Search NASA⌕ Search

SEARCH · Search NASA

Results for “test particle simulations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

ArCS: A Magnetized LArTPC in a Test Beam

Over the past few decades, Liquid Argon Time Projection Chambers (LArTPCs) have emerged as a central technology for rare-event detection, due to their calorimetric and imaging capabilities. Adding a magnetic field to LArTPCs would enable charge identification and momentum measurements via curvature. For neutrino experiments, this is crucial for wrong-sign neutrino rejection, electron/positron and electron/photon discrimination, and improved momentum reconstruction. The ArCS (Argon detector with Charge Separation) experiment at Fermilab's Test Beam Facility will place a 47 40 90 cm LArTPC inside a 0.7 T magnet to: (i) establish charge sign discrimination for electrons and positrons, (ii) reconstruct particle momenta via curvature, and (iii) determine the minimal magnetic field needed for these measurements. This poster will present the project status, with updates on installation and simulations of expected performance.

Cicogna, Giulia [Bologna U.]↗

symfind : Addressing the Fragility of Subhalo Finders and Revealing the Durability of Subhalos

Abstract A major question in ΛCDM is what this theory actually predicts for the properties of subhalo populations. Subhalos are difficult to accurately simulate and to find within simulations, and this propagates into uncertainty in theoretical predictions for satellite galaxies. We present Symfind , a new particle-tracking-based subhalo finder, and demonstrate that it can track subhalos to orders-of-magnitude lower masses than commonly used halo-finding tools, with a focus on Rockstar and consistent-trees . These longer survival times mean that at a fixed peak subhalo mass, we find ≈ 15%–40% more subhalos within the virial radius, R vir , and ≈35%–120% more subhalos within R vir /4 in the Symphony dark-matter-only simulation suite. More subhalos are found as the resolution is increased, in contrast to the Rockstar halo finder, which appears to be converged at smaller subhalo counts. We perform extensive numerical testing. In agreement with idealized simulations, we show that the v max , the maximum circular velocity, is systematically biased low until high resolutions ( n peak ≳ 3 × 10 4 ) are achieved, but that mass loss itself can be resolved at much more modest resolutions ( n peak ≳ 4 × 10 3 ). We show that Rockstar converges to false solutions for the mass function, radial distribution, and disruption masses of subhalos. We argue that our new method can trace resolved subhalos until the point of typical galaxy disruption without invoking post hoc orphan modeling. We outline a concrete set of steps for determining whether other subhalo finders meet the same criteria. We publicly release Symfind catalogs and particle data for the Symphony simulation suite at http://web.stanford.edu/group/gfc/symphony .

79 ASTRONOMY AND ASTROPHYSICS↗

Neural network model of neutral beam injection in the EAST tokamak to enable fast transport simulations

The neutral beam injection (NBI) system in EAST produces energetic neutral particles, which collide with electrons and ions in tokamak plasmas and heat the plasmas through Coulomb collisions. Moreover, it drives a non-inductive source of current, due to the charge-exchange collision between neutral particles and ions, and injects toroidal torque, which generates a toroidal rotation of the plasma. The effect caused by the NBI system, such as plasma heating, current drive, total neutron rate, momentum transfer, and shine-through, are modeled by a comprehensive module called NUBEAM. However, NUBEAM is computationally intensive since it relies on Monte Carlo methods. In this work, a neural network model has been developed as a surrogate model for NUBEAM in EAST. The database for neural-network model training, validation and testing is generated by running TRANSP for experimental discharges from recent EAST campaigns (after the latest NBI upgrade) while using the NUBEAM module. Simulation results illustrate that the trained neural network has the capability of replicating the predictions made by NUBEAM while demanding a significantly shorter execution time. Finally, these results indicate that surrogate models like the one proposed in this work could enable fast transport simulations for EAST after integrating them into a control-oriented predictive code such as COTSIM.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The potential role of organics in new particle formation and initial growth in the remote tropical upper troposphere

Abstract. Global observations and model studies indicate that new particle formation (NPF) in the upper troposphere (UT) and subsequent particles supply 40 %–60 % of cloud condensation nuclei (CCN) in the lower troposphere, thus affecting the Earth's radiative budget. There are several plausible nucleation mechanisms and precursor species in this atmospheric region, which, in the absence of observational constraints, lead to uncertainties in modeled aerosols. In particular, the type of nucleation mechanism and concentrations of nucleation precursors, in part, determine the spatial distribution of new particles and resulting spatial distribution of CCN from this source. Although substantial advances in understanding NPF have been made in recent years, NPF processes in the UT in pristine marine regions are still poorly understood and are inadequately represented in global models. Here, we evaluate commonly used and state-of-the-art NPF schemes in a Lagrangian box model to assess which schemes and precursor concentrations best reproduce detailed in situ observations. Using measurements of aerosol size distributions (0.003 < Dp < 4.8 µm) in the remote marine troposphere between ∼0.18 and 13 km altitude obtained during the NASA Atmospheric Tomography (ATom) mission, we show that high concentrations of newly formed particles in the tropical UT over both the Atlantic and Pacific oceans are associated with outflow regions of deep convective clouds. We focus analysis on observations over the remote Pacific Ocean, which is a region less perturbed by continental emissions than the Atlantic. Comparing aerosol size distribution measurements over the remote Pacific with box model simulations for 32 cases shows that none of the NPF schemes most commonly used in global models, including binary nucleation of sulfuric acid and water (neutral and ion-assisted) and ternary involving sulfuric acid, water, and ammonia, are consistent with observations, regardless of precursor concentrations. Through sensitivity studies, we find that the nucleation scheme among those tested that is able to explain most consistently (21 of 32 cases) the observed size distributions is that of Riccobono et al. (2014), which involves both organic species and sulfuric acid. The method of Dunne et al. (2016), involving charged sulfuric acid–water–ammonia nucleation, when coupled with organic growth of the nucleated particles, was most consistent with the observations for 5 of 32 cases. Similarly, the neutral sulfuric acid–water–ammonia method of Napari (2002), when scaled with a tuning factor and with organic growth added, was most consistent for 6 of 32 cases. We find that to best reproduce both nucleation and growth rates, the mixing ratios of gas-phase organic precursors generally need to be at least twice that of SO2, a proxy for dimethyl sulfide (DMS). Unfortunately, we have no information on the nature of oxidized organic species that participated in NPF in this region. Global models rarely include organic-driven nucleation and growth pathways in UT conditions where globally significant NPF takes place, which may result in poor estimates of NPF and CCN abundance and contribute to uncertainties in aerosol–cloud–radiation effects. Furthermore, our results indicate that the organic aerosol precursor vapors may be important in the tropical UT above marine regions, a finding that should guide future observational efforts.

54 ENVIRONMENTAL SCIENCES↗

The Effect of Pressure on NO x Entitlement and Reaction Timescales in a Premixed Axial Jet-In-Crossflow

This paper investigates the pressure dependency of a lean premixed jet injected into a lean vitiated crossflow with an experimentally verified detailed chemistry computational fluid dynamics (CFD) model and 53 species considered. Experimental data were taken in an axially staged combustor with an optically accessible test section, allowing the use of particle image velocimetry (PIV) and CH* chemiluminescence techniques as well as point measurement of species concentration, temperature, and pressure. The experimental data cases at one, three, and five atmospheres were selected to describe the flame stabilization dependency on pressure and gain the required knowledge for an extrapolation to engine condition. Simulated exit nitrogen oxide levels were validated with experimental emission data, and a global emission trend for the NO reduction at elevated pressure and constant turbine inlet temperature level was defined. The nitrogen oxide benefit at elevated operating pressure was justified with the significantly smaller flame surface area: the analysis of the simulated spanwise and top-view profiles showed a relatively short receded core flame with nitrogen oxide production in the center at high pressure relative to a longer and larger shear layer flame at atmospheric condition that produced NO toward the inner and outer side of the flame. Furthermore, decomposition of the Damköhler number revealed the strong influence of the reaction timescales with higher reaction rates at elevated pressure, along with a moderate influence of the turbulent timescales, showing higher turbulence intensity in the lee-side recirculation zone at lower pressure.

03 NATURAL GAS↗

Final Technical Report for the SciDAC Center for the Study of Plasma Microturbulence

This final technical report for the SciDAC Center for the Study of Plasma Microturbulence documents contributions from MIT to the project over the period of the award (February 15, 2011 to February 14, 2020). This project focused on the development of neoclassical and gyrokinetic simulation capabilities relevant for the description of particle, momentum and energy transport in tokamak fusion plasmas. Extensive validation against experimental results from Alcator C-Mod and DIII-D experiments was performed. Overall areas of emphasis included gyrokinetic simulations, experiments, and observation of density gradient driven Trapped Electron Mode (TEM) turbulence relevant to burning plasmas; theory and gyrokinetic simulations of the parametric variation of the nonlinear upshift of the TEM critical density gradient; identification of a new mechanism for the isotope effect due to density gradient driven TEM turbulence; new synthetic diagnostics based on full-wave simulations which enabled unprecedented agreement between gyrokinetic simulations and measured fluctuation spectra with and without strong electron heating; development of new continuum pedestal neoclassical and turbulence codes; formulation and implementation of the first gyrokinetic exact Fokker-Planck collision operator in gyrokinetic turbulence simulations; development of new spectral approaches in velocity space for highly efficient treatments of collisions; new model collision operators implemented in the discontinuous Galerkin gyrokinetic edge turbulence code GKEYLL; and a new model and spectral code to study the interaction of ion- and electron-scale turbulence, which will serve as an efficient test-bed for multi-rate and multi-scale methods. These fundamental advances contribute to the development of a validated, predictive capability for turbulent and collisional particle, momentum and energy transport in both the core and edge of magnetically confined fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Viscous Gubser flow with conserved charges to benchmark fluid simulations

We present semi-analytical solutions for the evolution of both the temperature and chemical potentials for viscous Gubser flow with conserved charges. Such a solution can be especially useful in testing numerical codes intended to simulate relativistic fluids with large chemical potentials. The freeze-out hypersurface profiles for constant energy density are calculated, along with the corresponding normal vectors, and presented as a new unit test for numerical codes. We also compare the influence of the equation of state on the semi-analytical solutions. We benchmark the newly developed smoothed particle hydrodynamics code ccake that includes both shear viscosity and three conserved charges. Here, the numerical solutions are in excellent agreement with the semi-analytical solution and are also able to accurately reproduce the hypersurface at freeze-out.

Hydrodynamic models↗

Cherenkov and Transition Radiation as Low-Energy Background Sources in SuperCDMS Detectors

The Weakly Interacting Massive Particle (WIMP) has historically been a prime candidate for dark matter due to its elegant compatibility with the Minimally Supersymmetric Standard Model (MSSM). Recent dark matter experiments have ruled out much of the GeV-TeV mass range predicted by the MSSM, however, and the newest generation of direct detection experiments, such as SuperCDMS SNOLAB, have begunto explore sub-GeV dark matter. As experiments push towards lower masses, sensitivity to eV-scale electron recoil events has become increasingly important. A variety of unexplained excesses at energy deposits of 1-100 eV have been found inmany such low-mass experiments, across different detection techniques and at different excess rates. These low-energy events are not thought to be dark matter, and they must be understood and effectively removed to further improve detector energy resolution. This thesis will outline the simulation of one possible source of low-energy excess at SuperCDMS: optical photons produced from charges in uniform motion, specifically from Cherenkov radiation (CR), transition radiation (TR), and the intermediate hybrid transition-Cherenkov radiation (HR). In the latter case, the standard formulae for HR contain divergences at certain angles in transparent media, which are an artifact of their derivation and become problematic to simulate. To rsolve this, we present a novel approach to normalize the divergent HR peaks, which allows HR to transition smoothly between TR and CR in a numerical simulation. We also add TR and CR as a physics process to the SuperCDMS Monte Carlo simulation package SuperSim, based on the Geant4 simulation toolkit. To verify the physics of our addition, we show some test simulations in comparison to theoretical predictions of optical radiation intensity. We also use the simulation to make some preliminary predictions on the contribution of TR and CR to the low energy background, with the expectation that more thorough analyses will be conducted in the future.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A multi-dimensional dataset for two-phase instability in low pressure natural circulation based on direct transient local measurement

Thermal hydraulic instability can challenge the control and the safety of nuclear reactors. This experimental research captures and investigates the instability in a low-pressure (1–10 atmospheres) natural circulation loop with an adiabatic chimney installed above the heated section. Direct transient local measurement of two-phase flow is performed at multiple axial locations along the flow channel with thermocouples and conductivity probes traversed by customized high-precision mechanisms. Based on the periodicity of oscillations, a post-processing method is proposed to align the data captured non-simultaneously to reconstruct the instability behavior in one representative period. The averaging operation over multiple oscillation cycles is performed to reduce the random errors. Cyclic phenomena are clearly demonstrated by the post-processed data, and rapid void fraction change induced by the flashing is observed to be significant in the driving mechanism for low pressure oscillations. Parametric effects of inlet subcooling, heat flux, inlet flow restriction and system pressure are studied within the experiment range, and qualitative results are explained and compared with existing literature. The ratio between the oscillation period and the travelling time of the fluid particle through the test section is compared with the theoretical value for the density wave oscillation. The new dataset contains directly measured transient multi-dimensional two-phase data along the flow channel for natural circulation under density wave oscillations. The generated dataset is valuable for the validation of system analysis codes and CFD codes in the simulation of natural circulation phenomena and dynamic two-phase flow.

42 ENGINEERING↗

Reconstruction of Six-Dimensional Phase Space

A phase space is a mathematical representation of all possible physical states of a system. Particle beams at Fermilab exist within a six-dimensional (6D) phase space defined by three positional components, (x, y, z) and three momentum components, (px, py, pz). To reconstruct this space implies taking measurement data from detectors and mapping out particle behavior using computational methods. The beam detectors, however, are only able to detect spatial distribution among the events of the beam, therefore being limited to positional data. Also, due to the vast number of events in a particle beam, it is extremely difficult to analyze and differentiate every single one’s behavior. However, with Machine Learning (ML), which can distinguish between patterns and map out particle behavior more efficiently. We first used the particle beam software, G4beamline, to simulate a 10,000-event muon beam, adjusting parameters such as initial momentum magnitude (p¬0) and virtual detector position. Using ten virtual detectors, we analyzed p0 values such that minimum 9,990 events were analyzed by every detector. We then input the data from these beam simulations to a C++ program, that randomly selects 100 events, and creates a 2D histogram based on spatial distribution, detector position, and event intensity. This process is repeated 100 times to create 100 histograms per p0 value. These images were then input to a modified ResNet18 Convolutional Neural Network (CNN) for training, and to predict p0 from some unseen set of histograms. The model was accurate when trained on momentum increments of 5 MeV/c and provided with denser training samples around highly variable test values. These results displayed machine learning being able to accurately predict p0 from being trained on different particle behaviors.

Shirlee, Jermain [Fermilab]↗

Mitigating municipal solid waste fouling in biofuel conversion via screw surface modifications

Here, municipal solid waste (MSW)'s 40–60 % carbon content makes it a feedstock for biofuel production via pyrolysis. One challenge in the conversion process is MSW fouling due to thermal decomposition. The accumulated deposit on the injection screw often leads to plugging and constriction. This study examined the morphology and composition of the MSW fouling deposit and conducted a thermal simulation to understand the temperature gradience of the injection screw. Surface modifications including smoothening and anti-adhesion coating were proposed for the injection screw to address the deposit problem. For evaluating the candidate mitigations, a bench-scale fouling test was developed with the gas environment, temperature, and sliding speed relevant to the contact interface between the MSW particles and the screw. Results suggested that a smoother screw surface could reduce the grip and a non-metallic coating with a lower surface energy could decrease adhesion, consequently leading to less fouling. Specifically, reducing the roughness from 2 to 0.6 and then to 0.2 μm proportionally decreased the amount of deposit, and the diamond-like-carbon, CrN, and NiCr–CrC composite coatings effectively hindered the fouling process. This study provides fundamental insights into the MSW fouling and proof-of-concept of potential mitigations through the screw surface modification.

09 BIOMASS FUELS↗

Machine learning surrogates for ion energy–angle distributions in thermal and RF plasma sheaths

Ion energy–angle distributions (IEADs) at material surfaces are a critical input for plasma–material interaction (PMI) studies in fusion devices, yet they are computationally expensive to obtain using particle-in-cell (PIC) simulations. In this work, we develop a machine learning surrogate based on a deep deconvolutional neural network (DDeCNN) trained on large databases generated with the hPIC2 code. The surrogate is capable of reconstructing IEADs from sheath parameters for both thermal and radio-frequency (RF) plasmas, including cases with multiple ion species. Across thousands of test cases, the model achieves high accuracy, with over 97 % of predictions classified as good or average based on standard error metrics (MAE, MSE, L2). Even in the more challenging RF and multi-species regimes, the surrogate reliably captures the multi-peak structure of PIC results. Once trained, the surrogate produces IEADs in milliseconds on a common workstation, yielding speedups of six to seven orders of magnitude compared with running a full PIC simulation. This computational gain enables dense parameter scans and direct coupling of IEAD predictions with PMI and erosion models on whole-device scales in fusion-relevant conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Deconvoluting experimental decay energy spectra: The O 26 case

In nuclear reaction experiments, the measured decay energy spectra can give insights into the shell structure of decaying systems. However, extracting the underlying physics from the measurements is challenging due to detector resolution and acceptance effects. The Richardson-Lucy (RL) algorithm, a deblurring method that is commonly used in optics and has proven to be a successful technique for restoring images, was applied to our experimental nuclear physics data. The only inputs to the method are the observed energy spectrum and the detector's response matrix also known as the transfer matrix. We demonstrate that the technique can help access information about the shell structure of particle-unbound systems from the measured decay energy spectrum that is not immediately accessible via traditional approaches such as χ-square fitting. For a similar purpose, we developed a machine learning model that uses a deep neural network (DNN) classifier to identify resonance states from the measured decay energy spectrum. We tested the performance of both methods on simulated data and experimental measurements. Then, we applied both algorithms to the decay energy spectrum of 26 O → 24 O + n + n measured via invariant mass spectroscopy. Here, the resonance states restored using the RL algorithm to deblur the measured decay energy spectrum agree with those found by the DNN classifier. Both deblurring and DNN approaches suggest that the raw decay energy spectrum of 26 O exhibits three peaks at approximately 0.15 MeV, 1.50 MeV, and 5.00 MeV, with half-widths of 0.29 MeV, 0.80 MeV, and 1.85 MeV, respectively.

Spectrometers & spectroscopic techniques↗

Design of a 10 MeV beamline at the Upgraded Injector Test Facility for e-beam irradiation

Electron beam irradiation near 10 MeV is suitable for wastewater treatment. The Upgraded Injector Test Facility (UITF) at Jefferson Lab is a CW superconducting linear accelerator capable of providing an electron beam of energy up to 10 MeV and up to 100 µA current. This contribution presents the beam transport simulations for a beamline to be used for the irradiation of wastewater samples at the UITF. The simulations were done using the code General Particle Tracer with the goal of obtaining an 8 MeV electron beam of radius (3-σ) of ~2.4 cm. The achieved energy spread is ~74.5 keV. The space charge effects were investigated when the bunch charge is varied to be up to 1000 times and the results showed that they do not affect the beam quality significantly.

Li, X.↗

Design of a 10 MeV beamline at the Upgraded Injector Test Facility for e-beam irradiation

Electron beam irradiation near 10 MeV is suitable for wastewater treatment. The Upgraded Injector Test Facility (UITF) at Jefferson Lab is a CW superconducting linear accelerator capable of providing an electron beam of energy up to 10 MeV and up to 100 µA current. This contribution presents the beam transport simulations for a beamline to be used for the irradiation of wastewater samples at the UITF. The simulations were done using the code General Particle Tracer with the goal of obtaining an 8 MeV electron beam of radius (3-σ) of ~2.4 cm. The achieved energy spread is ~74.5 keV. The space charge effects were investigated when the bunch charge is varied to be up to 1000 times and the results showed that they do not affect the beam quality significantly.

Li, X.↗

Design and Testing of the Vortex Ring Facility

This document summarizes the efforts of building an experimental test facility to study the evolution of the cloud following a nuclear detonation above ground level and support the development of numerical models to describe it. The experimental facility allows nonintrusive flow visualization and measurements of buoyant vortex ring formation and evolution using background-oriented Schlieren and particle image velocimetry techniques. In addition, 3D unsteady computational fluid dynamics simulations using unsteady Reynolds-averaged Navier–Stokes and volume-of-fluid numerical methods were performed to support the experimental design as well as to provide insight about the formation and evolution of the vortex ring.

42 ENGINEERING↗

Rapid Demonstration of Bremsstrahlung Diode Optimization

Optimization of the radiation pattern from a Bremsstrahlung target for a given application is possible by controlling the electron beam that impacts the high-atomic-number target. In this work, the electron beam is generated by a 13MV vacuum diode that terminates a coaxial magnetically insulted transmission line (MITL) on the HERMES-III machine at Sandia National Labs. Work by Sanford introduced a geometry for vacuum diodes that can control the flow within bounds. The "indented anode", as coined by Sanford, can straighten out the electron beam in a high-current diode that would otherwise be prone to beam pinching. A straighter beam will produce a more forwardly directed radiation pattern while a pinching electron beam will yield a focal point or hot spot on axis and a more diffuse radiation pattern. Either one of these may be desirable depending on the application. This work serves as a first attempt to optimize the radiation pattern in the former sense of collimating the radiation pattern given a limited parameter space. The optimization is attempted first using electromagnetic particle-in-cell simulations in the EMPIRE code suite. The setup of the models used in EMPIRE is discussed along with some basic theory behind some of the models used in the simulations such as anode heating and secondary ions. Theoretical work performed by Allen Garner and his students at Purdue is included here, which concerns the impact of collisions in these vacuum diodes. The EMPIRE simulations consider both an aggressive and a conservative design. The aggressive design is inherently riskier while the conservative design is chosen as something that, while still a risk, is more likely to perform as expected. The ultimate goal of this work was to validate the EMPIRE code results with experimental data. While the experiment that tested the diode designs proposed by the simulation results fell outside of the fiscal boundaries of this project (and for that reason the results of which are not included in this report), the hardware for the experiment was designed and drafted within those same fiscal boundaries, and is thus included in this report. However, there was yet another experiment performed in this project that tested a key feature of the diode: the hemispherical cathode. Those results are documented here as well, which show that the cathode tip is an important aspect to controlling the diode flow. A short series of simulations on this diode were also performed after the experiment in order to gain a better understanding of the effect of ions. on the flow pattern and faceplate dose profile.

43 PARTICLE ACCELERATORS↗

Characterization and controllability of radiated power via extrinsic impurity seeding in strongly negative triangularity plasmas in DIII-D

Experiments with extrinsic impurity seeding in strongly negative triangularity shapes in DIII-D achieved radiated power fractions (relative to input power) of up to ≈85% total radiation and ≈55% core radiation in steady-operating conditions. The relationship between core and total radiation was sensitive to impurity species and input power. Attempts to reach higher radiation levels via higher impurity flows resulted in radiative collapse disruptions. Nitrogen, neon, argon, and krypton were tested. Injection was by gas puffing, usually controlled by feeding back real-time estimates for core or total radiating fractions ($P_\textrm{rad} / P_\textrm{input}$). Argon and krypton were controlled by feeding back total radiating fraction, whereas neon was controlled by feeding back the core radiating fraction, due to the lower efficiency of neon as a divertor radiator. Nitrogen flows were pre-programmed. Reasonable total $P_\textrm{rad}$ control target following was achieved with argon or krypton. Control was more challenging with the neon/core radiation configuration, which was more prone to slow response and overshooting of the control target. Poor particle removal contributed to the control challenge: neon particle inventory within the last closed flux surface was roughly constant for up to 1 s (the longest duration tested) after neon injection was halted. However, separate experiments with laser-blow off of non-recycling impurities measured a short impurity confinement time, on the scale of the energy confinement time of ∼100 ms. Modeling with the Aurora impurity transport simulation matched experimental neon density profiles with full recycling (R = 1.0) and weak pumping but predicted rapid decreases in neon inventory if pumping were increased or recycling decreased. This indicates that changes outside the confined plasma (adding a well-placed pump) would improve controllability for all highly recycling species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗