Self-consistent Profiles Research Articles

Self-consistent Atmosphere Representation and Interaction in Photon Monte Carlo Simulations

We present a self-consistent representation of the atmosphere and implement the interactions of light with the atmosphere using a photon Monte Carlo approach. We compile global climate distributions based on historical data, self-consistent vertical profiles of thermodynamic quantities, spatial models of cloud variation and cover, and global distributions of four kinds of aerosols. We then implement refraction, Rayleigh scattering, molecular interactions, and Tyndall–Mie scattering to all photons emitted from astronomical sources and various background components using physics first principles. This results in emergent image properties that include: differential astrometry and elliptical point spread functions (PSFs) predicted completely to the horizon, arcminute-scale spatial-dependent photometry variations at 20 mmag for short exposures, excess background spatial variations at 0.2% due to the atmosphere, and a PSF wing due to water droplets. We use a common atmosphere representation framework to self-consistently model all phenomena by simulating individual photons. We reproduce the well-known correlations in image characteristics: correlations in altitude with absolute photometry (overall transmission) and relative photometry (spectrally dependent transmission), anticorrelations of altitude with differential astrometry (nonideal astrometric patterns) and background levels, and an anticorrelation in absolute photometry with cloud depth. However, we also find further subtle correlations including an anticorrelation of temperature with background and differential astrometry, a correlation of temperature with absolute and relative photometry, an anticorrelation of absolute photometry with humidity, a correlation of humidity with lunar background, a significant correlation of PSF wing with cloud depth, an anticorrelation of background with cloud depth, and a correlation of lunar background with cloud depth.

Parameterizing pressure–temperature profiles of exoplanet atmospheres with neural networks

Context. Atmospheric retrievals (AR) of exoplanets typically rely on a combination of a Bayesian inference technique and a forward simulator to estimate atmospheric properties from an observed spectrum. A key component in simulating spectra is the pressure–temperature (PT) profile, which describes the thermal structure of the atmosphere. Current AR pipelines commonly use ad hoc fitting functions here that limit the retrieved PT profiles to simple approximations, but still use a relatively large number of parameters. Aims. In this work, we introduce a conceptually new, data-driven parameterization scheme for physically consistent PT profiles that does not require explicit assumptions about the functional form of the PT profiles and uses fewer parameters than existing methods. Methods. Our approach consists of a latent variable model (based on a neural network) that learns a distribution over functions (PT profiles). Each profile is represented by a low-dimensional vector that can be used to condition a decoder network that maps P to T. Results. When training and evaluating our method on two publicly available datasets of self-consistent PT profiles, we find that our method achieves, on average, better fit quality than existing baseline methods, despite using fewer parameters. In an AR based on existing literature, our model (using two parameters) produces a tighter, more accurate posterior for the PT profile than the five-parameter polynomial baseline, while also speeding up the retrieval by more than a factor of three. Conclusions. By providing parametric access to physically consistent PT profiles, and by reducing the number of parameters required to describe a PT profile (thereby reducing computational cost or freeing resources for additional parameters of interest), our method can help improve AR and thus our understanding of exoplanet atmospheres and their habitability.

Magnetically driven coupling in relativistic radiation-mediated shocks

ABSTRACT The radiation drag in photon-rich environments of cosmic explosions can seed kinetic instabilities by inducing velocity spreads between relativistically streaming plasma components. Such microturbulence is likely imprinted on the breakout signals of radiation-mediated shocks. However, large-scale, transverse magnetic fields in the deceleration region of the shock transition can suppress the dominant kinetic instabilities by preventing the development of velocity separations between electron–positron pairs and a heavy ion species. We use a 1D five-fluid radiative transfer code to generate self-consistent profiles of the radiation drag force and plasma composition in the deceleration region. For increasing magnetization, our models predict rapidly growing pair multiplicities and a substantial radiative drag developing self-similarly throughout the deceleration region. We extract the critical magnetization parameter σc, determining the limiting magnetic field strength at which a three-species plasma can develop kinetic instabilities before reaching the isotropized downstream. For a relativistic, single ion plasma drifting with γu = 10 in the upstream of a relativistic radiation-mediated shock, we find the threshold σc ≈ 10−7 for the onset of microturbulence. Suppression of plasma instabilities in the case of multi-ion composition would likely require much higher values of σc. Identifying high-energy signatures of microturbulence in shock breakout signals and combining them with the magnetization limits provided in this work will allow a deeper understanding of the magnetic environment of cosmic explosions like supernovae, gamma-ray bursts, and neutron star binary mergers.

Persistent current noise in narrow Josephson junctions

Josephson junctions have broad applications in metrology, quantum information processing, and remote sensing. For these applications, the electronic noise is a limiting factor. In this work we study the thermal noise in narrow Josephson junctions using a tight-binding Hamiltonian. For a junction longer than the superconducting coherence length, several self-consistent gap profiles appear close to a phase difference $\pi$. They correspond to two stable solutions with an approximately constant phase gradient over the thin superconductor connected by a $2\pi$ phase slip, and a solitonic branch. The current noise power spectrum has pronounced peaks at the transition frequencies between the different states in each branch. We find that the noise is reduced in the gradient branches in comparison to the zero-length junction limit. In contrast, the solitonic branch exhibits an enhanced noise and a reduced current due to the pinning of the lowest excitation energy to close to zero energy.

Self-Consistent Schrödinger-Poisson Study of Electronic Properties of GaAs Quantum Well Wires with Various Cross-Sectional Shapes.

Quantum wires continue to be a subject of novel applications in the fields of electronics and optoelectronics. In this work, we revisit the problem of determining the electron states in semiconductor quantum wires in a self-consistent way. For that purpose, we numerically solve the 2D system of coupled Schrödinger and Poisson equations within the envelope function and effective mass approximations. The calculation method uses the finite-element approach. Circle, square, triangle and pentagon geometries are considered for the wire cross-sectional shape. The features of self-consistent band profiles and confined electron state spectra are discussed, in the latter case, as functions of the transverse wire size and temperature. Particular attention is paid to elucidate the origin of Friedel-like oscillations in the density of carriers at low temperatures.

A deep insight into the ion foreshock with the help of test particle two-dimensional simulations

Abstract. Two-dimensional (2D) test particle simulations based on shock profiles issued from 2D full particle-in-cell (PIC) simulations are used in order to analyze the formation processes of ions back streaming within the upstream region after interacting with a quasi-perpendicular curved shock front. Two different types of simulations have been performed based on (i) a fully consistent expansion (FCE) model, which includes all self-consistent shock profiles at different times, and (ii) a homothetic expansion (HE) model in which shock profiles are fixed at certain times and artificially expanded in space. The comparison of both configurations allows one to analyze the impact of the front nonstationarity on the back-streaming population. Moreover, the role of the space charge electric field El is analyzed by either including or canceling the El component in the simulations. A detailed comparison of these last two different configurations allows one to show that this El component plays a key role in the ion reflection process within the whole quasi-perpendicular propagation range. Simulations provide evidence that the different field-aligned beam (FAB) and gyro-phase bunched (GPB) populations observed in situ are essentially formed by a Et×B drift in the velocity space involving the convective electric field Et. Simultaneously, the study emphasizes (i) the essential action of the magnetic field component on the GPB population (i.e., mirror reflection) and (ii) the leading role of the convective field Et in the FAB energy gain. In addition, the electrostatic field component El is essential for reflecting ions at high θBn angles and, in particular, at the edge of the ion foreshock around 70∘. Moreover, the HE model shows that the rate BI% of back-streaming ions is strongly dependent on the shock front profile, which varies because of the shock front nonstationarity. In particular, reflected ions appear to escape periodically from the shock front as bursts with an occurrence time period associated to the self-reformation of the shock front.

Validation of the BEAMS3D neutral beam deposition model on Wendelstein 7-X

The neutral beam deposition model in the BEAMS3D code is validated against neutral beam attenuation data from Wendelstein 7-X (W7-X). A set of experimental discharges where the neutral beam injection system of W7-X was utilized were reconstructed. These discharges scanned the magnetic configurations and plasma densities of W7-X. The equilibrium reconstructions were performed using STELLOPT which calculates three-dimensional self-consistent ideal magnetohydrodynamic equilibria and kinetic profiles. These reconstructions leveraged new capabilities to incorporate electron cyclotron emission and x-ray imaging diagnostics in the STELLOPT code. The reconstructed equilibria and profiles served as inputs for BEAMS3D calculations of neutral beam deposition in W7-X. It is found that if reconstructed kinetic profiles are utilized, good agreement between measured and simulated beam attenuation is found. As deposition models provide initial conditions for fast-ion slowing down calculations, this work provides a first step towards validating our ability to predict fast ion confinement in stellarators.

Influence of Oxygen Ions on the Structure of the Thin Current Sheet in the Earth’s Magnetotail

During geomagnetic substorms, the current sheet in the Earth’s magnetotail can transversely reduce in thickness from a few radii of the Earth (RE) to one to several proton gyroradii, 250–2000 km. It is the key structure in which the energy of the magnetic field is stored and later released due to the development of instability and magnetic reconnection during the substorm period. Despite its small thickness, the thin current sheet has a complex multiscale structure with a hierarchy of embedded layers that determines its properties. During substorms, single-charged oxygen ions enter the Earth’s magnetotail from the ionosphere and their concentrations can be comparable to those of protons. The interaction of oxygen ions with the current sheet, which results in changes in its structure and properties, is not well studied. The self-consistent profiles of the magnetic field, current densities, and plasma in the multicomponent magnetotail plasma are analyzed in a wide range of system parameters within the hybrid model of the quasi-equilibrium current sheet. It is shown that the current sheet is a multiscale structure embedded in a wide plasma layer. The increase in the concentration of oxygen ions in the current sheet leads to its thickening and formation of additional embedded scale. At the same time, breaks characterizing the transition from the oxygen-ion dominated region in the current sheet to the proton- and electron-dominated region appear on the profiles of the magnetic field and current density. The amplitude of the current density of such an embedded layer decreases in proportion to the concentration of oxygen ions. The dependence of the embedding parameter on relative concentrations of heavy ions, as well as their thermal and drift velocities, is studied.

Stellar Activity Effects on Moist Habitable Terrestrial Atmospheres around M Dwarfs

Abstract Transit spectroscopy of terrestrial planets around nearby M dwarfs will be a primary goal of space missions in coming decades. Three-dimensional climate modeling has shown that slow-synchronous rotating terrestrial planets may develop thick clouds at the substellar point, increasing the albedo. For M dwarfs with T eff > 3000 K, such planets at the inner habitable zone (IHZ) have been shown to retain moist greenhouse conditions, with enhanced stratospheric water vapor (fH 2O > 10−3) and low Earth-like surface temperatures. However, M dwarfs also possess strong UV activity, which may effectively photolyze stratospheric H2O. Prior modeling efforts have not included the impact of high stellar UV activity on the H2O. Here, we employ a 1D photochemical model with varied stellar UV, to assess whether H2O destruction driven by high stellar UV would affect its detectability in transmission spectroscopy. Temperature and water vapor profiles are taken from published 3D climate model simulations for an IHZ Earth-sized planet around a 3300 K M dwarf with an N2–H2O atmosphere; they serve as self-consistent input profiles for the 1D model. We explore additional chemical complexity within the 1D model by introducing other species into the atmosphere. We find that as long as the atmosphere is well-mixed up to 1 mbar, UV activity appears to not impact detectability of H2O in the transmission spectrum. The strongest H2O features occur in the James Webb Space Telescope MIRI instrument wavelength range and are comparable to the estimated systematic noise floor of ∼50 ppm.

Dynamics of plasma confinement during ECR heating in the L-2M stellarator

Dynamics of plasma confinement was considered in the experiments on ECR plasma heating in the L-2M stellarator. It was ascertained that four stages can be distinguished in the process of plasma heating and further cooling. In each stage, plasma confinement has its own distinctive features. In the first stage, plasma confinement is determined by radiation loss. In the second stage, the self-consistent profiles of electron temperature and density form in plasma and the quasi-stationary confinement mode ensues. After ECRH switching off, the third stage begins. The plasma starts cooling and its parameters change in accordance with the scaling of the L-2M stellarator, the self-consistent electron temperature and density profiles being maintained. After the plasma periphery becomes cooled, the fourth stage of plasma confinement starts, and radiation loss becomes a determinative factor again.

Development of a systematic, self-consistent algorithm for the K-DEMO steady-state operation scenario

An optimum plasma pressure/current density profile and corresponding heating/current drive (H/CD) determination scheme is newly developed by integrating equilibrium, stability, confinement, and H/CD, self-consistently subject to maximize the fusion gain for Korean fusion demonstration reactor (K-DEMO) steady-state operation scenarios. The integrated plasma modeling package, FASTRAN/IPS, is adopted for the integrated numerical apparatus. The target pressure profile with a pedestal structure is investigated by varying its peaking, pedestal height and width as a first step. Formation of stable equilibria is evaluated by solving the Grad–Shafranov equation and checking linear MHD stability. For the case of potentially stable equilibrium, required external heating distribution is calculated by considering both power balance and external current drive alignment to reproduce the pressure profile of the stable equilibrium. Electron/ion temperature and poloidal flux evolutions are solved with the derived heating configuration to find a steady-state scenario and achieve self-consistent plasma profiles. A self-consistent target steady-state pressure and current profile parameters are proposed through designed systematic algorithm with fusion power PF = 2070 MW, fusion gain Q = 19.7, and normalized beta βN = 2.8 at toroidal field BT = 7.4 T and plasma current IP = 15.5 MA. Feasibility of fusion power PF = 3000 MW operation is also explored with enhanced density and temperature limit assumption.

Theoretical prediction of Reynolds stresses and velocity profiles for barotropic turbulent jets

It is extremely uncommon to be able to predict the velocity profile of a turbulent flow. In two-dimensional flows, atmosphere dynamics, and plasma physics, large-scale coherent jets are created through inverse energy transfers from small scales to the largest scales of the flow. We prove that in the limits of vanishing energy injection, vanishing friction, and small-scale forcing, the velocity profile of a jet obeys an equation independently of the details of the forcing. We find another general relation for the maximal curvature of a jet and we give strong arguments to support the existence of a hydrodynamic instability at the point with minimal jet velocity. Those results are the first computations of Reynolds stresses and self-consistent velocity profiles from the turbulent dynamics, and the first consistent analytic theory of zonal jets in barotropic turbulence.

Transport properties of a hollow pressure filament in a magnetized plasma

A theoretical and numerical modeling study is made of a novel heating configuration recently implemented in the Large Plasma Device at the University of California, Los Angeles. The injection of an electron beam from a masked LaB6 cathode into a magnetized plasma results in a hollow, cylindrical filament of elevated temperature. The hot cylindrical ring has an axial extent that is about one-thousand times larger than its thickness, and the peak temperature can be ten times larger than that of the surrounding plasma. The simultaneous positive and negative radial pressure gradients provide an ideal platform for the investigation of transport phenomena of contemporary interest, including avalanches [Van Compernolle et al., Phys. Rev. E 91, 031102 (2015)] and nonlocal transport. The present study delineates both the parameter regimes achievable by classical transport and the linear stability of the self-consistent profiles, including temperature and density gradients. An avalanche model is developed based on the self-consistent evolution of drift-wave eigenfunctions in nonlinearly modified profiles of electron temperature and plasma density.

Formation of self-consistent pressure profiles in simulation of turbulent convection in tokamak plasmas

The formation of pressure profiles in turbulent tokamak plasmas in ohmic heating regimes and transient regimes induced by turning-on of electron-cyclotron resonance (ECR) heating is investigated. The study is based on self-consistent modeling of low-frequency turbulent plasma convection described by an adiabatically reduced set of hydrodynamic-type equations. The simulations show that, in the ohmic heating stage, turbulence forms and maintains profiles of the total plasma pressure corresponding to turbulentrelaxed states. These profiles are close to self-consistent profiles of the total plasma pressure experimentally observed on the T-10 tokamak in ohmic regimes with different values of the safety factor qL at the limiter. Simulations of nonstationary regimes induced by turning-on of on- and off-axis ECR heating show that the total plasma pressure profiles in the transient regimes remain close to those in the turbulent-relaxed state, as well as to the profiles experimentally observed on T-10.

Thermodynamic approach to the interpretation of self-consistent pressure profiles in a tokamak

The phenomenon of invariable pressure profiles in tokamaks is interpreted in the framework of the thermodynamic approach suggesting that invariable self-consistent states correspond to the minimum of free energy. Solutions qualitatively consistent with the experiment are obtained under the assumption that the mechanism for the formation of self-consistent profiles is directly related to equilibrium diamagnetic currents. The dynamics of the system and specific transport phenomena, such as energy and particle pinching and a decrease in the local density under auxiliary electron cyclotron resonance heating (density pump-out), are analyzed in the vicinity of an equilibrium state characterized by a stable pressure profile. The scaling for the energy confinement time deduced from the transport model agrees qualitatively with the ITER scaling based on the analysis of experimental data obtained in many tokamaks. The possibility of using generalized Tsallis statistics to analyze pressure profiles is considered.

Prediction of the dependence of the line tension on the composition of linactants and the temperature in phase separated membranes.

We calculate the line tension between domains in phase separated, ternary membranes that comprise line active molecules (linactants) that tend to increase the compatibility of the two phase separating species. The predicted line tension, which depends explicitly on the linactant composition and temperature, is shown to decrease significantly as the fraction of linactants in the membrane increases toward a Lifshitz point, above which the membrane phase separates into a modulated phase. We predict regimes of zero line tension at temperatures close to the mixing transition and clarify the two different ways in which the line tension can be reduced: (1) The linactants uniformly distribute in the system and reduce the compositional mismatch between the two bulk domains. (2) The linactants accumulate at the interface with a preferred orientation. Both of these mechanisms have been observed in recent experiments and simulations. The second one is unique to line active molecules, and our work shows that it is increasingly important at large fraction of linactants and is necessary for the emergence of a regime of zero line tension. The methodology is based on the ternary mixture model proposed by Palmieri and Safran [Palmieri, B.; Safran, S. A. Langmuir 2013, 29, 5246], and the line tension is calculated via variationally derived, self-consistent profiles for the local variation of composition and linactant orientation in the interface region.

Integrated modeling of H-mode tokamak discharges with ASTRA and B2SOLPS numerical codes

The numerical codes ASTRA and B2SOLPS5.2 are coupled to perform an integrated modeling of particle and energy transport and to obtain continuous self-consistent profiles of the main plasma parameters from the magnetic axis up to target plates. The unique distinguishing feature of the new coupling scheme is the presence of a region of overlap of the 1D and 2D computational domains, where the 1D solution coincides with the 2D one at the equatorial midplane. In the 2D transport equation system, all relevant drift flows and currents are taken into account, which allows us to calculate the poloidal variation of the density, temperatures and electrostatic potential, and obtain neoclassical radial fluxes in a self-consistent manner. Such an approach allows us to model tokamaks for which neoclassical effects give a significant contribution to the ion heat transport, and in particular, spherical tokamaks.

Reconciling lattice and continuum models for polymers at interfaces

It is well known that lattice and continuum descriptions for polymers at interfaces are, in principle, equivalent. In order to compare the two models quantitatively, one needs a relation between the inverse extrapolation length c as used in continuum theories and the lattice adsorption parameter Δχ(s) (defined with respect to the critical point). So far, this has been done only for ideal chains with zero segment volume in extremely dilute solutions. The relation Δχ(s)(c) is obtained by matching the boundary conditions in the two models. For depletion (positive c and Δχ(s)) the result is very simple: Δχ(s) = ln(1 + c/5). For adsorption (negative c and Δχ(s)) the ideal-chain treatment leads to an unrealistic divergence for strong adsorption: c decreases without bounds and the train volume fraction exceeds unity. This due to the fact that for ideal chains the volume filling cannot be accounted for. We extend the treatment to real chains with finite segment volume at finite concentrations, for both good and theta solvents. For depletion the volume filling is not important and the ideal-chain result Δχ(s) = ln(1 + c/5) is generally valid also for non-ideal chains, at any concentration, chain length, or solvency. Depletion profiles can be accurately described in terms of two length scales: ρ = tanh(2)[(z + p)/δ], where the depletion thickness (distal length) δ is a known function of chain length and polymer concentration, and the proximal length p is a known function of c (or Δχ(s)) and δ. For strong repulsion p = 1/c (then the proximal length equals the extrapolation length), for weaker repulsion p depends also on chain length and polymer concentration (then p is smaller than 1/c). In very dilute solutions we find quantitative agreement with previous analytical results for ideal chains, for any chain length, down to oligomers. In more concentrated solutions there is excellent agreement with numerical self-consistent depletion profiles, for both weak and strong repulsion, for any chain length, and for any solvency. For adsorption the volume filling dominates. As a result c now reaches a lower limit c ≈ -0.5 (depending slightly on solvency). This limit follows immediately from the condition of a fully occupied train layer. Comparison with numerical SCF calculations corroborates that our analytical result is a good approximation. We suggest some simple methods to determine the interaction parameter (either c or Δχ(s)) from experiments. The relation Δχ(s)(c) provides a quantitative connection between continuum and lattice theories, and enables the use of analytical continuum results to describe the adsorption (and stretching) of lattice chains of any chain length. For example, a fully analytical treatment of mechanical desorption of a polymer chain (including the temperature dependence and the phase transitions) is now feasible.

Plasma size scaling of avalanche-like heat transport in tokamaks

The influence of plasma size on global ion temperature gradient turbulence is studied with the full-f Eulerian code GT5D (Idomura et al 2009 Nucl. Fusion 49 065029). The gyrokinetic model includes a consistent neoclassical electric field as well as a fixed-power source operator, enabling long-time simulations with self-consistent turbulent transport and equilibrium profiles. The effects of plasma size (from ρ* = 1/100 to ρ* = 1/225) are studied by scaling the minor radius a and the input power. For the first time, worse-than-Bohm scaling is observed under experimentally realistic conditions. For all plasma sizes, avalanches propagate over significant radii but their propagation depends on the radial electric shear. It is found that this quantity does not scale with ρ* due to the building up of intrinsic momentum. Such a dependence can be inferred from a force balance relation, which remains approximately valid in nonlinear simulations. An adaptive parallel momentum source has been implemented in GT5D to damp the parallel momentum profile. The new scan then reveals that the radial electric shear scales with ρ* while the transport is globally higher. These simulations therefore suggest that intrinsic momentum reduces heat transport. This work also addresses another important issue in gyrokinetics: it is shown that for fixed initial physical parameters the turbulent quasi-steady-state is statistically independent of the initial conditions.

Self-consistent microscopic calculations for nonlocal transport through nanoscale superconductors

We implement self-consistent microscopic calculations in order to describe out-of-equilibrium nonlocal transport in normal-metal-superconductor-normal-metal hybrid structures in the presence of a magnetic field and for arbitrary interface transparencies. A four-terminal setup simulating usual experimental situations is described by means of a tight-binding model. We present results for the self-consistent order-parameter and current profiles within the sample. These profiles illustrate a crossover from a quasiequilibrium to a strong nonequilibrium situation when increasing the interface transparencies and the applied voltages. We analyze in detail the behavior of the nonlocal conductance in these two different regimes. While in quasiequilibrium conditions this can be expressed as the difference between elastic cotunneling and crossed Andreev transmission coefficients, in a general situation additional contributions due to the voltage dependence of the self-consistent order parameter have to be taken into account. The present results provide a first step toward a self-consistent theory of nonlocal transport including nonequilibrium effects and describe qualitatively a recent experiment [P. Cadden-Zimansky and V. Chandrasekhar, Phys. Rev. Lett. 97, 237003 (2006)].