The rate coefficient for dissociative recombination (DR) of CH + is needed to model clouds in the interstellar medium (ISM). Theoretical data for DR are typically obtained in the form of cross sections as a function of collision energy. However, astrochemical modelers need rate coefficients as a function of the kinetic temperature of the gas, i.e., the cross section averaged over the electron velocity distribution of the plasma. Molecules in the ISM are typically in their lowest energy states. To this end, we have calculated the kinetic temperature rate coefficients for DR of electronically, vibrationally, and rotationally cold CH + over a temperature range of 1–5000 K, using theoretical cross sections from J. Forer et al. We have also fit our results to two commonly used modeling formulae and present the corresponding fit parameters.

We have explored a combination of two methods to control the internal excitation of H 3 + produced in a duoplasmatron ion source. The H 3 + was formed starting from a gas of H2. The first control method varied the H2 pressure in the ion source to collisionally relax any internally excited ( H 3 + ) ∗ . The second method added Ar to the source to chemically destroy ( H 3 + ) ∗ with internal excitation energies E int ⩾ 0.57 eV, using the endoergic reaction H 3 + + Ar → ArH + + H 2 . To infer the H 3 + internal temperature, T int , representative of internal excitation under the hypothesis of thermodynamic equilibrium, we used merged-beams rate coefficient measurements of the endoergic deuterating reaction H 3 + + D → H 2 D + + H 2 and a semi-empirical theoretical model. We found that using collisional relaxation alone, we could vary T int over the range ≈ 1300 − 2200 K. Combining collisional relaxation and chemical destruction, we reduced the minimum to T int ≈ 1130 K. Over this temperature range, the fraction of H 3 + where all vibrational modes are in their v = 0 level varies from ≈ 0.88 at the lowest temperature to ≈ 0.44 at the highest temperature. This combination of cooling methods offers a potentially powerful means for studying reactive scattering processes as a function of the internal excitation of the H 3 + .

Mercury has a very tenuous atmosphere starting at the surface, which is referred to as a surface-bound exosphere, where there are no collisions between exospheric particles. Having a surface-bound exosphere means that the particles in the exosphere have their origin on Mercury’s surface; thus, the composition of the exosphere is connected to the composition of the surface. In situ composition measurements of the exosphere can contribute to the study of the composition of the surface, together with a range of remote sensing techniques (ultraviolet, visible, infrared, X-ray, gamma-ray, and neutron spectroscopy). The external drivers for the particle release from the surface are solar photons, solar wind plasma, and micrometeoroid impacts. These drivers also cause space weathering of the surface, resulting in significant physical and chemical alterations in the regolith, ranging from the very surface to depths up to one meter. Modifications of the surface by space weathering must be considered when interpreting the composition measurements of the exosphere as well as the composition measurements of the surface by the established remote sensing techniques, because their information comes from the space-weathered volume of the surface. Therefore, the particle populations in the exosphere, space weathering, and the composition of the surface are intimately connected and must be studied together. In the following, we will review the connections between the surface and the exosphere of Mercury.

We have explored a combination of two methods to control the internal excitation of H-3(+) produced in a duoplasmatron ion source. The H-3(+) was formed starting from a gas of H-2. The first control method varied the H-2 pressure in the ion source to collisionally relax any internally excited (H-3(+))& lowast;. The second method added Ar to the source to chemically destroy (H-3(+))& lowast; with internal excitation energies E-int >= 0.57 eV, using the endoergic reaction H-3(+)+Ar -> ArH+ +H-2. To infer the H-3(+) internal temperature, T-int, representative of internal excitation under the hypothesis of thermodynamic equilibrium, we used merged-beams rate coefficient measurements of the endoergic deuterating reaction H-3(+)+D -> H2D++H-2 and a semi-empirical theoretical model. We found that using collisional relaxation alone, we could vary T-int over the range approximate to 1300-2200 K. Combining collisional relaxation and chemical destruction, we reduced the minimum to T-int approximate to 1130 K. Over this temperature range, the fraction of H-3(+) where all vibrational modes are in their v = 0 level varies from approximate to 0.88 at the lowest temperature to approximate to 0.44 at the highest temperature. This combination of cooling methods offers a potentially powerful means for studying reactive scattering processes as a function of the internal excitation of the H-3(+).

We present revised point-spread functions (PSFs) for the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. These PSFs provide a robust estimate of the light diffracted by the meshes holding the entrance and focal plane filters and the light that is diffusely scattered over the detector by the microroughness of the mirrors. We first calibrate the diffracted light using flare images. Our modeling of the diffracted light provides reliable determinations of the mesh parameters and finds that about 24%–33% of the collected light is diffracted, depending on the AIA channel. Then, we fit the diffuse scattered light using partially lunar-occulted images. We find that the diffuse scattered light can be modeled as a superposition of two power-law functions that scatter light over the entire detector. The amount of diffuse scattered light ranges from 10% to 35%, depending on the AIA channel. In total, AIA diffracts and diffusely scatters about 37%–55% of the collected light over the detector. When correcting for this, bright image regions increase in intensity by about 30%, dark image regions decrease by up to 90%, and the associated differential emission measure analysis of solar features is affected accordingly. Finally, we compare the image reconstructions using our new PSFs to those from the AIA team and B. Poduval et al. We find that our PSFs outperform the others, better correcting for the flare diffraction pattern and far more accurately predicting long-distance scattered light in lunar occultations.

One of the demanding frontiers in ultracold quantum science is identifying laser cooling schemes for complex atoms and molecules out of their vast spectra of internal states. Motivated by the prospect of expanding the set of available ultracold molecules for applications in fundamental physics, chemistry, astrochemistry, and quantum simulation, we propose and demonstrate an automated graph-based search approach for viable laser cooling schemes. The method is time efficient, reproduces the results of previous manual searches, and reveals a plethora of new potential laser cooling schemes. We discover laser cooling schemes for YO, C_{2}, OH^{+}, CN, and CO_{2}, including surprising schemes that start from highly excited states or do not rely on a strong main transition. A central insight of this work is that the reinterpretation of quantum states and transitions between them as a graph can dramatically enhance the ability to identify new quantum control schemes for complex quantum systems. As such, this approach will also apply to complex atoms and, in fact, any complex many-body quantum system with a discrete spectrum of internal states.

We investigate the properties and relationship between Doppler velocity fluctuations and intensity fluctuations in the off-limb quiet Sun corona. These are expected to reflect the properties of Alfvénic and compressive waves, respectively. The data come from the Coronal Multichannel Polarimeter (COMP). These data were studied using spectral methods to estimate the power spectra, amplitudes, perpendicular correlation lengths, phases, trajectories, dispersion relations, and propagation speeds of both types of fluctuations. We find that most velocity fluctuations are due to Alfvénic waves but that intensity fluctuations come from a variety of sources, likely including fast and slow mode waves, as well as aperiodic variations. The relation between the velocity and intensity fluctuations differs depending on the underlying coronal structure. On short closed loops, the velocity and intensity fluctuations have similar power spectra and speeds. In contrast, on longer nearly radial trajectories, the velocity and intensity fluctuations have different power spectra, with the velocity fluctuations propagating at much faster speeds than the intensity fluctuations. Considering the temperature sensitivity of COMP, these longer structures are more likely to be closed fields lines of the quiet Sun rather than cooler open field lines. That is, we find the character of the interactions of Alfvénic waves and density fluctuations depends on the length of the magnetic loop on which they are traveling.

We have measured the perpendicular correlation length L _⊥ of Alfvénic waves in the corona using data from the Daniel K. Inouye Solar Telescope (DKIST) Cryogenic Near Infrared Spectropolarimeter (Cryo-NIRSP) instrument. These data have high spatial resolution and were collected using a raster, enabling us to unambiguously identify the parallel and perpendicular directions with respect to the wave propagation. We find that the measured median L _⊥ ≈ 3.5 Mm, which is about half the value found by previous measurements. We ascribe the smaller value measured here to the improved spatial resolution of DKIST. There is a gradual decrease of L _⊥ as a function of frequency. We also computed the spatial correlation length of the observed static density structures and found that their typical correlation lengths of ≈8.4 Mm were significantly larger than those of the waves.

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.

Introduction: Na, Ar and He are some of the most abundant confirmed neutral species in Mercury’s exosphere. Whereas the source of He is from the solar wind (SW), the source of the Na is potentially due to sputtering from silicates on the Hermean surface (1, 2). As SW ions impact the surface, they deposit energy, leading to sputtered atoms from the substrate (3, 4). The yield and energy distributions of the sputtered atoms depends on the energy of the impacting ions and the composition of the impacted surface. Understanding the role SW ions play on surface sputtering of Mercury is critical to any exosphere model (3). The most common sputtering models use the binary collision approximation (BCA) and thus consider sputtering to be a result of binary collision cascades (5). These models can be used to predict the energy distribution and yield of sputtered atoms as a function of incoming ion type, energy, and impacting angle. A fundamental physical parameter for BCA models is the surface binding energy (SBE) of atoms in the substrate (6, 7). The SBE is a user defined value in SDTrimSP (8), a BCA sputtering simulation tool, and in the commonly referenced Thompson energy distribution of the sputtered atoms (9). Despite the clear importance of the SBE, its actual value is not well understood for many substrates. For single component substrates, the SBE is often approximated as the heat of sublimation for the substrate atoms (10). However, previous research has suggested that this approach can underestimate the SBE by 20-40% (7). More importantly for planetary science, there is no universal approach to estimating the SBE for multicomponent substrates where the Na is likely bonded to other atomic species. SDTrimSP recommends using the pure heat of sublimation of each atomic species as the SBE for sputtering from a compound, which is 1.1 eV for Na (8). However, this approach assumes that the SBE is independent of the bonds formed with the other atoms within the substrate. In contrast, Lammer et al. (12) predict a value between 2-2.65 eV but note that this is not well determined due to a lack of experimental data. Given that BCA methods rely on a user defined SBE, this can be a significant source of error for sputtering predictions. To address this issue, we have performed molecular dynamics (MD) simulations to better constrain the SBE of Na from silicates. We then consider the effect these modified inputs have on the predicted yield and energy distributions of sputtered Na due to SW impacts. Methods: MD simulations were conducted to determine the SBE of Na for various crystalline silicates: sodium metasilicate (Na2SiO3), sodium orthosilicate (Na4SiO4), and albite (NaAlSi3O8). An iterative method was used to determine the minimum energy needed to remove one Na atom completely from the substrate surface. Simulations were conducted using a many-body reactive potential that was previously shown to be suitable for a variety of sodium silicate crystals (13). BCA models were then used to determine how the resulting SBE values affected the predicted yield and energy distribution of sputtered Na. The commonly referenced Thompson distribution was used to determine the energy distribution vs. SBE. SDTrimSP was used to calculate the sputtering yield of Na vs. SBE. To capture the most common components of the SW, 1 keV H+ and He2+ impacts were simulated on sodium silicate surfaces. Results: The MD simulations yielded a range of SBEs from sodium silicates: 2.6 eV for sodium orthosilicate, 4.4 eV for sodium metasilicate, and 7.9 eV for albite. In contrast, the individual cohesive energy of pure Na is only 1.1 eV. Therefore, SBEs from a compound can be drastically different than their atomistic cohesive energies. These results show that the SBE of a specific atom is a function of the compound in which the atom is bound. The newly predicted Na SBE values were then used to determine the sputtering yield and energy distribution of the sputtered atoms using SDTrimSP and the Thompson energy distribution. We find that increasing the SBE from 1.1 to 7.9 eV had a significant effect on predicted energy distribution (Fig. 1). Therefore, the characteristics of sputtered atoms are highly dependent on the SBE used for the simulations. Similarly, the Na yield from albite was highly dependent on the Na SBE (Fig. 2). For example, the Na yield from albite for a 1keV H impact decreased by a factor of almost 15 when the SBE was increased from 1.1 eV to the SBE for Na from albite (7.9 eV). Overall, this study demonstrates that the SBE within in a compound can be significantly different than the monatomic cohesive energy. The results demonstrate the potential of MD to better understand and constrain these values, though laboratory measurements are still needed to benchmark these calculations. In summary, an accurate SBE is critical to obtaining realistic models of SW sputtering contribution to the Hermean exosphere.Fig 1. Normalized Energy distribution of sputtered Na atoms as a function of SBE\Fig 2. Sodium sputtering yield as a function of surface binding energy References:[1] McCoy TJ, et al. 2018. Mercury. View after MESSENGER, pp. 176–90 [2] McClintock WE, et al. Mercur. View after MESSENGER, pp. 371–406 [3] Killen RM, et al. 2001. J. Geophys. Res. Planets. 106(E9):20509–25 [4] Domingue DL, et al. 2014. Space Sci. Rev. 181(1–4):121–214 [5] Eckstein W, Urbassek HM. 2007. In Sputtering by Particle Bombardment, pp. 21–31. Springer [6] Stepanova M, Dew SK. 2001. J. Vac. Sci. Technol. A Vacuum, Surfaces, Film. 19(6):2805–16 [7] Yang X, Hassanein A. 2014. Appl. Surf. Sci. 293:187–90 [8] Mutzke A, et al. 2019 [9] Thompson MW. 1968. Philos. Mag.18(152):377–414 [10] Kelly R. 1986. Nucl. Instruments Methods Phys. Res. Sect. B Beam Interact. with Materials and Atoms. 18(1–6):388–98 [11] Leblanc F, Johnson RE. 2003. Icarus. 164(2):261–81 [12] Lammer H, et al. 2003. Icarus. 166(2):238–47 [13] Hahn SH, et al. 2018. J. Phys. Chem. C. 122(34):19613–24

We provide an overview of our understanding of the dust environment at Mercury and the role that dust plays in shaping the planet's surface and exosphere. Our understanding of the role that dust impacts play in the generation of Mercury's atmosphere has evolved considerably with continued analysis of results from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission. Recent models have provided evidence for the probable release of refractory species into Mercury's exosphere via impacts. However, there remain significant questions regarding the relative contributions of atoms released via impacts versus other mechanisms (e.g., photon-stimulated desorption) to the overall exospheric budget. We also discuss the state of observational and modeling efforts to constrain the dust environment at Mercury, including sources from the zodiacal cloud, cometary trails, and interstellar dust. We describe the advancements that will be made in our characterization of dust at Mercury with BepiColombo, providing observational constraints on the dust clouds themselves and the role that impacts play in exospheric generation. On Mercury's surface, there remain outstanding questions regarding the role that dust impacts play in the regolith cycling and development. We review how improved modeling efforts to understand grain lifetimes as a function of impactor flux will further our understanding of Mercury's regolith. Finally, there are few constraints on the role of dust impacts on the space weathering of Mercury's surface, particularly the expected chemical, physical, and spectral alterations to the regolith. Here we discuss the importance of laboratory experiments to simulate these processes for the interpretation of data from MESSENGER and BepiColombo.

We have experimentally studied dissociative recombination (DR) of electronically and vibrationally relaxed ArH+ in its lowest rotational levels, using an electron-ion merged-beams setup at the Cryogenic Storage Ring. We report measurements for the merged-beams rate coefficient of ArH+ and compare it to published experimental and theoretical results. In addition, by measuring the kinetic energy released to the DR fragments, we have determined the internal state of the DR products after dissociation. At low collision energies, we find that the atomic products are in their respective ground states, which are only accessible via nonadiabatic couplings to neutral Rydberg states. Published theoretical results for ArH+ have not included this DR pathway. From our measurements, we have also derived a kinetic temperature rate coefficient for use in astrochemical models. Published by the American Physical Society 2024

Abstract We compare a method for inferring the photospheric vector magnetic field using only spectroscopy to a conventional method based on polarimetry. The magnetic field strength B and inclination angle can be inferred from the Zeeman splitting using only Stokes I. We applied this method to a sunspot observed with the Vacuum Tower Telescope and compared the results to vector magnetograms from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory, which used a polarimetric inversion. The spectroscopic inversion tends to show higher values in B compared to the polarimetric data. In quiet regions the discrepancy in B was typically a factor of two. In the strong sunspot fields, the differences averaged ≈22%. These discrepancies are significant, but comparable to those typically found among magnetograms from different instruments. Our results support the use of the spectroscopic inversion technique to provide a fast and reasonable estimate of B.

We present a high-resolution spectral study of Fe L-shell extinction by the diffuse interstellar medium (ISM) in the direction of the X-ray binaries Cygnus X-1 and GX 339-4, using the XMM-Newton reflection grating spectrometer. The majority of interstellar Fe is suspected to condense into dust grains in the diffuse ISM, but the compounds formed from this process are unknown. Here, we use the laboratory cross sections from Kortright & Kim (2000) and Lee et al. (2009) to model the absorption and scattering profiles of metallic Fe, and the crystalline compounds fayalite (Fe$_2$SiO$_4$), ferrous sulfate (FeSO$_4$), hematite ($\alpha$-Fe$_2$O$_3$), and lepidocrocite ($\gamma$-FeOOH), which have oxidation states ranging from Fe$^{0}$ to Fe$^{3+}$. We find that the observed Fe L-shell features are systematically offset in energy from the laboratory measurements. An examination of over two dozen published measurements of Fe L-shell absorption finds a 1-2 eV scatter in energy positions of the L-shell features. Motivated by this, we fit for the best energy-scale shift simultaneously with the fine structure of the Fe L-shell extinction cross sections. Hematite and lepidocrocite provide the best fits ($\approx +1.1$ eV shift), followed by fayalite ($\approx +1.8$ eV shift). However, fayalite is disfavored, based on the implied abundances and knowledge of ISM silicates gained by infrared astronomical observations and meteoritic studies. We conclude that iron oxides in the Fe$^{3+}$ oxidation state are good candidates for Fe-bearing dust. To verify this, new absolute photoabsorption measurements are needed on an energy scale accurate to better than 0.2 eV.

R-matrix with pseudostates (RMPS) calculations have been carried out for photoionization of atomic sodium near threshold. The large RMPS atomic orbital and configuration basis allows for very accurate computations of low-energy photoionization cross sections up to approximate to 30 eV, the energy range for which the RMPS calculations were optimized. Consistency checks for accuracy include, first, the excellent agreement found between lengthand velocity-gauge theoretical results, a necessary but not sufficient requirement for having a converged wave function. A second accuracy quantification is the excellent prediction of the position of the Cooper minimum compared to experimental results. Particular attention is paid to the Cooper minimum occurring just above threshold, and the spin-orbit splitting of minima, resulting in a nonzero total cross section. Our RMPS results away from the minimum are found to be lower than the experimental data, and we make the case that the experimental magnitudes are an overestimate. A third important affirmation of the present accuracy is the continuity found between the 3s -> np bound-bound discrete oscillator strength density below threshold-see Wiese et al. [W. L. Wiese, M. W. Smith, and B. M. Miles, Atomic Transition Probabilities, Vol. 2: Sodium Through Calcium; A Critical Data Compilation (US Government Printing Office, Washington, DC, 1969)]-and the 3s -> cp bound-continuum RMPS oscillator strength density above threshold. These three somewhat independent tests of the accuracy of the computed cross sections add confidence to our recommending the present RMPS results as the most reliable extant data for low-energy Na photoionization (and the earlier Wiese et al. results for the discrete states).

Our understanding of the ion-sputtering contribution to the formation of exospheres on airless bodies has been hindered by the lack of accurate surface binding energies (SBEs) of the elements in the various mineral and amorphous compounds expected to be on the surfaces of these bodies. The SBE for a given element controls the predicted sputtering yield and energy distribution of the ejecta. Here, we use molecular dynamics computations to provide SBE data for the range of elements sputtered from plagioclase feldspar crystalline end members, albite and anorthite, which are expected to be important mineral components on the surfaces of the Moon and Mercury. Results show that the SBE is dependent on the crystal orientation and the element’s coordination, meaning multiple SBEs are possible for a given element. Variation in the SBEs among the different surface positions has a significant effect on the predicted yield and energy distribution of the ejecta. We then consider sputtering by H, He, and a solar wind mixture of 96% H and 4% He. For each of these cases, we derive best-fit elemental SBE values to predict the ejecta energy distribution from each of the (001), (010), and (011) cleavage planes. We demonstrate that the He contribution to the sputtering yield cannot be accounted for by multiplying the 100% H results by some factor. Lastly, we average our results over all three possible lattice orientations and provide best-fit elemental SBE values that can be easily incorporated into sputtering yield models.

Bombardment by solar wind ions is one of the main drivers of space weathering on airless bodies. Here, we simulate the solar-wind-driven spectral alteration of loosely packed olivine powders by irradiation with 1.2 keV helium ions (He+). We measured the reflectance spectra of the olivine powder in the ultraviolet-visible-near-infrared (UV-Vis-NIR) wavelength range (0.2-2 mu m) as a function of ion fluence. In the Vis-NIR range, we observed spectral darkening, absorption band shallowing, and spectral reddening, in agreement with lunar-style space weathering and previous laboratory studies. In the UV-Vis, spectral darkening was also observed. However, a spectral bluing took place at wavelengths below 400 nm. As the simulated space weathering progressed, the spectral slopes shifted from steep-UV/shallow-NIR slopes to shallow-UV/steep-NIR slopes. Moreover, the change in the UV slope was almost 10 times larger than in the NIR, supporting the hypothesis that the UV spectral slope could be an earlier indicator of space weathering.

Solar physicists routinely utilize observations of Ar-like Fe IX and Cl-like Fe X emission to study a variety of solar structures. However, unidentified lines exist in the Fe IX and Fe X spectra, greatly impeding the spectroscopic diagnostic potential of these ions. Here, we present measurements using the Lawrence Livermore National Laboratory EBIT-I electron beam ion trap in the wavelength range 238-258 A. These studies enable us to unambiguously identify the charge state associated with each of the observed lines. This wavelength range is of particular interest because it contains the Fe IX density diagnostic line ratio 241.74 A/244.91 A, which is predicted to be one of the best density diagnostics of the solar corona, as well as the Fe X 257.26 A magnetic-field-induced transition. We compare our measurements to the Fe IX and Fe X lines tabulated in CHIANTI v10.0.1, which is used for modeling the solar spectrum. In addition, we have measured previously unidentified Fe X lines that will need to be added to CHIANTI and other spectroscopic databases.

We have measured the absolute doubly differential angular sputtering yield for 20 keV Kr+ impacting a polycrystalline Cu slab at an incidence angle of θi = 45° relative to the surface normal. Sputtered Cu atoms were captured using collectors mounted on a half dome above the sample, and the sputtering distribution was measured as a function of the sputtering polar, θs, and azimuthal, ϕs, angles. Absolute results of the sputtering yield were determined from the mass gain of each collector, the ion dose, and the solid angle subtended, after irradiation to a total fluence of ∼1 × 1018 ions/cm2. Our approach overcomes shortcomings of commonly used methods that only provide relative yields as a function of θs in the incidence plane (defined by the ion velocity and the surface normal). Our experimental results display an azimuthal variation that increases with increasing θs and is clearly discrepant with simulations using binary collision theory. We attribute the observed azimuthal anisotropy to ion-induced formation of micro- and nano-scale surface features that suppress the sputtering yield through shadowing and redeposition effects, neither of which are accounted for in the simulations. Our experimental results demonstrate the importance of doubly differential angular sputtering studies to probe ion sputtering processes at a fundamental level and to explore the effect of ion-beam-generated surface roughness.

We report the first experimental detection of a reflected Alfvén wave from an Alfvén-speed gradient under conditions similar to those in coronal holes. The experiments were conducted in the Large Plasma Device at the University of California, Los Angeles. We present the experimentally measured dependence of the coefficient of reflection versus the wave inhomogeneity parameter, i.e., the ratio of the wavelength of the incident wave to the length scale of the gradient. Two-fluid simulations using the Gkeyll code qualitatively agree with and support the experimental findings. Our experimental results support models of wave heating that rely on wave reflection at low heights from a smooth Alfvén-speed gradient to drive turbulence.