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At least 415 records · Page 23

High Energy Density Physics of Inertial Confinement Fusion Ablator Materials

The historic December 5, 2022 experiment at Lawrence Livermore National Lab’s (LLNL) National Ignition Facility (NIF) reached fusion energy ignition for the first time. This is the most important scientific breakthrough of the 21st century paves the way to future clean inertial fusion energy (IFE). The diamond (high density carbon (HDC)) ablator material used in this experiment displays detrimental effects due to the development of hydrodynamic instabilities at the diamond/fuel interface under shock compression. New alternatives to diamond ablators are required to step up the energy yield in ICF experiments. The unique combination of mechanical strength (approaching that of diamond), the ability to accommodate high-Z dopants (in contrast to diamond), and the tunability of the properties (through synthesis material with varying sp 3 content) make amorphous carbon (a-C) a promising material for next-generation IFE ablative capsules. However, despite its critical importance to the IFE program, the behavior of a-C carbon at extreme temperatures and pressures remains largely unexplored. The primary goals of this project were to perform groundbreaking dynamic compression experiments and predictive simulations to uncover the fundamental high-energy-density physics of amorphous carbon. Our goals were (1) to uncover the metastability range of amorphous carbon and probe phase transitions to diamond or metastable supercooled liquid carbon; (2) to acquire high-quality equation of state (EOS) data and develop an experimentally validated EOS from machine-learning MD simulations of the complex states of carbon; and (3) to uncover the complex behavior of carbon liquid in both thermodynamically stable and metastable supercooled states by accessing large areas of carbon phase diagram with amorphous samples with variable sp 3 content. Our proposed experimental program included measurements of equation of state and diffraction measurements using the Omega EP laser at the Laboratory of Laser Energetics at the University of Rochester. The theoretical/simulation program involved the development of machine-learning models of the complex response of amorphous carbon under dynamic compression by performing molecular dynamics simulations at experimental time and length scales using leadership class DOE supercomputers. Simulations guided experiments to observe predicted phenomena and acquire critical experimental data in specific pressure-temperature domains to validate theoretical models. This research delivered fundamental properties of novel amorphous carbon IFE ablator material, including phase diagram and EOS. These results will aid in IFE target design and implosion experiments. A unique combination of predictive simulations and dynamic and static experiments provided a highly inspirational intellectual environment for graduate students and postdocs involved in this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement of interfacial thermal resistance in high-energy-density matter

Heat transport across interfaces is a ubiquitous phenomenon with many unresolved aspects. In particular, it is unknown if an interfacial thermal resistance (ITR) occurs in matter with high-energy-density where free electrons dominate the heat conduction. Here, we report on the first experimental evidence that a significant heat barrier is present between two different regions of high-energy-density matter: a strongly heated tungsten wire and a surrounding plastic layer that stays relatively cold. We use diffraction-enhanced imaging to track the time evolution of density discontinuities and reconstruct the temperature evolution in the quasi-stationary stage. The clear signatures of a temperature jump demonstrate the importance of the ITR for strongly heated systems with far-reaching implications for interpreting experiments and applications like inertial confinement fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma–surface interaction in the stellarator W7-X: conclusions drawn from operation with graphite plasma-facing components

W7-X completed its plasma operation in hydrogen with island divertor and inertially cooled test divertor unit (TDU) made of graphite. A substantial set of plasma-facing components (PFCs), including in particular marker target elements, were extracted from the W7-X vessel and analysed post-mortem. The analysis provided key information about underlying plasma–surface interactions (PSI) processes, namely erosion, transport, and deposition as well as fuel retention in the graphite components. The net carbon (C) erosion and deposition distribution on the horizontal target (HT) and vertical target (VT) plates were quantified and related to the plasma time in standard divertor configuration with edge transform ι = 5/5, the dominant magnetic configuration of the two operational phases (OP) with TDU. The operation resulted in integrated high net C erosion rate of 2.8 mg s -1 in OP1.2B over 4809 plasma seconds. Boronisations reduced the net erosion on the HT by about a factor 5.4 with respect to OP1.2A owing to the suppression of oxygen (O). In the case of the VT, high peak net C erosion of 11μm at the strike line was measured during OP1.2B which converts to 2.5 nm s -1 or 1.4 mg s -1 when related to the exposed area of the target plate and the operational time in standard divertor configuration. PSI modelling with ERO2.0 and WallDYN-3D is applied in an interpretative manner and reproduces the net C erosion and deposition pattern at the target plates determined by different post-mortem analysis techniques. This includes also the 13 C tracer deposition from the last experiment of OP1.2B with local 13 CH 4 injection through a magnetic island in one half module. The experimental findings are used to predict the C erosion, transport, and deposition in the next campaigns aiming in long-pulse operation up to 1800 s and utilising the actively cooled carbon-fibre composite (CFC) divertor currently being installed. The CFC divertor has the same geometrical design as the TDU and extrapolation depends mainly on the applied plasma boundary. Extrapolation from campaign averaged information obtained in OP1.2B reveals a net erosion of 7.6 g per 1800 s for a typical W7-X attached divertor plasma in hydrogen.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scaling Exponents of Turbulent Static Pressure Structure Function in the Inertial Subrange

The measured variations in the turbulent static pressure structure function D pp (r) with scale $r$ in the roughness sublayer above a subarctic forest are empirically shown to exhibit exponents that are smaller than $r$ 4/3 predicted for the inertial subrange (ISR). Three hypotheses are offered to explain these deviations. The first is based on conventional intermittency correction to the averaged turbulent kinetic energy dissipation rate, the second is based on shearing introducing deviations from locally isotropic state that must be sensed by both velocity and pressure structure functions, and the third is based on large and inertial scale pressure interactions that persist at values of $r$ within the resolvable ISR. The third hypothesis is shown to yield superior results, which allows a new formulation for D pp (r) to be derived that accommodates such finite interactions.

structure function↗

On-target uniformity of the OMEGA 60-beam inertial confinement fusion laser

Successful direct-drive inertial confinement fusion (ICF) experiments require excellent on-target laser 9 irradiance uniformity maintained over the duration of the pulse. Achieving this symmetry relies on maintaining an 10 energy, power, and fluence balance among all beams in a multibeam laser system. As a result of the improvements 11 described in this paper, the OMEGA 60-beam laser performance has been assessed at approximately 2% on-target 12 irradiance nonuniformity using an updated performance assessment metric that accounts for the laser diagnostic noise 13 floor. The performance is measurement-limited, prompting the need for an improved diagnostic suite. This manuscript 14 provides a comprehensive first-order assessment of extant status of on-target energy, power, and fluence uniformity 15 and explores avenues for improvements.

Diagnostics↗

Burn mode signatures enabled by high dynamic range fusion reaction history

The evolution of the fusion burn of a compressed inertial confinement fusion (ICF) implosion gives information about the evolution of the temperature, mass, and volume of the hot spot. Currently, the fusion reaction history has been measured with about a decade of dynamic range, giving information about just the peak of the fusion burn. There are proposals for extending the dynamic range to 1000×, measuring the rising edge of the burn earlier in time. Using fusion hot spot theory and a set of ICF simulations, we identify and categorize different stages of fusion burn and what signatures could be measured. For ice layered implosions, the details, conditions, and dynamics of the fusion burn propagation could be observed. For double shell and OMEGA scale implosions, the evolution of the final compression and rebounding shock before ignition could be observed. Higher dynamic range expands investigation into the logarithmic derivative, α, as a signature of various mechanisms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An experimentally informed design process for future inertial confinement fusion facilities

The achievement of ignition in the laboratory has renewed interest in defining the requirements for a future high-gain inertial confinement fusion (ICF) facility. Our best chance of predicting future ICF performance is with 3-D radiation hydrodynamic simulations that have been benchmarked against experimental data, but their high computational cost is prohibitive for use in practical design studies. We introduce a hierarchical approach where 3-D simulations are tuned to match experimental measurements and used to train 3-D degradation models in 1-D simulations allowing for accurate predictions over the entire OMEGA direct-drive database. A genetic algorithm was used in combination with the trained 1-D simulations to search for optimal direct-drive implosion designs at driver energies ranging from 20 kJ to 10 MJ. As the fidelity of 3-D codes improves, this approach will provide a viable experimentally informed tool for defining the next ICF facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement of Energy Reduction of Inertial Alfvén Waves Propagating through Parallel Gradients in the Alfvén Speed

We have studied the propagation of inertial Alfvén waves through parallel gradients in the Alfvén speed using the Large Plasma Device at the University of California, Los Angeles. The reflection and transmission of Alfvén waves through inhomogeneities in the background plasma are important for understanding wave propagation, turbulence, and heating in space, laboratory, and astrophysical plasmas. Here we present inertial Alfvén waves under conditions relevant to solar flares and the solar corona. We find that the transmission of the inertial Alfvén waves is reduced as the sharpness of the gradient is increased. Any reflected waves were below the detection limit of our experiment, and reflection cannot account for all of the energy not transmitted through the gradient. Our findings indicate that, for both kinetic and inertial Alfvén waves, the controlling parameter for the transmission of the waves through an Alfvén speed gradient is the ratio of the Alfvén wavelength along the gradient divided by the scale length of the gradient. Furthermore, our results suggest that an as-yet-unidentified damping process occurs in the gradient.

79 ASTRONOMY AND ASTROPHYSICS↗

A novel high frequency, high bandwidth, three phase Mach–Zehnder optical data link

In inertial confinement fusion, hydrogen isotopes are fused together under high pressures and temperatures. Typically, the duration of these experiments is incredibly short, on the order of around 60–150 ps. Due to the high radiation environment, a detector’s signal is typically data linked far distances to a protected location. The diagnostic challenge for fusion reaction history measurements is to measure signals of interest maximizing dynamic range while also maintaining time resolution on the order of 10 ps. In this work, we present a new experimental optical data link used to efficiently transport diagnostic signals over great distances to the recording system while not restricting the dynamic range. The concept of a three phase Mach–Zehnder modulator system is introduced as well as a description of the physical prototype. The initial results from testing at the OMEGA facility show that this system is a viable method for signal transportation.

47 OTHER INSTRUMENTATION↗

Utilizing the deuterium-tritium fusion resonance to diagnose thermal runaway in igniting plasmas

For high-efficiency inertial confinement fusion implosions, it is predicted that a burning hot spot will successfully encompass all surrounding fuel and then transition into a thermal runaway where the internal energy increase from fusion occurs on a timescale faster than the expansion of the fuel is able to quench the fusion chain reaction after ignition occurs. Observation of this dynamic phase transition would indicate distinct burn properties and indicate an implosion's robustness. A technique for diagnosing the presence of thermal runaway from measurements of nuclear reaction history is presented. The technique is based on taking the logarithmic derivative of the nuclear reaction history, called the 𝛼 curve, and allowing a mathematical decoupling of the mass, volume, and thermal reactivity in the fusion reaction rate equation. During thermal runaway, where the thermal temperature dominates the burn dynamics, a maximum in the 𝛼 curve is found where there is a maximum in the first derivative of the thermal fusion reactivity, an effect to the deuterium-tritium (DT) fusion cross-section resonance. This provides a distinct signature related to the fundamental nature of the DT fusion nuclear resonance and signifies the transition into the fusion thermal instability. Impacts of charged particle transport on the effect are also assessed and the analytical formulas are compared and found to be in agreement with radiation hydrodynamic codes.

high-energy-density plasmas↗

Investigating performance and variability of NIF ICF experiments with deep learning

The parameter space involved in designing an inertial confinement fusion shot at the National Ignition Facility (NIF) is massively multi-dimensional and the cost of a single shot makes a comprehensive set of sensitivity studies in the laboratory impractical. The use of machine learning to overcome these challenges has gained popularity and has had several successful applications by the scientific community. We extend on these efforts by training a neural network (NN) on information about the experimental design, engineering elements, and drive asymmetry to predict with uncertainty the neutron yield of an experiment. We find the measured and model predicted values are in good agreement, with an R 2 value of 0.91 for a randomly selected test dataset. Almost all the predicted 95% credible intervals contain the corresponding measured value for both training and test datasets. We identify correlations picked up by the NN between the shot design, yield, and variability and use them to motivate shot sensitivity studies. The first shot to exceed the Lawson-like ignition criteria (N210808) was conducted at the NIF and subsequent shots studied the design’s robustness. In a follow-up shot to N210808, our model predicts capsule quality to be the main performance degradation mechanism that prevented the shot from repeating previous performance levels. Shot N221204 was the first shot to exceed a target energy gain of 1. Our model predicts increased yield with reduced coast time for a N221204 study and greater variability for designs with lower peak powers at constant yield. The model’s fast prediction speed and uncertainty prediction are useful for identifying interesting design paths that could warrant further investigation with conventional simulations to search for robust high yield designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toward an improved nonlocal thermodynamic equilibrium model for more predictive simulations of ignition scale hohlraums

Recently, nonlocal thermodynamic equilibrium (NLTE) modeling has been identified as the primary reason for discrepant predictions of the peak neutron production time in indirectly driven inertial confinement fusion (ICF) platforms. It has also been observed that predictions of collisional excitation rates differ by as much as 50% from measurements. Theoretical uncertainties in dielectronic recombination rates have also been posited as possibly contributing to errors in NLTE predictions. This work examines the impact of multipliers on collisional excitation and dielectronic recombination rates on simulations of a directly driven gold sphere and an indirect drive ICF implosion. It is found that multipliers on the collisional excitation rates have a strong impact on radiant intensity and electron temperature and a weaker impact on ionization state, whereas multipliers on dielectronic recombinations rates strongly impact ionization state with a smaller impact on radiant intensity and electron temperature. A self-consistent NLTE model which places multipliers on differing transitions, as motivated by experimental measurements and more detailed atomic physics predictions, improves agreement but does not completely eliminate discrepancies with measurements of the radiant intensity within the 2–4 keV spectral range.

Farmer, W. A. [Lawrence Livermore National Laborat↗

Comparison of Orion Flywheel to Commercially Available Flywheel Device

INTRODUCTION: The chosen exercise device for the Orion Multi-purpose Crew Vehicle (MPCV) for Artemis missions is the Orion Flywheel (OFW), which was selected in 2017 from a pool of exercise devices. The Orion Flywheel is to be installed in the MPCV for its first use during the Artemis II mission and will be utilized for subsequent Artemis missions. The OFW provides the capability to perform both resistive and aerobic exercises while taking up a small volume and not requiring power. Aerobic exercise consists of rowing while resistive exercise includes the deadlift, harness squat, and deadlift high pull among others. The efficacy of the OFW as an exercise countermeasure to spaceflight deconditioning has not yet been fully evaluated. A future HRP-funded study using head-down tilt bed rest is planned to evaluate the efficacy of the OFW to mitigate aerobic and muscular deconditioning. The OFW, made by KBR, is a specialized device that poses high costs for purchase and maintenance. The aim of the study is to determine if a commercially available alternative could be used as a backup for the OFW during the bed rest study or as an alternative in other studies. This study seeks to compare the loading profile and mechanics of a commercial flywheel device (kBox Pro) with the three resistance settings of the OFW using a controlled, instrumented setup to validate its acceptability as a backup. METHODS: An experimental setup was designed to simulate human use of the OFW. Flywheel devices can have varied actuated inertial mass and strap length. The inertial mass refers to the flywheel itself or the object that spins as the result of the movement of the strap. The OFW has three gears actuated with a lever, with the low gear used for aerobic rowing and the medium and high gears used for resistance exercises. These gears correspond to increasing flywheel inertia, which corresponds to a certain number and sizes of inertial plates on a commercial flywheel. The kBox Pro has varied sizes of inertial discs that are installed to the external shaft of the device and can be configured to roughly match the inertia seen in the OFW per gear setting. The strap length can be adjusted to allow for different ranges of motion. The experimental setup allows for the simulation of rowing, harness squats, and deadlift high pulls with corresponding exercise strap lengths. All three OFW gears are to be tested, as well as multiple combinations of kBox discs. The setup was created using a system of pulleys and cables to minimize friction loss. The system is actuated through the dropping of a connected mass which, through the pulley system, pulls the strap of the exercise device upwards as if a human was exercising. A string potentiometer and tensile force transducer are used to measure strap displacement and strap force, respectively. The masses dropped are exercise chains that simulate the decrease in force observed throughout a typical exercise. As the chains are lowered to the ground, they begin to spool and therefore are no longer subjecting the exercise device’s strap to their load. This setup was designed to provide realistic loads and protect the OFW from damage, an important precaution because it’s the only available unit for research and ground operations. Data is to be collected across simulated exercises and with different strap lengths, with the same conditions collected on both the OFW and the kBox Pro. RESULTS: Data collection is ongoing for the kBox and the Orion Flywheel. CONCLUSIONS: Study results will inform if the OFW and a kBox Pro device can be deemed mechanically similar. Depending on the results, additional data collection may be required to assess the user experience between the devices. A key result of this study is a mechanical characterization of the OFW device, demonstrating the load and force profile using a repeatable test method. This data will guide next steps on potential kBox Pro modifications needed to produce a comparable exercise experience to the OFW.

Exercise↗

Development of Biomorphic Flyers

Biomorphic flyers have recently been demonstrated that utilize the approach described earlier in "Bio-Inspired Engineering of Exploration Systems" (NPO-21142), NASA Tech Briefs, Vol. 27, No. 5 (May 2003), page 54, to distill the principles found in successful, nature-tested mechanisms of flight control. Two types of flyers are being built, corresponding to the imaging and shepherding flyers for a biomorphic mission described earlier in "Cooperative Lander- Surface/Aerial Microflyer Missions for Mars Exploration" (NPO-30286), NASA Tech Briefs, Vol. 28, No. 5 (May 2004), page 36. The common features of these two types of flyers are that both are delta-wing airplanes incorporating bio-inspired capabilities of control, navigation, and visual search for exploration. The delta-wing design is robust to approx.40 G axial load and offers ease of stowing and packaging. The prototype that we have built recently is shown in the figure. Such levels of miniaturization and autonomous navigation are essential to enable biomorphic microflyers (<1 kg) that can be deployed in large numbers for distributed measurements and exploration of difficult terrain while avoiding hazards. Individual bio-inspired sensors that will be incorporated in a biomorphic flyer have been demonstrated recently. These sensors include a robust, lightweight (~6 g), and low-power (~40 mW) horizon sensor for flight stabilization. It integrates successfully the principles of the dragonfly ocelli. The ocelli are small eyes on the dorsal and forward regions of the heads of many insects. The ocelli are distinct from the compound eyes that are most commonly associated with insect vision. In many insects, the ocelli are little more than single-point detectors of short-wavelength light and behavioral responses to ocelli stimuli are hard to observe. The notable exception is found in dragonflies, where flight control is notably degraded by any interference with the ocellar system. Our team has discovered recently that the ocelli are a dedicated horizon sensor, with substantial optical processing and multiple spectral sensitivity. To our knowledge, this is the world s first demonstrated use of a "biomorphic ocellus" as a flight-stabilization system. The advantage of the ocelli over a similarly sized system of rate gyroscopes is that both attitude control and rate damping can be realized in one device. A full inertial unit and significant processing would otherwise be required to achieve the same effect. As a prelude to full autonomy, substantial stability augmentation is provided to the pilot at very low cost in terms of space, power, and mass. The sensor is about 40 times lighter than a comparable inertial attitude reference system. Other significant features of the biomorphic flyer shown in the figure include its ability to fly at high angles of attack ~30 and a deep wing chord which allows scaling to small size and low Reynold s number situations. Furthermore, the placement of the propulsion system near the center of gravity allows continued control authority at low speeds. These attributes make such biomorphic flyers uniquely suited to planetary and terrestrial exploration where small size and autonomous airborne operation are required.

Thakoor, Sarita↗

Creation and characterization of warm dense matter isochorically heated by an intense laser-driven proton beam to temperatures exceeding 100 eV

The warm dense matter (WDM) is an exotic state of matter encountered in inertial confinement implosions for fusion energy, as well as the interiors of giant planets like Jupiter, brown dwarfs, the atmospheres of white dwarfs, neutron star crusts, and newly discovered exo-planets. One efficient way to create WDM is to use protons accelerated by a high-intensity short-pulse laser to isochorically heat dense samples to WDM states. Despite its importance, direct temperature measurements within WDM targets are scarce. This study utilizes an intense proton beam generated by the kilojoule EP laser further focused and guided by a curved foil and cone structure to efficiently heat a thin copper sample. A high-resolution streaked spectrometer tuned to copper K α fluorescence lines provided bulk temperature measurements every ~2 ps, revealing temperatures exceeding 100 eV in under 50 ps. Particle-in-cell simulations of proton transport and energy deposition closely matched the observed heating dynamics, including transverse temperature gradients revealed by the broadening of K α lines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Studies of localized mix and asymmetry caused by the stalk in inertial fusion experiments at OMEGA

In an inertially confined fusion experiment, a capsule of fusion fuel is compressed to high temperatures and densities using lasers, creating a hot plasma in which thermonuclear fusion reactions take place. To achieve efficient conversion of laser energy to fuel heating, the implosion must be as spherically symmetric as possible. One common source of asymmetry that degrades performance is the stalk and glue spot that hold the capsule in place before the experiment. The exact nature and magnitude of this perturbation had not been previously quantified. In this work, inertially confined fusion experiments were executed with an additional stalk on the capsule to measure and quantify the effect of the stalk and glue spot on the symmetry and performance. It is found that the stalk drives low-mode asymmetry by shadowing the laser drive on the part of the shell near the glue spot, enhancing the hot-spot velocity toward the stalk by 40–80 km/s and elongating the hot-spot along the stalk axis. It is also found that localized mix due to the additional stalk has a negligible effect on implosion performance. Two-dimensional radiation-hydrodynamic simulations using the xRAGE code reproduce the direction of the experimentally observed change to hot-spot velocity and implosion performance metrics, but not the observed elongation, suggesting that this feature results from an interaction between stalk perturbations and other preexisting asymmetry seeds, such as laser drive asymmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterizing laser-heated polymer foams with simultaneous x-ray fluorescence spectroscopy and Thomson scattering at the Matter in Extreme Conditions Endstation at LCLS

Understanding the behavior of polymer foams at high energy density conditions is crucial to advance inertial fusion energy research. Here, we present a new experimental platform designed to measure the thermodynamic state of these materials at megabar pressures. At the Matter in Extreme Conditions Endstation of the Linac Coherent Light Source, we heat samples using an optical, high-intensity, femtosecond laser and dynamically probe them with ultra-short, coherent x-ray pulses of high peak brightness. We perform x-ray Thomson scattering measurements in forward and backward scattering geometries to capture both collective and non-collective electron behavior in the sample. Simultaneously, x-ray fluorescence spectroscopy is used to measure the emission from a mid-Z dopant, providing complementary information on the plasma conditions. By combining these techniques, we obtain temporally resolved temperature measurements of the transient warm dense matter states. Our initial experiments designed to benchmark the platform with carbon samples yielded data resolving the ultrafast response to laser heating with sub-picosecond resolution, measuring plasma temperatures exceeding 50 eV. These findings lay the foundation for precision studies of the dynamic evolution of laser-heated polymer foams.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Droplet breakup by multimodal nonlinear Rayleigh Taylor instability

A droplet impacted by a shock wave will undergo a process of fragmentation due to the development of interfacial hydrodynamic instabilities. The interface experiences variable acceleration and shear that result in the development of both inertial (Rayleigh–Taylor) and shear (Kelvin–Helmholtz) instabilities. These perturbations grow in time and drive the fragmentation and breakup of the deformed droplet. Experiments are performed on nominally 0.86 mm water droplet subjected to a Mach 7.6 detonation wave, resulting in a high Weber number (~36,000) breakup event. Perturbation growth is measured from a series of high-speed (> MHz) shadowgraph images. It is proposed that, given the size of the large-scale perturbations observed in experiments, these instabilities are growing in the non-linear regime and can be described by bubble-merger models for nonlinear mixing. Calculations are performed for the growth rates and size of these instabilities using deformation and external flow models to establish the time-dependent boundary conditions. The concurrence of the measured perturbation widths and the predictions of the simple model lend credence to the theory. This novel approach serves to open a new avenue in the characterization of droplet breakup via hydrodynamic instabilities.

Droplet breakup↗