Estimation Of Electron Density Research Articles

Non-uniform electron density estimation based on electromagnetic wave attenuation in plasma

Abstract The surface of a high-speed vehicle reentering the atmosphere is surrounded by plasma sheath. Due to the influence of the inhomogeneous flow field around the vehicle, understanding the electromagnetic properties of the plasma sheath can be challenging. Obtaining the electron density of the plasma sheath is crucial for understanding and achieving plasma stealth of vehicles. In this work, the relationship between electromagnetic wave attenuation and electron density is deduced theoretically. The attenuation distribution along the propagation path is found to be proportional to the integral of the plasma electron density. This result is used to predict the electron density profile. Furthermore, the average electron density is obtained using a back-propagation neural network algorithm. Finally, the spatial distribution of the electron density can be determined from the average electron density and the normalized derivative of attenuation with respect to the propagation depth. Compared to traditional probe measurement methods, the proposed approach not only improves efficiency but also preserves the integrity of the plasma environment.

LIBS plasma diagnostics with SuperCam on Mars: Implications for quantification of elemental abundances

The Perseverance rover landed in Jezero Crater, Mars, in 2021 to explore an ancient delta for signs of past life and collect samples for a future Mars Sample Return Mission. SuperCam, onboard Perseverance, uses Laser Induced Breakdown Spectroscopy (LIBS) to quantify the elements in the rocks/soils encountered along the rover's traverse. LIBS is desirable for planetary science missions because of its effectiveness at a distance and with different target types (rock, soil, etc). However, decreased laser irradiance with distance and changing coupling efficiency in different targets could cause the physical conditions of the plasma plume to vary, with important implications for SuperCam's elemental calibration. This study examines the characteristics of laser-induced plasmas on Mars by estimating apparent temperature via the multiline Boltzmann plot method and electron density using Stark broadening of the H-α line. We find that apparent plasma temperatures do not decrease with distance or vary systematically with target type (rock vs soil). The variability in plasma temperatures seen on Mars is fully represented in the laboratory dataset used for SuperCam's elemental calibration, which suggests that our elemental calibration is likely robust against observed changes in apparent plasma temperature. These results imply that SuperCam can make reliable LIBS observations to at least 8 m. Estimated electron density is 1.4× higher in soils than rock targets, which is likely related to the dependence of the H-α line on topographic relief, a poorly understood mechanism which contributes to the difficulty of quantifying hydrogen abundance in Mars spectra.

JWST NIRSpec High-resolution Spectroscopy of MACS0647–JD at z = 10.167: Resolved [O ii] Doublet and Electron Density in an Early Galaxy

We present JWST/NIRSpec high-resolution G395H/F290LP spectroscopy of MACS0647−JD, a gravitationally lensed galaxy merger at z = 10.167. The new spectroscopy, which is acquired for the two lensed images (JD1 and JD2), detects and resolves emission lines in the rest-frame ultraviolet and blue optical, including the resolved [O ii] λ λ3726, 3729 doublet, [Ne iii] λ3870, He i λ3890, Hδ, Hγ, and [O iii] λ4363. This is the first observation of the resolved [O ii] λ λ3726, 3729 doublet for a galaxy at z > 8. We measure a line flux ratio [O ii] λ3729/λ3726 = 0.9 ± 0.3, which corresponds to an estimated electron density of log(ne/cm−3)=2.9±0.5 . This is significantly higher than the electron densities of local galaxies reported in the literature. We compile measurements from the literature and further analyze the redshift evolution of n e . We find that the redshift evolution follows the power-law form of n e = A × (1 + z) p with A=54−23+31 cm−3 and p=1.2−0.4+0.4 . This power-law form may be explained by a combination of metallicity and morphological evolution of galaxies, which become, on average, more metal poor and more compact with increasing redshift.

Determination of the electron temperature and electron density in reduced pressure hydrogen peroxide (H2O2) discharge.

A reduced pressure glow discharge is produced by passing a high-power pulsed DC source of 0-500W with a frequency of 50Hz across two parallel disk electrodes. A hydrogen peroxide aqueous solution is used as a flowing gas for discharge generation. Optical emission spectroscopy is employed to diagnose the discharge generated at a reduced pressure of 0.2mbar with an electrode gap of 4cm. The spectra are recorded at a power density of 9.4 mW/cm3 and typically lie in the visible wavelength range of 380-880nm. The spectra are analyzed using the line intensity ratio method to estimate electron temperature and density. The results indicated that the electron temperature and density are, respectively, 0.87eV and 6.4 × 1014cm-3.

Feasibility of dose calculation for treatment plans using electron density maps from a novel dual-layer detector spectral CT simulator

BackgroundConventional single-energy CT can only provide a raw estimation of electron density (ED) for dose calculation by developing a calibration curve that simply maps the HU values to ED values through their correlations. Spectral CT, also known as dual-energy CT (DECT) or multi-energy CT, can generate a series of quantitative maps, such as ED maps. Using spectral CT for radiotherapy simulations can directly acquire ED information without developing specific calibration curves. The purpose of this study is to assess the feasibility of utilizing electron density (ED) maps generated by a novel dual-layer detector spectral CT simulator for dose calculation in radiotherapy treatment plans.Methods30 patients from head&neck, chest, and pelvic treatment sites were selected retrospectively, and all of them underwent spectral CT simulation. Treatment plans based on conventional CT images were transplanted to ED maps with the same structure set, including planning target volume (PTV) and organs at risk (OARs), and the dose distributions were then recalculated. The differences in dose and volume histogram (DVH) parameters of the PTV and OARs between the two types of plans were analyzed and compared. Besides, gamma analysis between these plans was performed by using MEPHYSTO Navigator software.ResultsIn terms of PTV, the homogeneity index (HI), gradient index (GI), D2%, D98%, and Dmean showed no significant difference between conventional plans and ED plans. For OARs, statistically significant differences were observed in parotids D50%, brainstem in head&neck plans, spinal cord in chest plans and rectum D50% in pelvic plans, whereas the variance remained minor. For the rest, the DVH parameters exhibited no significant difference between conventional plans and ED plans. All of the mean gamma passing rates (GPRs) of gamma analysis were higher than 90%.ConclusionCompared to conventional treatment plans relying on CT images, plans utilizing ED maps demonstrated similar dosimetric quality. However, the latter approach enables direct utilization in dose calculation without the requirements of establishing and selecting a specific Hounsfield unit (HU) to ED calibration curve, providing an advantage in clinical applications.

Optical and H i observations of IC 443 and G189.6 + 3.3 in a complex environment

ABSTRACT The supernova remnant (SNR) IC 443 is one of the best-studied Galactic SNRs at many wavelengths. It is interacting with a very complex environment, including the SNR G189.6 + 3.3 and H ii regions. In this paper, we report on observations of IC 443 and G189.6 + 3.3 using 1.5- and 1-m telescopes to better understand the nature of these SNRs in the optical band. We obtain H$\alpha$ images showing both filamentary and diffuse structures, and long-slit spectra from many locations, with Balmer and forbidden lines detected for IC 443 and G189.6 + 3.3. The [S ii]/ H$\alpha$ ratios confirm the SNR nature of G189.6 + 3.3. The ranges of our estimated electron density and pre-shock cloud density clearly indicate the complex structure surrounding IC 443 and G189.6 + 3.3. We also investigate the archival H i data and newly find some shell-like distributions of H i that are possibly associated with G189.6 $+$ 3.3.

Electron density estimation using MPPC-based photon-counting CT for radiation therapy planning

Photon-counting computed tomography (PCCT) has been attracting attention recently, as a potential alternative to the conventional computed tomography (CT). With PCCT, the photon energy can be obtained, and the amount of exposure can be reduced compared with the conventional CT. We developed a detector system composed of a scintillator and multi-pixel photon counter (MPPC). This makes the system simple and inexpensive compared with the semiconductor-based PCCT, like CdTe and CZT. In this study, we propose estimating electron density for radiation therapy planning using a six-threshold MPPC-based photon-counting detector. Electron density is an essential information for determining beam energy in radiation therapy planning. Therefore, accurate electron density estimation is required. The estimation method used in this study is based on the method proposed by Saito et al. (2012) PCCT images of electron-density-known phantoms were acquired, and information of the two out of the six energy bands was used for estimation. As a result, we succeeded in estimating the electron density with an accuracy of 4.59% root-mean-square error. However, the lung phantoms, which had a relatively low electron density, still had a large deviation from the true value. In addition, dual-energy CT and PCCT estimation results were compared. PCCT results has not yet surpassed the accuracy of dual-energy CT (DECT) results; however, the high electron density materials were obtained almost at the same level of accuracy. In future, we will continue to work on more accurate electron density estimation using multiple energy band information.

Mapping high spatial resolution ionospheric total electron content by integrating Time Series InSAR with International Reference Ionosphere model

Total electron content (TEC) is a key parameter for characterizing the ionosphere. Conventional TEC measurement methods have low spatial resolution, hindering accurate representation of ionospheric spatial characteristics. Synthetic Aperture Radar (SAR) and Interferometric SAR (InSAR) have shown their potential for high-spatial-resolution TEC estimation. However, SAR-based absolute TEC estimation typically relies on full-polarimetric SAR images, while the InSAR-based method can only extract differential TEC. This study proposes a novel TEC mapping method integrating Time Series InSAR (TS-InSAR) with the International Reference Ionospheric (IRI) model and does not leverage full-polarimetric SAR data. The Advanced Land Observing Satellite-1 (ALOS-1) SAR images covering the Chile and Greenland regions were collected to test the proposed method. The TECs derived from the IRI model and International GNSS Service (IGS) and the electron density observed by the Incoherent Scattering Radar (ISR) site of SONDRESTROM were acquired to evaluate the performance and validate the accuracy of the proposed method, respectively. The results show that the proposed method can achieve TEC mapping with resolutions of tens of meters, much higher than the tens or hundreds of kilometers of the IRI and IGS TECs. The spatial features of our method-derived TECs show overall good consistency with those of the IRI and IGS TECs, but the described spatial information is more detailed. Also, compared to the original IRI model, the improvement rates of root-mean-square errors (RMSEs) between the estimated electron density and ISR observations exceeded 21.67% after the update using the TEC obtained from the proposed method. These experiments demonstrate the proposed method’s feasibility and reliability for ionospheric TEC mapping.

Assimilating Space‐Based Thermospheric Neutral Density (TND) Data Into the TIE‐GCM Coupled Model During Periods With Low and High Solar Activity

AbstractThe global estimation of Thermospheric Neutral Density (TND) and electron density (Ne) on various altitudes are provided by upper atmosphere models, however, the quality of their forecasts needs to be improved. In this study, we present the impact of assimilating space‐based TNDs, measured along Low Earth Orbit (LEO) mission, into the NCAR Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM). In these experiments, the Ensemble Kalman Filter (EnKF) merger of the Data Assimilation Research Testbed (DART) community software is applied. To cover various space‐based TND data and both low and high solar activity periods, we used the measurements of CHAMP (Challenging Minisatellite Payload) and Swarm‐C as assimilated observations. The TND forecasts are then validated against independent TNDs of GRACE (Gravity Recovery and Climate Experiment mission) and Swarm‐B, respectively. To introduce the impact of the thermosphere on estimating ionospheric parameters, the outputs of Ne are validated against the radio occultation data. The Data Assimilation (DA) results indicate that TIE‐GCM overestimates (underestimates) TND and Ne during low (high) solar activity. Considerable improvements are found in forecasting TNDs after DA, that is, the Root Mean Squared Error (RMSE) is reduced by 79% and 51% during low and high solar activity periods, respectively. The reduction values for Ne are found to be 52.3% and 40.4%, respectively.

Measurement of medium-voltage AC air arc temperature and particle number density based on dual-wavelength Moiré deflection technology

AC air arcs are generated in medium-voltage (MV) power systems under the effect of harsh weather conditions, equipment aging, and high penetration of distributed generation, threatening equipment and public safety. The arc current and temperature are low due to the wide application of arc suppression devices. In this scenario, the MV AC air arc does not satisfy the local thermodynamic equilibrium (LTE) condition. In addition, the repeated arcing and extinguishing processes further complicate the arc discharge mechanism, which bring challenges in the modeling and detection of MV AC air arcs. Experimental methods are a direct and efficient approach to determine the properties of arc plasmas. In this study, a dual-wavelength Moiré deflection diagnostic system was established to determine the time evolution of the particle density and radial distribution of the temperature in an MV AC air arc without relying on the LTE assumption. The electron number density and heavy particle number density change transiently during the arc discharge process and change gradient along the radial direction. The heavy particle temperature and electron temperature were then calculated based on the measured particle number density. During the arcing stage, the temperature of the electrons exceeded that of the heavy particles significantly, and the arc deviated from LTE. Finally, the limitations of the traditional single-wavelength Moiré deflection method are analyzed. The classic single-wavelength Moiré deflection method, while capable of estimating heavy particle temperature in plasma, exhibits a significant error in electron density estimation compared to the dual-wavelength Moiré deflection method.

MV-based relative electron density estimation (iMREDe) for MR-LINAC dose calculation.

MR-LINAC systems have been increasingly utilized for real-time imaging in adaptive treatments worldwide. Challenges in MR representation of air cavities and subsequent estimation of electron density maps impede planning efficiency and may lead to dose calculation uncertainties. To demonstrate the generation of accurate electron density maps using the primary MV beam with a flat-panel imager. The ViewRay MRIdian MR-LINAC system was modeled digitally for Monte Carlo simulations. Iron shimming, the magnetic field, and the proposed flat panel detector were included in the model. The effect of the magnetic field on the detector response was investigated. Acquisition of projections over 360 degrees was simulated for digital phantoms of the Catphan 505 phantom and a patient treated for Head and Neck cancer. Shim patterns on the projections were removed and detector noise linearity was assessed. Electron density maps were generated for the digital patient phantom using the flat-panel detector and compared with actual treatment planning CT generated electron density maps of the same patient. The effect of the magnetic field on the detector point-spread function (PSF) was found to be substantial for field strengths above 50 mT. Shims correction in the projection images using air normalization and in-painting effectively removed reconstruction artifacts without affecting noise linearity. The relative difference between reconstructed electron density maps from the proposed method and electron density maps generated from the treatment planning CT was 11% on average along all slices included in the iMREDe reconstruction. The proposed iMREDe technique demonstrated the feasibility of generating accurate electron densities for the ViewRay MRIdian MR-LINAC system with a flat-panel imager and the primary MV beam. This work is a step towards reducing the time and effort required for adaptive radiotherapy in the current ViewRay MR-LINAC systems.

Assessing the influence of non-thermal plasma treatment on sprouting of mosaic yard long beans (Vigna unguiculata)

This study examined the impact of non-thermal plasma (NTP) treatment on the germination of mosaic yard long beans (MYLB) (Vigna unguiculata). The NTP discharge utilized 5.01 W of power and had an estimated electron density of 2.5 × 1011 cm−3. Optical emission spectra analysis confirmed the generation of nitrogen ions using the dielectric barrier discharge system. Seeds exposed to NTP for varying durations exhibited enhanced germination rates and higher vigor, with the highest percentage observed for 120 s of treatment. Seeds treated for 60 and 120 s displayed faster and more synchronized germination based on the Mean Germination Time and Coefficient of Velocity of Germination values. The NTP treatment resulted in mass loss in the seeds, with the greatest loss occurring after 120 s of treatment. NTP-treated seeds demonstrated improved water uptake capacity compared to untreated seeds. Water contact angle measurements indicated a shift from hydrophobic to hydrophilic behavior in NTP-treated seeds, indicating enhanced surface wettability. Scanning electron microscopy analysis revealed erosion and roughening of the seed coat following NTP treatment. These findings suggest that NTP treatment enhances the germination performance of MYLB by promoting faster and more uniform germination, improving water uptake capacity, and modifying the seed coat surface.

Exploring the influence of the ‘Smiley Sun’ on the dynamics of inner solar corona and near-Earth space environment

ABSTRACT The image captured by SDO/AIA (Solar Dynamics Observatory) in the 193 Å ultraviolet channel from 2022 October 25–27, unveiled a remarkable trio of dark coronal holes near the heliocentric equator, forming a distinctive smiling face. Serendipitously, during that period, coronal radio science experiments were being conducted using the Akatsuki spacecraft to investigate turbulence regimes in the inner-middle corona and track the acceleration of solar wind streams. By analysing Doppler frequency residuals, we derived valuable insights into plasma turbulence characteristics, estimated electron density fluctuations and flow speeds using isotropic quasi-static turbulence methods. The analysis consistently unveiled a shallow turbulence spectrum and flow speeds ranging from 180 to 400 km s−1 at heliocentric distances of 3–9 Rs. During this period, the solar wind flow speed, recorded at the L1 point near Earth, was of the order of 600–650 km s−1. This presented a unique opportunity to delve into turbulence within the inner corona and explore the mechanisms responsible for energizing and accelerating high-speed streams emanating from these trans-equatorial coronal holes. The study also suggests the innovative use of spacecraft signals as radio beacons for enhanced forecasting of potential space weather events triggered by Earth-directed high-speed solar wind streams.

Treatment of azo, direct, and reactive dyes in surface dielectric barrier discharge: Valorization of effluent, the influence of wastewater characteristics, and plasma modeling by Stark broadening technique

The paper demonstrates the versatility of surface dielectric barrier discharge (SDBD) in degrading brilliant red X3B (azo dye), direct yellow 44 (direct dye), and turquoise blue H5G (reactive dye) in textile wastewater. The influence of wastewater characteristics, such as pH (4‐10), background inorganic salts (NaCl, Na2SO4, and Na2CO3), and type of pollutant, on the system performance was studied, and their interactions with •OH were established. Using the Stark broadening technique, the electron density of plasma was analyzed (2.48 × 1015/cm3 at 60 W), demonstrating its suitability for wastewater treatment. Complete degradation of 50 mg/L of brilliant red X3B, direct yellow 44, and turquoise blue H5G was achieved in 24, 32, and 96 min. The corresponding energy yield of 416, 312, and 250 mg/kWh achieved at 60 W indicates the system is energy efficient. Solution pH, background salts, dye type, and molecular size influence degradation efficiency. Alkaline pH enhances reaction rates, while acidic pH reduces reactor performance. Salts such as NaCl, Na2SO4, and Na2CO3 increased degradation time by 1.5‐2.0 times due to the scavenging effect. A simple and reliable strategy was employed to recycle the treated effluent and transform it into a calcium nitrate-based liquid fertilizer. The phytotoxicity studies prove that the final effluent is non-toxic to plants and can significantly enhance seeds' germination by 120–140 % compared to tap water-grown seeds. The study established the application of SDBD in wastewater treatment by electron density estimation by the Stark broadening technique and extensive dye degradation and mineralization studies under various environmental conditions.

Microwave attenuation measurement as a diagnostic method to estimate electron density in planar surface barrier discharge plasma

Microwave attenuation measurement as a diagnostic method to estimate electron density in planar surface barrier discharge plasma

Estimation of electron density, temperature and electrical characterization of silica seeded arc plasma at atmospheric pressure

Plasma technology stands at the forefront of numerous industrial applications, offering versatile solutions from materials processing to aerospace engineering. This study employs a single Langmuir probe technique operating at atmospheric pressure to scrutinize the transformative impact of silica seeding on low-temperature arc plasma. The investigation unveils a dynamic interplay of electrons and ions within the plasma, unveiling key electrical properties. The I–V electrical properties of the arcs plasma before seeding, having a floating voltage of –39 V, demonstrate electron and ion currents for varied probe voltages. The electrons’ density is calculated to be 2.11×1013 m–3, and the electrons’ temperature is at 6.25 eV. The I–V characteristics show a floating potential of about –35 V and –37 V after seeding an arc plasma using silica in the presence of aluminum oxide (2 % by weight) powder and grain, respectively. After seeding, it is discovered that the electron temperature falls to 1.18 eV for powder while 1.16 eV for grain and electron density rises to 2×1016 m–3 for powder and 1.84×1016 m–3 for grain. In addition, a notable fall in electron temperature and a discernible rise in electron density are seen. This non-equilibrium behavior is related to silica’s catalytic function, which is enhanced by the presence of aluminum oxide. Additionally, increased ionizing activity brought on by inelastic electron collisions causes the electron temperatures in the silica-seeded arcs plasma to rise with discharge voltage. These findings can be essential for enhancing plasma-based technologies in a variety of industrial applications because they provide insightful information on how silica seeding affects arc plasma properties

Spectroscopic Diagnostic of Laser-Induced Zn Plasma

The sample's physical characteristics and laser parameters impact the generation and characterization of Laser-Induced Plasma (LIP), which is a relevant phenomenon in many applications. We investigated the effect of laser energy on laser-induced Zn plasma characterization in this study. A Zn plasma with a repeating frequency of 6 Hz, a first wavelength of 1064 nm, a pulse duration of 10 ns, and a laser energy range of 300 mJ to 500 mJ was created using a Q-switched ND: YAG laser. The basic plasma properties, such as electron temperature and density, were estimated using optical emission spectroscopy (OES). The electrons' temperature was measured by the Boltzmann plot method, and the value of the electrons' temperature ranged from 1.6 eV to 2.051 eV in the laser energy range (300-500) mJ. In electron density estimation using the Stark broadening methods, the density value range from 12.75×1017 cm-3 to 19.50×1017 cm-3, in laser energy range (300-500 ) mJ. In addition, various plasma characteristics such as plasma frequency (fp), the number of particles in the Debye sphere (ND), and Debye length (λD) were estimated. We found that laser energy affects every plasma parameter.

Effect of Working Gas and Applied Voltage on the Estimation of Power and Electron Density in Gliding Arc Discharge (GAD) System

Abstract: Atmospheric pressure gliding arc plasma is generated by a 50 Hz (0-13 kV) AC power supply. The electrical properties of the produced plasma are investigated with the help of an oscilloscope. In this work, the relationship between applied voltage, breakdown voltage, and discharge current is studied for air, argon, oxygen, and nitrogen gases. Similarly, the effect of the nature of gases on breakdown voltage and discharge current is studied. The power consumed by the discharge for different gases is obtained by current-voltage characteristics. It is found that among air, nitrogen, argon, and oxygen, argon consumes minimum and nitrogen consumes maximum power. Specifically, at the maximum applied voltage of 10.2 kV, oxygen and nitrogen consume approximately 56-57% more power than argon. Electron density, one of the most essential plasma parameters, is evaluated and compared using an electrical approach for several fading gases. The electron density is found to be increasing with the increase in applied voltage, and the value of electron density is found to be larger in argon discharge. Keywords: Gliding arc discharge, I–V characteristics, Power consumption, Discharge voltage, Electron density.

Use of electrical measurements for non-invasive estimation of plasma electron density in the inductively coupled SPIDER ion source

SPIDER (source for the production of ions of deuterium extracted from RF plasma) is the full-scale prototype of the ITER neutral beam injector ion source. The plasma heating takes place inside eight drivers via inductive coupling, through the radiofrequency (RF) coil. To achieve optimum conditions during source operation it is necessary to know the plasma behavior under various operational conditions. One of the essential parameters is the plasma electron density. It is possible to experimentally measure this parameter and, currently, different methods are being explored, such as the estimations coming from a Langmuir probe and optical emission spectroscopy. However, these methods are either available for temporary measurements or require dedicated analyses with large uncertainties. In this regard, alternative, reliable, and fast diagnostic tools will be beneficial for the estimation of the order of magnitude of electron density inside the driver. Two models for the estimation of electron density are recalled, discussed, and further modified in this work: one is based on the classical power balance equation, and the other is recently described in the literature and relies on classical plasma conductivity. Both models use equivalent electrical parameters of the driver derived from available electrical measurements at the output of the RF generator and through the knowledge of the matching network and the transmission line length. This work explicitly focuses on the application of these models to estimate the plasma electron density in a single driver of SPIDER. Furthermore, the estimations are compared with the first experimental results obtained from temporary electrostatic probe measurements and are found to be in good agreement in terms of magnitude and trends.

A JWST/NIRSpec Exploration of the Connection between Ionization Parameter, Electron Density, and Star-formation-rate Surface Density in z = 2.7–6.3 Galaxies

We examine the factors responsible for the variation in the ionization parameter (U) of high-redshift star-forming galaxies based on medium-resolution JWST/NIRSpec observations obtained by the Cosmic Evolution Early Release Science survey. The sample consists of 48 galaxies with redshifts z spec = 2.7−6.3, which are largely representative of typical galaxies at these redshifts. The [S ii] λ λ6718, 6733 doublet is used to estimate electron densities (n e ), and dust-corrected Hα luminosities are used to compute ionizing photon rates (Q). Using composite spectra of galaxies in bins of [O iii] λ λ4960, 5008/[O ii] λ λ3727, 3730 (O32) as a proxy for U, we determine that galaxies with higher O32 have 〈n e 〉 ≃ 500 cm−3 that are ≳5 × larger than that of lower-O32 galaxies. We do not find a significant difference in 〈Q〉 between low- and high-O32 galaxies. Photoionization modeling indicates a large spread in of ≈1.5 dex at a fixed Z neb. On the other hand, the data indicate a highly significant correlation between U and star-formation-rate surface density (ΣSFR), which appears to be redshift invariant at z ∼ 1.6−6.3, and possibly up to z ∼ 9.5. We consider several avenues through which metallicity and ΣSFR (or gas density) may influence U, including variations in n e and Q, internal dust extinction of ionizing photons, and the effects of gas density on the volume filling fraction. Based on these considerations, we conclude that gas density may play a more central role than metallicity in modulating U at these redshifts.