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At least 145 records · Page 8

Evaluating Mean State Cloud Properties in the Simple Cloud‐Resolving E3SM Atmosphere Model (SCREAM)

Accurately simulating clouds remains a key challenge in global climate models, primarily because cloud formation involves sub-grid processes that are parameterized and crudely represented in models. This study examines the performance of DOE's Simple Cloud-Resolving Energy Exascale Earth System (E3SM) Atmosphere Model (SCREAM) in simulating cloud properties and their spatio-temporal distribution by comparing against satellite observations. Two horizontal resolutions of SCREAM (3 and 12 km) are examined, and both depict a realistic spatial structure of mean-state cloud cover but underestimate its global mean magnitude. SCREAM 3 km reasonably reproduces the distribution of mean-state cloud properties across various cloud optical thickness and cloud-top pressure regimes, with performance comparable to CMIP5 and CMIP6 ensemble and marginally outperforming SCREAM 12 km. Still, SCREAM 3 km tends to underpredict low clouds and optically thin clouds, highlighting the need for continued improvement in representing unresolved processes. This study provides a basis for confidence in the representation of clouds in SCREAM, as simulating mean-state clouds is a necessary prerequisite for trusting its cloud responses to changes in aerosols and greenhouse gases.

Geosciences↗

Climatology Perspective of Sensitive Regimes and Active Regions of Aerosol Indirect Effect for Cirrus Clouds over the Global Oceans

Long-term satellite climate data records (CDRs) of clouds and aerosols are used to investigate the aerosol indirect effect (AIE) of cirrus clouds over the global oceans from a climatology perspective. Our study focuses on identifying the sensitive regimes and active regions where AIE signatures easily manifest themselves in the sense of the long-term average of cloud and aerosol variables. The aerosol index (AIX) regimes of AIX < 0.18 and 0.18 < AIX < 0.46 are respectively identified as the sensitive regimes for negative and positive aerosol albedos and lifetime effects of cirrus clouds. Relative humidity first decreases (along with upward motions) and then reverses to increase (along with downward motions) in the first regime of negative aerosol albedo and lifetime effects. Relatively wet and strong upward motions are the favorable meteorological conditions for the second regime of positive aerosol albedo and lifetime effects. Two swath regions extending from 15°N to 30°N over the east coastal oceans of China and the USA are the active regions of positive aerosol albedo effects. Positive aerosol lifetime effects are only active or easy to manifest in the regions where a positive aerosol albedo effect is active. The results based on the long-term averaged satellite observations are valuable for the evaluation and improvement of aerosol-cloud interactions for cirrus clouds in global climate models.

54 ENVIRONMENTAL SCIENCES↗

CoURAGE KAZR b1 Processing: Corrections, Calibrations, and Processing Report

The U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) User Facility supports atmospheric and earth system research through a comprehensive network of fixed and mobile observatories. These facilities provide long-term and intensive campaign-based observations of clouds, aerosols, precipitation, radiation, and meteorological state variables. ARM observations are designed to improve the physical understanding and numerical representation of atmospheric processes in earth system models, with particular emphasis on cloud-radiation interactions and precipitation processes. The Coast-Urban-Rural Atmospheric Gradient Experiment (CoURAGE) deploys one of the ARM Mobile Facilities (AMF) to the Mid-Atlantic region surrounding Baltimore, Maryland, for the period 1 December 2024 through 30 November 2025. This deployment focuses on characterizing atmospheric structure, cloud properties, and precipitation processes across strong land-use and surface heterogeneity gradients associated with urban, rural, and coastal (Chesapeake Bay) environments. The CoURAGE deployment complements the Baltimore Social-Environmental Collaborative (BSEC), a DOE Urban Integrated Field Laboratory (UIFL), by providing high-quality atmospheric observations needed to connect urban surface processes, emissions, and meteorology to cloud and precipitation responses. In addition to the central urban site, ancillary observing sites were deployed to rural Maryland northwest of Baltimore and to an island site in Chesapeake Bay. These measurements further complement a long-term atmospheric observatory operated in Beltsville, Maryland, by Howard University in collaboration with the Maryland Department of the Environment. Together, these assets form a four-node regional atmospheric observatory network representing Baltimore and its three primary surrounding environments—urban, rural, and coastal/bay. This coordinated observational strategy enables investigation of spatial gradients in boundary-layer structure, cloud occurrence, precipitation evolution, and aerosol-cloud interactions across complex surface regimes. Within this network, vertically pointing cloud radars play a critical role by providing continuous, high-resolution measurements of cloud and precipitation vertical structure.

54 ENVIRONMENTAL SCIENCES↗

The ENSO Effects on Tropical Clouds and Top-of-Atmosphere Cloud Radiative Effects in CMIP5 Models

The El Nino-Southern Oscillation (ENSO) effects on tropical clouds and top-of-atmosphere (TOA) cloud radiative effects (CREs) in Coupled Model Intercomparison Project Phase5 (CMIP5) models are evaluated using satellite-based observations and International Satellite Cloud Climatology Project satellite simulator output. Climatologically, most CMIP5 models produce considerably less total cloud amount with higher cloud top and notably larger reflectivity than observations in tropical Indo-Pacific (60 degrees East - 200 degrees East; 10 degrees South - 10 degrees North). During ENSO, most CMIP5 models considerably underestimate TOA CRE and cloud changes over western tropical Pacific. Over central tropical Pacific, while the multi-model mean resembles observations in TOA CRE and cloud amount anomalies, it notably overestimates cloud top pressure (CTP) decreases; there are also substantial inter-model variations. The relative effects of changes in cloud properties, temperature and humidity on TOA CRE anomalies during ENSO in the CMIP5 models are assessed using cloud radiative kernels. The CMIP5 models agree with observations in that their TOA shortwave CRE anomalies are primarily contributed by total cloud amount changes, and their TOA longwave CRE anomalies are mostly contributed by changes in both total cloud amount and CTP. The model biases in TOA CRE anomalies particularly the strong underestimations over western tropical Pacific are, however, mainly explained by model biases in CTP and cloud optical thickness (tau) changes. Despite the distinct model cloud biases particularly in tau regime, the TOA CRE anomalies from cloud amount changes are comparable between the CMIP5 models and observations, because of the strong compensations between model underestimation of TOA CRE anomalies from thin clouds and overestimation from medium and thick clouds.

Su, Wenying↗

Ice in Convective Storm Environments: Assessing Impacts of Microphysics on Simulated Reflectivities

Satellite radar retrievals of clouds and precipitation rely on assumptions about the microphysical properties of hydrometeors such as particle size distributions (PSDs) and massdimensional relationships, which have been shown to vary in distinct environments. A deeper understanding of linkages between mass-dimensional relationships, ice crystal shape, and radar reflectivities across cloud and precipitation regimes is necessary for developing new retrievals for upcoming satellite radar missions, including the INvestigation of Convective UpdraftS (INCUS), as well as future missions that will feature space-borne radars observing clouds, convection, and precipitation. This study investigates ice microphysical characteristics through aircraft in-situ and remote sensing observations from two convective events during the Mid-latitude Continental Convective Clouds Experiment (MC3E) in the Southern Great Plains, and tests implications for ice particle habit in forward modeled radar observations. During MC3E, the Ka/Ku- band High Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) was onboard the NASA ER-2 aircraft, while in-situ measurements were taken onboard the University of North Dakota Citation. In-situ PSDs and particle shape information from optical array probe data are used to forward model radar reflectivities from particle scattering databases and are compared against HIWRAP reflectivities. Various particle combinations can be used to find agreement with HIWRAP observations, and the forward modeled reflectivities were sensitive to particle type. Varying the riming on the aggregate and graupel particles resulted in larger than 10 dB differences in reflectivities. The in-situ and radar observations imply the occurrence of aggregation, size sorting and lofting particles.

Julia A. Shates↗

How Difficult is it to Reduce Low-Level Cloud Biases With the Higher-Order Turbulence Closure Approach in Climate Models?

Low-level clouds cover nearly half of the Earth and play a critical role in regulating the energy and hydrological cycle. Despite the fact that a great effort has been put to advance the modeling and observational capability in recent years, low-level clouds remains one of the largest uncertainties in the projection of future climate change. Low-level cloud feedbacks dominate the uncertainty in the total cloud feedback in climate sensitivity and projection studies. These clouds are notoriously difficult to simulate in climate models due to its complicated interactions with aerosols, cloud microphysics, boundary-layer turbulence and cloud dynamics. The biases in both low cloud coverage/water content and cloud radiative effects (CREs) remain large. A simultaneous reduction in both cloud and CRE biases remains elusive. This presentation first reviews the effort of implementing the higher-order turbulence closure (HOC) approach to representing subgrid-scale turbulence and low-level cloud processes in climate models. There are two HOCs that have been implemented in climate models. They differ in how many three-order moments are used. The CLUBB are implemented in both CAM5 and GDFL models, which are compared with IPHOC that is implemented in CAM5 by our group. IPHOC uses three third-order moments while CLUBB only uses one third-order moment while both use a joint double-Gaussian distribution to represent the subgrid-scale variability. Despite that HOC is more physically consistent and produces more realistic low-cloud geographic distributions and transitions between cumulus and stratocumulus regimes, GCMs with traditional cloud parameterizations outperform in CREs because tuning of this type of models is more extensively performed than those with HOCs. We perform several tuning experiments with CAM5 implemented with IPHOC in an attempt to produce the nearly balanced global radiative budgets without deteriorating the low-cloud simulation. One of the issues in CAM5-IPHOC is that cloud water content is much higher than in CAM5, which is combined with higher low-cloud coverage to produce larger shortwave CREs in some low-cloud prevailing regions. Thus, the cloud-radiative feedbacks are exaggerated there. The turning exercise is focused on microphysical parameters, which are also commonly used for tuning in climate models. The results will be discussed in this presentation.

Xu, Kuan-Man↗

Sources of stochasticity in the growth of cloud droplets: supersaturation fluctuations versus turbulent transport

The role played by fluctuations of supersaturation in the growth of cloud droplets is examined in this study. The stochastic condensation framework and the three regimes of activation of cloud droplets – namely, mean-dominant, fluctuation-influenced, and fluctuation-dominant, are used for analyzing the data from high-resolution large-eddy simulations of the Pi convection-cloud chamber. Based on a detailed budget analysis the significance of all the terms in the evolution of the droplet size distribution equation is evaluated in all three regimes. The analysis indicates that the mean-growth rate is a dominant process in shaping the droplet size distribution in all three regimes. Turbulence introduces two sources of stochasticity, turbulent transport and particle lifetime, and supersaturation fluctuations. The transport of cloud droplets plays an important role in all three regimes, whereas the direct effect of supersaturation fluctuations is primarily related to the activation and growth of the small droplets in the fluctuation-influenced and fluctuation-dominant regimes. Here, we compare our results against the previous studies (experimental and theory) of the Pi chamber, and discuss the limitations of the existing models based on the stochastic condensation framework. Furthermore, we extend the discussion of our results to atmospheric clouds, and in particular focus on recent adiabatic turbulent cloud parcel simulations based on the stochastic condensation framework, and emphasize the importance of entrainment/mixing and turbulent transport in shaping the droplet size distribution.

54 ENVIRONMENTAL SCIENCES↗

The Green Ocean Over the Amazon: Implications for Cloud Electrification

A convective regime with distinct maritime characteristics (weak updraft, low CCN, prevalent coalescence and rainout, weak mixed phase reflectivity, low glaciation temperature, and little if any lightning) is documented over the Amazon basin of the South American continent, and dubbed the "green ocean". Radar, lightning, thermodynamic and AVHRR satellite observations are examined to shed light on the roles of updraft and aerosol in providing departures from the green ocean regime toward continental behavior. Extreme case studies are identified in which the updraft control is dominant and in which the aerosol control is dominant. The tentative conclusion gives importance to both updrafts and aerosol in shaping the electrification of tropical convection.

Williams, E.↗

Tracking the Large-scale Tropical Convective Systems and MJO Modulation

Science questions that motivate us − How well do Cloud-Precipitation Hybrid Regimes identify tropical convective systems? − Can we examine the life cycle of convective systems using the hybrid regimes? − What are the effects of MJO on the evolution of convective systems?

tropical convective systems↗

Low-Level Liquid-Bearing Clouds Contribute to Seasonal Lower Atmosphere Stability and Surface Energy Forcing over a High-Mountain Watershed Environment

Measurements of atmospheric structure and surface energy budgets distributed along a high-altitude moun tain watershed environment near Crested Butte, Colorado, from two separate, but coordinated, field campaigns, Surface Atmosphere Integrated field Laboratory (SAIL) and Study of Precipitation, the Lower Atmosphere, and Surface for Hydrometeorology (SPLASH), are analyzed. This study identifies similarities and differences in how clouds influence the radiative budget over one snow-free summer season (2022) and two snow-covered seasons (2021/22; 2022/23) for this alpine location. A relationship between lower-tropospheric stability stratification and longwave radiative flux from the presence or absence of clouds is identified. When low clouds persisted, often with signatures of supercooled liquid in win ter, the lower troposphere experienced weaker stability, while radiatively clear skies that are less likely to be influenced by liquid droplets were associated with appreciably stronger lower-tropospheric stratification. Corresponding surface turbu lent heat fluxes partitioned differently based upon the cloud–stability stratification regime derived from early morning radiosounding profiles. Combined with the differences in the radiative budget largely resulting from dramatic seasonal dif ferences in surface albedo, the lower atmosphere stratification, surface energy budget, and near-surface thermodynamics are shown to be modified by the effective longwave radiative forcing of clouds. The diurnal evolution of thermodynamics and surface energy components varied depending on the early morning stratification state. Thus, the importance of quies cent versus synoptically active large-scale meteorology is hypothesized as a critical forcing for cloud properties and associ ated surface energy budget variations. The physical relationships between clouds, radiation, and stratification can provide a useful suite of metrics for process understanding and to evaluate numerical models in such an undersampled, highly com plex terrain environment.

54 ENVIRONMENTAL SCIENCES↗

Cloud Morphology Evolution in Arctic Cold‐Air Outbreak: Two Cases During COMBLE Period

Abstract Cloud feedbacks play an important role in Arctic warming. Cloud morphology, for example, cloud size and spatial distributions, is among key factors that directly impact their radiative effects. In this work, we use two cases observed during the Cold‐air Outbreak (CAO) in the Marine Boundary Layer Experiment (COMBLE) to study the evolution of cloud size distributions as an air mass is advected from the Arctic over a comparatively warm ocean and cloud mesoscale organization changes from rolls to cells. Cloud objects are identified from Moderate Resolution Imaging Spectroradiometer (MODIS) reflectance images through an object segmentation procedure and roll breakup is identified by homogeneities in cloud water path (CWP). Roll breakup is found to be accompanied by a local minimum in wind shear and local maxima in cloud size and marine cold air outbreak index. The mean cloud horizontal aspect ratio has weak fetch dependency and is around 2 in roll, transition, and cell regimes. Regardless of distance from the ice edge, smaller clouds (<10 km 2 ) dominate the population number but not cloud cover. Cloud size distributions show bimodality in transition and cell regimes. For clouds with comparable sizes, mean nearest neighbor distances normalized by equivalent cloud radius converge to a single value for all regimes and for all but the smallest clouds, suggesting that clouds of comparable sizes in CAOs are separated by distance proportional to their sizes. The presented statistical results pave the way to evaluating model simulated cloud organizations during CAO events.

54 ENVIRONMENTAL SCIENCES↗

A high spectral resolution VLA search for H I absorption towards A496, A1795, and A2584

In this paper, we present the results of a Very Large Array (VLA) search for H I absorption with high spectral resolution (1.6 km/s) towards A496, A1795, A2584, and A2597. These observations are well matched to the properties of cold, optically thick H I clouds, where the line width is given by the width of an individual cloud rather than the dispersion in an ensemble of clouds. We do not detect any H I absorption with narrow linewidths in these clusters. Our limits mainly apply to clouds which are larger than a few tenths parsec-i.e., if the clouds are much smaller than the background radio source and have a low covering factor in velocity space, they could still escape detection. The estimated limits on column density (for clouds in this regime of parameter space) are 2-3 orders of magnitude less than the 10(exp 21)/sq cm required to explain the x-ray absorption seen in some cooling flow clusters. The combination of our high spectral resolution H I absorption searches with the existing lower spectral resolution H I absorption searches and the searches for H I emission makes it unlikely that atomic hydrogen is the dominant component of the cold x-ray absorbing gas in the inter-cloud medium (ICM).

O'Dea, Christopher P.↗

Pivotal Role of Cloud‐Planetary Boundary Layer Coupling to Explain Contrasting Aerosol‐Cloud Relationships

The radiative effect of aerosol on cloud albedo via altering cloud droplet effective radius (r e ) is a major uncertainty in the Earth's climate system. Remote sensing studies have reported either negative or positive relationships between re and aerosol number concentration (N a ) or other aerosol proxies. However, there are much fewer in situ observational evidences and physical explanation remains elusive for the contrasting N a -r e relationships. Here we quantify the N a -r e relationship by using in situ aircraft measurements, together with a re decomposition method. Our analysis reveals that the cloud-planetary boundary layer (PBL) coupling plays a pivotal role on the N a -r e relationship. Quantitative r e decomposition indicates that the contrasting N a -r e relationships in two cloud-PBL coupling regimes result from different balances of four distinct aspects. The widely recognized number effect may be outweighed by the joint effects of the remaining three that have been rarely investigated and largely ignored in N a -r e parameterizations.

54 ENVIRONMENTAL SCIENCES↗

Crowdsourcing the Frontier: Advancing Hybrid Physics‐ML Climate Simulation via a $\$$50,000 Kaggle Competition

Subgrid machine-learning (machine learning [ML]) parameterizations have the potential to introduce a new generation of climate models that incorporate the effects of higher-resolution physics without incurring the prohibitive computational cost associated with more explicit physics-based simulations. However, important issues, ranging from online instability to inconsistent online performance, have limited their operational use for long-term climate projections. To more rapidly drive progress in solving these issues, domain scientists and ML researchers opened up the offline aspect of this problem to the broader ML and data science community with the release of ClimSim, a NeurIPS Data sets and Benchmarks publication, and an associated Kaggle competition. This paper reports on the downstream results of the Kaggle competition by coupling emulators inspired by the winning teams' architectures to an interactive climate model (including full cloud microphysics, a regime historically prone to online instability) and systematically evaluating their online performance. Our results demonstrate that online stability in the low-resolution real-geography setting is reproducible across multiple diverse architectures, which we consider a key milestone. All tested architectures exhibit strikingly similar offline and online biases, though their responses to architecture-agnostic design choices (e.g., expanding the list of input variables) can differ significantly. Multiple Kaggle-inspired architectures achieve state-of-the-art results on certain metrics such as zonal mean bias patterns and global Root Mean Squared Error, indicating that crowdsourcing the essence of the offline problem is one path to improving online performance in hybrid physics-AI climate simulation.

Environmental sciences↗

X-ray phase contrast and absorption imaging for the quantification of transient cavitation in high-speed nozzle flows

In this work, high-flux synchrotron radiation has been employed in a time-resolved manner to characterise the distinct topology features and dynamics of different cavitation regimes arising in a throttle orifice with an abrupt flow-entry contraction. Radiographs obtained though both X-ray phase- contrast and absorption imaging have been captured at 67,890 frames per second. The flow lied in the turbulent regime (Re=35,500), while moderate (CN=2.0) to well-established (CN=6.0) cavitation conditions were examined encompassing the cloud and vortical cavitation regimes with pertinent transient features, such as cloud-cavity shedding. X-ray Phase-Contrast Imaging (XPCI), exploiting the shift in the X-ray wave phase during interactions with matter, offers sharp-refractive index gradients in the interface region. Hence, it is suitable for capturing fine morphological fluctuations of transient cavitation structures. Nevertheless, the technique cannot provide information on the quantity of vapour within the orifice. Such data have been obtained utilising absorption imaging, where beam attenuation is not associated with scattering and refraction events, and hence can be explicitly correlated with the projected vapour thickness in line-of-sight measurements. A combination of the two methods is proposed, as it has been found is capable of quantifying the vapour content arising in the complex nozzle flow, while also faithfully illustrating the dynamics of the highly-transient cavitation features.

42 ENGINEERING↗

Droplet Growth or Evaporation Does Not Buffer the Variability in Supersaturation in Clean Clouds

Abstract Water vapor supersaturation in clouds is a random variable that drives activation and growth of cloud droplets. The Pi Convection–Cloud Chamber generates a turbulent cloud with a microphysical steady state that can be varied from clean to polluted by adjusting the aerosol injection rate. The supersaturation distribution and its moments, e.g., mean and variance, are investigated for varying cloud microphysical conditions. High-speed and collocated Eulerian measurements of temperature and water vapor concentration are combined to obtain the temporally resolved supersaturation distribution. This allows quantification of the contributions of variances and covariances between water vapor and temperature. Results are consistent with expectations for a convection chamber, with strong correlation between water vapor and temperature; departures from ideal behavior can be explained as resulting from dry regions on the warm boundary, analogous to entrainment. The saturation ratio distribution is measured under conditions that show monotonic increase of liquid water content and decrease of mean droplet diameter with increasing aerosol injection rate. The change in liquid water content is proportional to the change in water vapor concentration between no-cloud and cloudy conditions. Variability in the supersaturation remains even after cloud droplets are formed, and no significant buffering is observed. Results are interpreted in terms of a cloud microphysical Damköhler number (Da), under conditions corresponding to , i.e., the slow-microphysics regime. This implies that clouds with very clean regions, such that is satisfied, will experience supersaturation fluctuations without them being buffered by cloud droplet growth. Significance Statement The saturation ratio (humidity) in clouds controls the growth rate and formation of cloud droplets. When air in a turbulent cloud mixes, the humidity varies in space and time throughout the cloud. This is important because it means cloud droplets experience different growth histories, thereby resulting in broader size distributions. It is often assumed that growth and evaporation of cloud droplets buffers out some of the humidity variations. Measuring these variations has been difficult, especially in the field. The purpose of this study is to measure the saturation ratio distribution in clouds with a range of conditions. We measure the in-cloud saturation ratio using a convection cloud chamber with clean to polluted cloud properties. We found in clouds with low concentrations of droplets that the variations in the saturation ratio are not suppressed.

54 ENVIRONMENTAL SCIENCES↗

Understanding changes in cloud simulations from E3SM version 1 to version 2

Abstract. This study documents clouds simulated by the Energy Exascale Earth System Model (E3SM) version 2 (E3SMv2) and attempts to understand what causes the model behavior change in clouds relative to E3SMv1. This is done by analyzing the last 30-year (1985–2014) data from the 165-year historical simulations using E3SMv1 and v2 and four sensitivity tests to isolate the impact of changes in model parameter choices in its turbulence, shallow convection, and cloud macrophysics parameterization (Cloud Layers Unified By Binormals, CLUBB); microphysical parameterization (MG2); and deep-convection scheme (ZM), as well as model physics changes in convective triggering. It is shown that E3SMv2 significantly improves the simulation of subtropical coastal stratocumulus clouds and clouds with optical depth larger than 3.6 over the stratocumulus-to-cumulus transition regimes, where the shortwave cloud radiative effect (SWCRE) is also improved, and the Southern Ocean (SO) while seeing an overall slight degradation in low clouds over other tropical and subtropical oceans. The better performance in E3SMv1 over those regions is partially due to error compensation between its simulated optically thin and intermediate low clouds for which E3SMv2 actually improves simulation of optically intermediate low clouds. Sensitivity tests indicate that the changes in low clouds are primarily due to the tuning done in CLUBB. The impact of the ZM tuning is mainly on optically intermediate and thick high clouds, contributing to an improved SWCRE and longwave cloud radiative effect (LWCRE). The impact of the MG2 tuning and the new convective trigger is primarily on the high latitudes and the SO. They have a relatively smaller impact on clouds than CLUBB tuning and ZM tuning do. This study offers additional insights into clouds simulated in E3SMv2 by utilizing multiple data sets and the Cloud Feedback Model Intercomparison Project (CFMIP) Observation Simulator Package (COSP) diagnostic tool as well as sensitivity tests. The improved understanding will benefit future E3SM developments.

58 GEOSCIENCES↗

Experimental Investigation of Electron Cloud Containment in a Nonuniform Magnetic Field

Dense clouds of electrons were generated and studied in an axisymmetric, nonuniform magnetic field created by a short solenoid. The operation of the experiment was similar to that of a low-pressure (approximately 0.000001 Torr) magnetron discharge. Discharge current characteristics are presented as a function of pressure, magnetic field strength, voltage, and cathode end-plate location. The rotation of the electron cloud is determined from the frequency of diocotron waves. In the space charge saturated regime of operation, the cloud is found to rotate as a solid body with frequency close to V sub a/phi sub a where V sub a is the anode voltage and phi suba is the total magnetic flux. This result indicates that, in regions where electrons are present, the magnetic field lines are electrostatic equipotentials (E bar, B bar = 0). Equilibrium electron density distributions suggested by this conditions are integrated with respect to total ionizing power and are found consistent with measured discharge currents.

Eninger, J. E.↗