.Results and Discussion: Depending on the application, the N-dimensional subspace approximation can be orders of magnitude faster. Furthermore, the method can easily be modified so that it can be used for any pitch-angle scattering equation.

Anisotropic grain boundary diffusion process in textured sintered and hot-deformed Nd-Fe-B magnets

A systematic study of the dependence of the Grain Boundary Diffusion Process (GBDP) on texture using Dy and Dy-Nd-Cu in microcrystalline sintered and nanocrystalline hot deformed Nd-Fe-B magnets was performed. Diffusion parallel or perpendicular to the texture direction, the nominal c-axes orientation in the polycrystals, was investigated. By measuring thin slices from the respective samples, coercivity as a function of (i) magnet thickness and (ii) diffusion depth was obtained showing that GBDP efficiency depends on the diffusion direction, diffusion source as well as the grain morphology originating from the magnet production route. In nanocrystalline hot deformed magnets perpendicular diffusion is superior due to the platelet-like shape of the grains. Microcrystalline sintered magnets consist of equiaxed grains hence the main effects originate in anisotropic lattice diffusion and pole surface hardening. The magnetic properties are correlated with a comprehensive analysis of microstructure, chemistry and magnetization reversal.

Interface Water Assists in Dimethyl Sulfoxide Crossing and Poration in Model Bilayer.

Understanding the mechanism of transport and pore formation by a commonly used cryoprotectant, dimethyl sulfoxide (DMSO), across cell membranes is fundamentally crucial for drug delivery and cryopreservation. To shed light on the mechanism and thermodynamics of pore formation and crossing behavior of DMSO, extensive all-atom molecular dynamics simulations of 1,2-dimyristoyl-rac-glycero-3-phosphocholine (DMPC) bilayers are performed at various concentrations of DMSO at a temperature above the physiological temperature. Our results unveil that DMSO partially depletes water from the interface and positions itself between lipid heads without full dehydration. This induces a larger area per headgroup, increased disorder, and enhanced fluidity without any disintegration even at the highest DMSO concentration studied. The enhanced disorder fosters local fluctuations at the interface that nucleate dynamic and transient pores. The potential of mean force (PMF) of DMSO crossing is derived from two types of biased simulations: a single DMSO pulling using the umbrella sampling technique and a cylindrical pore formation using the recently developed chain reaction coordinate method. In both cases, DMSO crossing encounters a barrier attributed to unfavorable polar nonpolar interactions between DMSO and lipid tails. As the DMSO concentration increases, the barrier height reduces along with the faster lateral and perpendicular diffusion of DMSO suggesting favorable permeation. Our findings suggest that the energy required for pore formation decreases when water assists in the formation of DMSO pores. Although DMSO displaces water from the interface toward the far interface region without complete dehydration, the presence of interface water diminishes pore formation free energy. The existence of interface water leads to the formation of a two-dimensional percolated water-DMSO structure at the interface, which is absent otherwise. Overall, these insights into the mechanism of DMSO crossing and pore formation in the bilayer will contribute to understanding cryoprotectant behavior under supercooled conditions in the future.

Modeling Ion Acceleration and Transport in Corotating Interaction Regions: The Mass-to-charge Ratio Dependence of the Particle Spectrum

We investigate the role of perpendicular diffusion in shaping the energetic ion spectrum in corotating interaction regions (CIRs), focusing on its mass-to-charge (A/Q) ratio dependence. We simulate a synthetic CIR using the EUropean Heliospheric FORecasting Information Asset and model the subsequent ion acceleration and transport by solving the focused transport equation incorporating both parallel and perpendicular diffusion. Our results reveal distinct differences in ion spectra between scenarios with and without perpendicular diffusion. In the absence of perpendicular diffusion, ion spectra near CIRs show a strong (A/Q) ϵ dependence with ϵ depending on the turbulence spectral index, agreeing with theoretical predictions. In contrast, the incorporation of perpendicular diffusion, characterized by a weak A/Q dependence, leads to similar spectra for different ion species. This qualitatively agrees with observations of energetic particles in CIRs.

Suppressing Zn pulverization with three-dimensional inert-cation diversion dam for long-life Zn metal batteries

Tremendous attention has been paid to the water-associated side reactions and zinc (Zn) dendrite growth on the electrode-electrolyte interface. However, the Zn pulverization that can cause continuous depletion of active Zn metal and exacerbate hydrogen evolution is severely neglected. Here, we disclose that the excessive Zn feeding that causes incomplete crystallization is responsible for Zn pulverization formation through analyzing the thermodynamic and kinetics process of Zn deposition. On the basis, we introduce 1-ethyl-3-methylimidazolium cations (EMIm+) into the electrolyte to form a Galton-board-like three-dimensional inert-cation (3DIC) region. Modeling test shows that the 3DIC EMIm+ can induce the Zn2+ flux to follow in a Gauss distribution, thus acting as elastic sites to buffer the perpendicular diffusion of Zn2+ and direct the lateral diffusion, thus effectively avoiding the local Zn2+ accumulation and irreversible crystal formation. Consequently, anti-pulverized Zn metal deposition behavior is achieved with an average Coulombic efficiency of 99.6% at 5 mA cm-2 over 2,000 cycles and superb stability in symmetric cell over 1,200 h at -30 °C. Furthermore, the Zn||KVOH pouch cell can stably cycle over 1,200 cycles at 2 A g-1 and maintain a capacity of up to 12 mAh.

Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates.

The purpose of the study is to identify differences between axisymmetric diffusion kurtosis imaging (DKI) and standard DKI, their consequences for biophysical parameter estimates, and the protocol choice influence on parameter estimation. Noise-free and noisy, synthetic diffusion MRI human brain data is simulated using standard DKI for a standard and the fast "199" acquisition protocol. First the noise-free "baseline" difference between both DKI models is estimated and the influence of fiber complexity is investigated. Noisy data is used to establish the signal-to-noise ratio at which the baseline difference exceeds noise variability. The influence of protocol choices and denoising is investigated. The five axisymmetric DKI tensor metrics (AxTM), the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor are used to compare both DKI models. Additionally, the baseline difference is also estimated for the five parameters of the WMTI-Watson model. The parallel and perpendicular kurtosis and all of the WMTI-Watson parameters had large baseline differences. Using a Westin or FA mask reduced the number of voxels with large baseline difference, that is, by selecting voxels with less complex fibers. For the noisy data, precision was worsened by the fast "199" protocol but adaptive denoising can help counteract these effects. For the diffusivities and mean of the kurtosis tensor, axisymmetric DKI with a standard protocol delivers similar results as standard DKI. Fiber complexity is one main driver of the baseline differences. Using the "199" protocol worsens precision in noisy data but adaptive denoising mitigates these effects.

Large-scale Anisotropy of Galactic Cosmic Rays as a Probe of Local Cosmic-Ray Propagation

Recent studies have shown that the anisotropy is of great value to decipher cosmic rays’ origin and propagation. We have built a unified scenario to describe the observations of the energy spectra and the large-scale anisotropy and called attention to their synchronous evolution with energy. In this work, the impact of the local regular magnetic field (LRMF) and corresponding anisotropic diffusion on large-scale anisotropy have been investigated. When the perpendicular diffusion coefficient is much smaller than the parallel one, the dipole anisotropy points to the LRMF and the observational phase below 100 TeV could be reproduced. Moreover, we find that the dipole phase above 100 TeV strongly depends on the evolution of local diffusion. But the current measurements at that energy are still scarce. We suggest that more precise measurements at that energy could be carried out to unveil the local diffusion and further the local turbulence.

Modeling energetic proton transport in a corotating interaction region

Aims. An energetic particle event related to a corotating interaction region (CIR) structure was observed by the Solar-Terrestrial Relations Observatory-A (STEREO-A) from 21 to 24 August 2016. Based on an analysis of measurement data, we suggest that instead of being accelerated by distant shocks, a local mechanism similar to diffusive shock acceleration (DSA) acting in the compression region could explain the flux enhancements of 1.8–10.0 MeV nucleon−1 protons. We created simulations to verify our hypothesis. Methods. We developed a coupled model composed of a data-driven analytical background model providing solar wind configuration and a particle transport model represented by the focused transport equation (FTE). We simulated particle transport in the CIR region of interest in order to obtain the evolution of proton fluxes and derive the spectra. Results. We find that the simulation is well correlated with the observation. The mechanism of particle scattering back and forth between the trap-like structure of interplanetary magnetic field (IMF) in the compression region is the major factor responsible for the flux enhancements in this energetic particle event, and perpendicular diffusion identified by a ratio of κ⊥/κ|| ∼ 10−2 plays an important role in the temporal evolution of proton fluxes.

Magnetic Trapping of Galactic Cosmic Rays in the Outer Heliosheath and Their Preferential Entry into the Heliosphere

This paper examines the geometry of interstellar magnetic field lines close to the boundary of the heliosphere in the direction of the unperturbed local interstellar magnetic field, where the field lines are spread apart by the heliopause (HP). Such field parting establishes a region of weaker magnetic field of about 300 au in size in the northern hemisphere that acts as a giant magnetic trap affecting the propagation of galactic cosmic rays (GCRs). The choice of an analytic model of the magnetic field in the very local interstellar medium allows us to qualitatively study the resulting magnetic field draping pattern while avoiding unphysical dissipation across the HP-impeding numerical magnetohydrodynamic (MHD) models. We investigate GCR transport in the region exterior to the heliosphere, including the magnetic trap, subject to guiding center drifts, pitch angle scattering, and perpendicular diffusion. The transport coefficients were derived from Voyager 1 observations of magnetic turbulence in the VLISM. Our results predict a ring current of energetic ions drifting around the interior of the magnetic trap. It is also demonstrated that GCRs cross the HP for the first time preferentially through a crescent-shaped region between the magnetic trap and the upwind direction. The paper includes results of MHD modeling of the heliosphere that provide the coordinates of the center of the magnetic trap in ecliptic coordinates. In addition to the heliosphere, we examine several extreme field draping configurations that could describe the astrospheres of other stars.

Atomic-Layer Controlled Transition from Inverse Rashba-Edelstein Effect to Inverse Spin Hall Effect in 2D PtSe2 Probed by THz Spintronic Emission.

2D materials, such as transition metal dichalcogenides, are ideal platforms for spin-to-charge conversion (SCC) as they possess strong spin-orbit coupling (SOC), reduced dimensionality and crystal symmetries as well as tuneable band structure, compared to metallic structures. Moreover, SCC can be tuned with the number of layers, electric field, or strain. Here, SCC in epitaxially grown 2D PtSe2 by THz spintronic emission is studied since its 1T crystal symmetry and strong SOC favor SCC. High quality of as-grown PtSe2 layers is demonstrated, followed by in situ ferromagnet deposition by sputtering that leaves the PtSe2 unaffected, resulting in well-defined clean interfaces as evidenced with extensive characterization. Through this atomic growth control and using THz spintronic emission, the unique thickness-dependent electronic structure of PtSe2 allows the control of SCC. Indeed, the transition from the inverse Rashba-Edelstein effect (IREE) in 1-3 monolayers (ML) to the inverse spin Hall effect (ISHE) in multilayers (>3 ML) of PtSe2 enabling the extraction of the perpendicular spin diffusion length and relative strength of IREE and ISHE is demonstrated. This band structure flexibility makes PtSe2 an ideal candidate to explore the underlying mechanisms and engineering of the SCC as well as for the development of tuneable THz spintronicemitters.

Anisotropic heat diffusion in stochastic magnetic fields

AbstractThe magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long.

The Effect of Solar Wind on Charged Particles’ Diffusion Coefficients

The transport of energetic charged particles through magnetized plasmas is ubiquitous in interplanetary space and astrophysics, and the important physical quantities are the parallel and perpendicular diffusion coefficients of energetic charged particles. In this paper, the influence of solar wind on particle transport is investigated. Using the focusing equation, we obtain parallel and perpendicular diffusion coefficients, accounting for the solar wind effect. For different conditions, the relative importance of the solar wind effect to diffusion is investigated. It is shown that, when energetic charged particles are close to the Sun, for parallel diffusion, the solar wind effect needs to be taken into account. These results are important for studying energetic charged particle transport processes in the vicinity of the Sun.