Stochastic Layer Research Articles

Characteristics of divertor heat flux distribution with an island divertor configuration on the J-TEXT tokamak

On J-TEXT, the temporal evolution of heat flux distribution on the high-field side (HFS) divertor plate has been measured by an infrared (IR) camera during the plasma operation with an island divertor configuration. In experiments, the island divertor configuration is an edge magnetic island chain structure surrounded by stochastic layers, which can be induced by resonant magnetic perturbations (RMPs). The experimental results show that the heat flux distribution on the HFS target plate depends significantly on the edge magnetic topology. Furthermore, the impact of hydrogen fueling using supersonic molecular beam injection (SMBI) on the divertor heat flux distributions is studied on J-TEXT with an island divertor configuration. It has been observed that power detachment can be achieved when the radiation front approaches the last closed flux surface (LCFS) after each SMBI pulse. This result may provide a method of access for divertor detachment on a fusion device with a three-dimensional (3D) boundary magnetic structure.

J-TEXT achievements in turbulence and transport in support of future device/reactor

Following the reconstruction of the TEXT tokamak at Huazhong University of Science and Technology in China, renamed as J-TEXT, a plethora of experimental and theoretical investigations has been conducted to elucidate the intricacies of turbulent transport within the tokamak configuration. These endeavors encompass not only the J-TEXT device’s experimental advancements but also delve into critical issues pertinent to the optimization of future fusion devices and reactors. The research includes topics on the suppression of turbulence, flow drive and damping, density limit, non-local transport, intrinsic toroidal flow, turbulence and flow with magnetic islands, turbulent transport in the stochastic layer, and turbulence and zonal flow with energetic particles or helium ash. Several important achievements have been made in the last few years, which will be further elaborated upon in this comprehensive review.

Paying attention to uncertainty: A stochastic multimodal transformers for post-traumatic stress disorder detection using video

Background and Objectives:Post-traumatic stress disorder is a debilitating psychological condition that can manifest following exposure to traumatic events. It affects individuals from diverse backgrounds and is associated with various symptoms, including intrusive thoughts, nightmares, hyperarousal, and avoidance behaviors. Methods:To address this challenge this study proposes a decision support system powered by a novel multimodal deep learning approach, based on a stochastic Transformer and video data. This Transformer has the ability to take advantage of its stochastic activation function and layers that allow it to learn sparse representations of the inputs. The method leverages a combination of low-level features extracted using three modalities, including Mel-frequency cepstral coefficients extracted from audio recordings, Facial Action Units captured from facial expressions, and textual data obtained from the audio transcription. By considering these modalities, our proposed model captures a comprehensive range of information related to post-traumatic stress disorder symptoms, including vocal cues, facial expressions, and linguistic content. Results:The deep learning model was trained and evaluated on the eDAIC dataset, which consists of clinical interviews with individuals with and without post-traumatic disorder. The model achieved state-of-the-art results, demonstrating its effectiveness in accurately detecting PTSD, showing an impressive Root Mean Square Error of 1.98, and a Concordance Correlation Coefficient of 0.722, signifying the model’s superior performance compared to existing approaches. Conclusion:This work introduces a new method for post-traumatic stress disorder detection from videos by utilizing a multimodal stochastic Transformer model. The model makes use of a variety of modalities, such as text, audio, and visual data, to gather comprehensive and varied information in order to make the detection.

Voltage-insensitive stochastic magnetic tunnel junctions with double free layers

Stochastic magnetic tunnel junction (s-MTJ) is a promising component of probabilistic bit (p-bit), which plays a pivotal role in probabilistic computers. For a standard cell structure of the p-bit, s-MTJ is desired to be insensitive to voltage across the junction over several hundred millivolts. In conventional s-MTJs with a reference layer having a fixed magnetization direction, however, the stochastic output significantly varies with the voltage due to spin-transfer torque (STT) acting on the stochastic free layer. In this work, we study a s-MTJ with a “double-free-layer” design theoretically proposed earlier, in which the fixed reference layer of the conventional structure is replaced by another stochastic free layer, effectively mitigating the influence of STT on the stochastic output. We show that the key device property characterized by the ratio of relaxation times between the high- and low-resistance states is one to two orders of magnitude less sensitive to bias voltage variations compared to conventional s-MTJs when the top and bottom free layers are designed to possess the same effective thickness. This work opens a pathway for reliable, nanosecond-operation, high-output, and scalable spintronics-based p-bits.

Deep L1 Stochastic Optimal Control Policies for Planetary Soft Landing

In this paper, a novel deep-learning-based solution is introduced to the Powered Descent Guidance problem, grounded in principles of nonlinear Stochastic Optimal Control (SOC) and Feynman–Kac theory. Our algorithm solves the problem by framing it as an L1-SOC problem for minimum fuel consumption. Additionally, it can handle practically useful control constraints and nonlinear dynamics and enforces state constraints as soft constraints. This is achieved by building off of recent work on deep forward-backward stochastic differential equations and differentiable neural-network layers for nonconvex optimization based on stochastic search. In contrast to previous approaches, our algorithm does not require convexification of the constraints or linearization of the dynamics and is empirically shown to be robust to stochastic disturbances and the initial conditions of the spacecraft. After training offline, our control policy can be activated once the spacecraft is within a prespecified radius of the landing zone and at a prespecified altitude, in other words, the base of an inverted cone with the tip at the landing zone. We demonstrate empirically that our controller can successfully and safely land all trajectories initialized in the vicinity of the base of this cone as well as with randomization in the starting velocities and spacecraft mass while minimizing fuel consumption.

Subdiffusive transport of runaway electrons in presence of small amplitude MHD perturbations in COMPASS

Radial transport of runaway electrons (REs) in tokamaks is affected by the presence of magnetic perturbations, either caused by internal magnetohydrodynamic instabilities or induced by external coils. The magnetic field configuration inside the plasma volume consists in general of intact magnetic surfaces alternated with magnetic islands and stochastic layers, which make the usual diffusive approach, based on the Rechester–Rosenbluth formula, inadequate to the study of transport. Here the fractional diffusion approach is employed to model RE transport in presence of intrinsic magnetic perturbations (magnetic islands) in the flat-top phase of RE-dedicated discharges on COMPASS tokamak. The character of RE transport is found to be subdiffusive. The degree of subdiffusion is evaluated by running simulations with the ORBIT code and a time-fractional diffusion equation is applied to calculate the time evolution of RE particle number. The results are compared with the observed RE losses, estimated from the time integrated neutron signal.

Patch-based stochastic attention for image editing

Attention mechanisms have become of crucial importance in deep learning in recent years. These non-local operations, which are similar to traditional patch-based methods in image processing, complement local convolutions. However, computing the full attention matrix is an expensive step with heavy memory and computational loads. These limitations curb network architectures and performances, in particular for the case of high resolution images. We propose an efficient attention layer based on the stochastic algorithm PatchMatch, which is used for determining approximate nearest neighbors. We refer to our proposed layer as a “Patch-based Stochastic Attention Layer” (PSAL). Furthermore, we propose different approaches, based on patch aggregation, to ensure the differentiability of PSAL, thus allowing end-to-end training of any network containing our layer. PSAL has a small memory footprint and can therefore scale to high resolution images. It maintains this footprint without sacrificing spatial precision and globality of the nearest neighbors, which means that it can be easily inserted in any level of a deep architecture, even in shallower levels. We demonstrate the usefulness of PSAL on several image editing tasks, such as image inpainting, guided image colorization, and single-image super-resolution. Our code is available at: https://github.com/ncherel/psal.

Semi-analytical estimates for the chaotic diffusion in the Second Fundamental Model of Resonance. Application to Earth’s navigation satellites

We discuss the applicability of the Melnikov and Landau–Teller theories in obtaining semi-analytical estimates of the speed of chaotic diffusion in systems driven by the separatrix-like stochastic layers of a resonance belonging to the ‘second fundamental model’ (SFM) (Henrard and Lemaitre, 1983). Stemming from the analytic solution for the SFM in terms of Weierstrass elliptic functions, we introduce stochastic Melnikov and Landau–Teller models allowing to locally approximate chaotic diffusion as a sequence of uncorrelated ‘jumps’ observed in the time series yielding the slow evolution of an ensemble of trajectories in the space of the adiabatic actions of the system. Such jumps occur in steps of one per homoclinic loop. We show how a semi-analytical determination of the probability distribution of the size of the jumps can be arrived at by the Melnikov and Landau–Teller approximate theories. Computing also the mean time required per homoclinic loop, we arrive at estimates of the chaotic diffusion coefficient in such systems. As a concrete example, we refer to the long-term diffusion of a small object (e.g. Earth navigation satellite or space debris) within the chaotic layers of the so-called 2g+h lunisolar resonance, which is of the SFM type. After a suitable normal form reduction of the Hamiltonian, we compute estimates of the speed of diffusion of these objects, which compare well with the results of numerical experiments.

Excitation of radially propagating electrostatic shear Alfvén wave during the formation of ambipolar radial electric field in a stochastic magnetic field

A radially propagating electrostatic shear Alfvén wave (ωH mode) is found during the formation of ambipolar radial electric field in a magnetic stochastic layer through gyrokinetic simulation. It is found that the times scale of the ambipolar radial electric field formation is the damping time of the ωH mode. The frequency and damping rate of the ωH mode are theoretical derived, which are in good agreement with the simulation results.

Nonlinear microtearing modes in MAST and their stochastic layer formation

First nonlinear gyrokinetic simulations of microtearing modes in the core of a MAST case are performed on two surfaces of the high-collisionality discharge used in Valovič et al (2011 Nucl. Fusion 51 073045) to obtain the favorable energy confinement scaling with collisionality, . On the considered surfaces microtearing modes dominate linearly at binormal length scales of the order of the ion Larmor radius. While the effect of electron collision frequency is moderate in linear simulations, a strong dependence on this parameter is found in nonlinear simulations at , where r and a are the surface and tokamak minor radius, respectively. The dynamics of magnetic islands generated by microtearing modes is analysed, showing that the radial extent of the stochastic region caused by islands overlapping plays an important role in determining the saturation level of the microtearing mode driven heat flux. Local nonlinear gyrokinetic simulations show that the microtearing mode driven heat flux, , is largely dominated by magnetic flutter and depends strongly on the magnetic shear, . Comparing two surfaces, and , reveals that is negligible at (), with the electron temperature gradient (ETG) driven heat flux, , comparable to the experimental electron heat flux, , while is significantly larger and comparable to and at (). Microtearing modes cause more experimentally significant transport in higher regions and may influence (together with ETG modes) the observed scaling of energy confinement time with collisionality (Valovič et al 2011 Nucl. Fusion 51 073045).

A landscape of peaks: The intermittency islands of the stochastic heat equation with Lévy noise

We show that the spatial profile of the solution to the stochastic heat equation features multiple layers of intermittency islands if the driving noise is non-Gaussian. On the one hand, as expected, if the noise is sufficiently heavy-tailed, the largest peaks of the solution will be taller under multiplicative than under additive noise. On the other hand, surprisingly, as soon as the noise has a finite moment of order 2d, where d is the spatial dimension, the largest peaks will be of the same order for both additive and multiplicative noise, which is in sharp contrast to the behavior of the solution under Gaussian noise. However, in this case a closer inspection reveals a second layer of peaks, beneath the largest peaks, that is exclusive to multiplicative noise and that can be observed by sampling the solution on the lattice. Finally, we compute the macroscopic Hausdorff and Minkowski dimensions of the intermittency islands of the solution. Under both additive and multiplicative noise, if it is not too heavy-tailed, the largest peaks will be self-similar in terms of their large-scale multifractal behavior. But under multiplicative noise, this type of self-similarity is not present in the peaks observed on the lattice.

EUV/VUV Spectroscopy for the Study of Carbon Impurity Transport in Hydrogen and Deuterium Plasmas in the Edge Stochastic Magnetic Field Layer of Large Helical Device

The ergodic layer in the Large Helical Device (LHD) consists of stochastic magnetic fields exhibiting a three-dimensional structure that is intrinsically formed by helical coils. Spectroscopic diagnostics was employed in the extreme ultraviolet (EUV) and vacuum ultraviolet (VUV) wavelength ranges to investigate emission lines of carbon impurities in both hydrogen (H) and deuterium (D) plasmas, aiming to elucidate the impact of distinct bulk ions on impurity generation and transport in the edge plasmas of the LHD. The emission intensity of carbon CIII, CIV, CV, and CVI lines is significantly higher in the D plasma compared to the H plasma, indicating a greater sputtering rate of carbon materials in the D plasma, resulting in a higher quantity of carbon impurities originating from the divertor plates. A Doppler profile measurement of the second order of CIV line emission (1548.20 × 2 Å) was attempted using a 3 m normal-incidence VUV spectrometer in the edge plasma at a horizontally elongated plasma position. The flow velocity reaches its maximum value close to the outermost region of the ergodic layer, and the observed flow direction aligns with the friction force in the parallel momentum balance. The flow velocity increases with the electron density in H plasmas, suggesting that the friction force becomes more dominant in the force balance at higher density regimes. This leads to an increase in the impurity flow, which can contribute to the impurity screening. In contrast, the flow velocity in the D plasma is smaller than that in the H plasma. The difference in flow values between D and H plasmas, when the friction force term dominates in the momentum balance, could be attributed to the mass dependence of the thermal velocity of the bulk ions.

State-space modeling for degrading systems with stochastic neural networks and dynamic Bayesian layers

To monitor the dynamic behavior of degrading systems over time, a flexible hierarchical discrete-time state-space model (SSM) is introduced that can mathematically characterize the stochastic evolution of the latent states (discrete, continuous, or hybrid) of degrading systems, dynamic measurements collected from condition monitoring sources (e.g., sensors with mixed-type outputs), and the failure process. This flexible SSM is inspired by Bayesian hierarchical modeling and recurrent neural networks without imposing prior knowledge regarding the stochastic structure of the system dynamics and its variables. The temporal behavior of degrading systems and the relationship between variables of the corresponding system dynamics are fully characterized by stochastic neural networks without having to define parametric relationships/distributions between deterministic and stochastic variables. A Bayesian filtering-based learning method is introduced to train the structure of the proposed framework with historical data. Also, the steps to utilize the proposed framework for inference and prediction of the latent states and sensor outputs are discussed. Numerical experiments are provided to demonstrate the application of the proposed framework for degradation system modeling and monitoring.

Influence of nano-sized horizontal inhomogeneities on surface profiling by means of XPS

Quantitative analysis of thin films surface is performed by means of X-ray electron spectroscopy (XPS) according to a calculation model assuming surface layers of the target to be homogeneous and parallel. However, almost every surface of an ultra-thin film is rough. A study of such surface using the plane-parallel layer model will lead to incorrect results. This work proposes to use the model of inhomogeneous stochastic nano-structured surface layer for ultra-thin film profiling. Surface stochastic nano-structured inhomogeneities are described by the normal Gauss distribution function. To determine these inhomogeneities, three parameters are specified: dispersion (spread of thicknesses by the layer), mean and maximal thickness of the surface layer. For the first time, the type of X-ray photoelectron spectrum of an inhomogeneous stochastic nano-structured surface is found that is determined by functions of photoelectron production and transmission through that surface layer. The designed model is based on the following assumptions: photoelectrons are produced in substance and travel straight-forward (Straight Line Approximation) along the surface, photoelectron flux density decreases in the layer according to the Bouguer–Lambert law, photoelectrons of different energies lose energy differently, photoelectron energy losses in bulk and on surface differ. Modeling of X-ray photoelectron spectra of an oxidized metal film is performed using different models: homogeneous plane-parallel layers, an island nano-structured surface layer and an inhomogeneous stochastic nano-structured surface layer. Ranges of applicability of plane-parallel layer models and simple periodical nano-structured island surface layer for inhomogeneous stochastic nano-structured surface profiling are determined. The model of homogeneous plane-parallel layers shows satisfactory profiling results by some values of parameters of an inhomogeneous stochastic surface layer. It is shown that the model of a simple periodically nano-structured island layer leads to inadequate results by profiling of an inhomogeneous stochastic surface. The investigation shows that for more accurate profiling of an inhomogeneous ultra-thin film, it is necessary to consider inhomogeneity of a real surface, otherwise the calculated results would not match the true profile.

Evolution, Structure, and Topology of Self-generated Turbulent Reconnection Layers

We present a 3D MHD simulation of two merging flux ropes exhibiting self-generated and self-sustaining turbulent reconnection (SGTR) that is fully 3D and fast. The exploration of SGTR is crucial for understanding the relationship between MHD turbulence and magnetic reconnection in astrophysical contexts including the solar corona. We investigate the pathway toward SGTR and apply novel tools to analyze the structure and topology of the reconnection layer. The simulation proceeds from 2.5D Sweet–Parker reconnection to 2.5D nonlinear tearing, followed by a dynamic transition to a final SGTR phase that is globally quasi-stationary. The transition phase is dominated by a kink instability of a large “cat-eye” flux rope and the proliferation of a broad stochastic layer. The reconnection layer has two general characteristic thickness scales, which correlate with the reconnection rate and differ by a factor of approximately six: an inner scale corresponding with current and vorticity densities, turbulent fluctuations, and outflow jets, and an outer scale associated with field line stochasticity. The effective thickness of the reconnection layer is the inner scale of the effective reconnection electric field produced by turbulent fluctuations, not the stochastic thickness. The dynamics within the reconnection layer are closely linked with flux rope structures that are highly topologically complicated. Explorations of the flux rope structures and distinctive intermediate regions between the inner core and stochastic separatrices (“SGTR wings”) are potentially key to understanding SGTR. The study concludes with a discussion on the apparent dualism between plasmoid-mediated and stochastic perspectives on SGTR.

Diffusion and Lyapunov timescales in the Arnold model.

In the present work, we focus on two dynamical timescales in the Arnold Hamiltonian model: the Lyapunov time and the diffusion time when the system is confined to the stochastic layer of its dominant resonance (guiding resonance). Following Chirikov's formulation, the model is revisited, and a discussion about the main assumptions behind the analytical estimates for the diffusion rate is given. On the other hand, and in line with Chirikov's ideas, theoretical estimations of the Lyapunov time are derived. Later on, three series of numerical experiments are presented for various sets of values of the model parameters, where both timescales are computed. Comparisons between the analytical estimates and the numerical determinations are provided whenever the parameters are not too large, and those cases are in fact in agreement. In particular, the case in which both parameters are equal is numerically investigated. Relationships between the diffusion time and the Lyapunov time are established, like an exponential law or a power law in the case of large values of the parameters.

Stochastic gate-based autoencoder for unsupervised hyperspectral band selection

Due to its strong feature representation ability, the deep learning (DL)-based method is preferable for the unsupervised band selection task of hyperspectral image (HSI). However, the current DL-based UBS methods have not further investigated the nonlinear relationship between spectral bands, a more robust DL model with effective loss function is desired. To solve the above problem, a novel stochastic gate-based autoencoder (SGAE) has been proposed for the UBS task. With the proposed stochastic gate layer, the desired band subset with learnable parameters can be directly obtained. For obtaining better UBS results, a nonlinear regularization term is added with the loss function to supervise the training process of SGAE. Furthermore, an early stopping criteria with a regularization term-based threshold is developed. Experimental results on four publicly available remote sensing datasets prove the effectiveness of our SGAE.

Confirmation of the Absence of Contact Between Edge Boundary Plasma and Inboard First Wall in LHD Discharges Based on Radial Profile Measurement of Hβ Line Emissions

In the Large Helical Device (LHD), a high-performance plasma has been obtained at the inwardly shifted magnetic axis position of Rax = 3.60 m in which a spatial distance between the first wall on the vacuum vessel and the outermost edge boundary of the stochastic magnetic field layer existing outside the last closed flux surface takes a minimum value of ~12 mm at the inboard side. In order to investigate contact between the edge plasma boundary and the inboard first wall, a radial profile of Hβ line emissions at 4861 Å has been measured using a Czerny-Turner visible spectrometer and a 40-channel optical fiber array. All Hβ profiles measured at different magnetic axis positions of Rax = 3.60, 3.75, and 3.90 m showed a centrally peaked profile except for a few fiber channels observing the outboard edge plasma. The Hβ emission near the inboard first wall was negligibly weak, in particular, in the case of Rax = 3.60 m, suggesting no significant contact between the edge boundary plasma and the vacuum vessel first wall. The radial Hβ profile was then analyzed in detail using the EMC3-EIRENE edge plasma simulation code. The simulation well reproduced the measured profiles, including the extremely weak Hβ emission around the inboard first wall in the Rax = 3.60 m configuration. The centrally peaked profiles are found to originate in the Hβ emissions around X-points, while hydrogen neutrals are dominantly localized near the divertor plates. These results confirm the formation of a complete open divertor configuration in the LHD discharge without significant contact with the first wall. The presence of a region with extremely short magnetic field connection lengths (Lc < 5 m) between the inboard first wall and the outermost edge boundary is a key point to eliminate the strong plasma-wall interaction because sustainment of a significant edge plasma is entirely difficult in such a low Lc region.

Role of the edge stochastic layer in density pump-out by resonant magnetic perturbations

The role of the edge stochastic layer on particle transport is addressed in DIII-D plasmas with applied resonant magnetic perturbations (RMPs) causing density pump-out (a term used to denote the density reduction at the top of the pedestal due to the applied RMPs). Using an analytical model that adds the stochastic parallel transport of electrons (Harvey et al 1981 Phys. Rev. Lett. 47 102) to the fluid equations, the ambipolar radial electric field and particle flux are calculated simultaneously. In this model the nonambipolar electron particle flux, driven by the stochastic magnetic field, is predominantly balanced by the nonambipolar perpendicular ion flux, driven by toroidal viscosity, across a narrow stochastic layer of order two percent of the plasma radius (0.98 < ψ n < 1). The model reproduces the level of density pump-out and its dependence on RMP amplitude near the separatrix for three plasma discharges for which the pedestal foot is at medium to high collisionality . The experimentally observed and numerically tested inverse density dependence of density pump-out (Hu et al 2020 Nucl. Fusion 60 076001) is accurately captured by the model: an increase in collisionality with density in the pedestal foot results in a decrease in stochastic diffusivity, and hence a decrease in the level of pump-out.

Turbulence Spreading into an Edge Stochastic Magnetic Layer Induced by Magnetic Fluctuation and Its Impact on Divertor Heat Load.

Turbulence spreading into the edge stochastic magnetic layer induced by magnetic fluctuation is observed at the sharp boundary region in the large helical device. The density fluctuation excited at the sharp boundary region with a large pressure gradient does not propagate into the boundary region due to the blocking of turbulence spreading by the large second derivative of the pressure gradient. Once the magnetic fluctuation appears at the boundary, the density fluctuation begins to penetrate the edge stochastic layer and the second derivative of the pressure gradient also decreases. The increase of density fluctuation in this layer results in the broadening and reduction of the peak divertor heat load. It is demonstrated that magnetic fluctuation plays a key role in controlling the turbulence spreading at the boundary of plasma which contributes to the reduction of divertor heat load.