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NASA NTRS2001

ESTAR Measurements During the Southern Great Plains Experiment (SGP99)

During the Southern Great Plains experiment, the synthetic aperture radiometer, ESTAR, mapped L-band brightness temperature over a swath about 50 km wide and about 300 km long extending west from Oklahoma City to El Reno and north from the Little Washita River watershed to the Kansas border. ESTAR flew on the NASA P-3B Orion aircraft at an altitude of 7.6 km and maps were made on 7 days between July 8-20, 1999. The brightness temperature maps reflect the patterns of soil moisture expected from rainfall and are consistent with values of soil moisture observed at the research sites within the SGP99 study area and with previous measurements in this area. The data add to the resources for hydrologic modeling in this area and are further validation of the technology represented by ESTAR as a potential path to a future mission to map soil moisture globally from space.

LeVine, D. M.↗
NASA NTRS2003

Long-Range Solar Activity Predictions: A Reprieve from Cycle #24's Activity

We discuss the field of long-range solar activity predictions and provide an outlook into future solar activity. Orbital predictions for satellites in Low Earth Orbit (LEO) depend strongly on exospheric densities. Solar activity forecasting is important in this regard, as the solar ultra-violet (UV) and extreme ultraviolet (EUV) radiations inflate the upper atmospheric layers of the Earth, forming the exosphere in which satellites orbit. Rather than concentrate on statistical, or numerical methods, we utilize a class of techniques (precursor methods) which is founded in physical theory. The geomagnetic precursor method was originally developed by the Russian geophysicist, Ohl, using geomagnetic observations to predict future solar activity. It was later extended to solar observations, and placed within the context of physical theory, namely the workings of the Sun s Babcock dynamo. We later expanded the prediction methods with a SOlar Dynamo Amplitude (SODA) index. The SODA index is a measure of the buried solar magnetic flux, using toroidal and poloidal field components. It allows one to predict future solar activity during any phase of the solar cycle, whereas previously, one was restricted to making predictions only at solar minimum. We are encouraged that solar cycle #23's behavior fell closely along our predicted curve, peaking near 192, comparable to the Schatten, Myers and Sofia (1996) forecast of 182+/-30. Cycle #23 extends from 1996 through approximately 2006 or 2007, with cycle #24 starting thereafter. We discuss the current forecast of solar cycle #24, (2006-2016), with a predicted smoothed F10.7 radio flux of 142+/-28 (1-sigma errors). This, we believe, represents a reprieve, in terms of reduced fuel costs, etc., for new satellites to be launched or old satellites (requiring reboosting) which have been placed in LEO. By monitoring the Sun s most deeply rooted magnetic fields; long-range solar activity can be predicted. Although a degree of uncertainty in the long-range predictions remains, requiring future monitoring, we do not expect the next cycle's + 2-sigma value will rise significantly above solar cycle #23's activity level.

Richon, K.↗
NASA NTRS2012

A New Method to Constrain Supernova Fractions Using X-ray Observations of Clusters of Galaxies

Supernova (SN) explosions enrich the intracluster medium (ICM) both by creating and dispersing metals. We introduce a method to measure the number of SNe and relative contribution of Type Ia supernovae (SNe Ia) and core-collapse supernovae (SNe cc) by directly fitting X-ray spectral observations. The method has been implemented as an XSPEC model called snapec. snapec utilizes a single-temperature thermal plasma code (apec) to model the spectral emission based on metal abundances calculated using the latest SN yields from SN Ia and SN cc explosion models. This approach provides a self-consistent single set of uncertainties on the total number of SN explosions and relative fraction of SN types in the ICM over the cluster lifetime by directly allowing these parameters to be determined by SN yields provided by simulations. We apply our approach to XMM-Newton European Photon Imaging Camera (EPIC), Reflection Grating Spectrometer (RGS), and 200 ks simulated Astro-H observations of a cooling flow cluster, A3112.We find that various sets of SN yields present in the literature produce an acceptable fit to the EPIC and RGS spectra of A3112. We infer that 30.3% plus or minus 5.4% to 37.1% plus or minus 7.1% of the total SN explosions are SNe Ia, and the total number of SN explosions required to create the observed metals is in the range of (1.06 plus or minus 0.34) x 10(exp 9), to (1.28 plus or minus 0.43) x 10(exp 9), fromsnapec fits to RGS spectra. These values may be compared to the enrichment expected based on well-established empirically measured SN rates per star formed. The proportions of SNe Ia and SNe cc inferred to have enriched the ICM in the inner 52 kiloparsecs of A3112 is consistent with these specific rates, if one applies a correction for the metals locked up in stars. At the same time, the inferred level of SN enrichment corresponds to a star-to-gas mass ratio that is several times greater than the 10% estimated globally for clusters in the A3112 mass range.

Observations↗
NASA NTRS2013

Real-Time Minimization of Tracking Error for Aircraft Systems

This technology presents a novel, stable, discrete-time adaptive law for flight control in a Direct adaptive control (DAC) framework. Where errors are not present, the original control design has been tuned for optimal performance. Adaptive control works towards achieving nominal performance whenever the design has modeling uncertainties/errors or when the vehicle suffers substantial flight configuration change. The baseline controller uses dynamic inversion with proportional-integral augmentation. On-line adaptation of this control law is achieved by providing a parameterized augmentation signal to a dynamic inversion block. The parameters of this augmentation signal are updated to achieve the nominal desired error dynamics. If the system senses that at least one aircraft component is experiencing an excursion and the return of this component value toward its reference value is not proceeding according to the expected controller characteristics, then the neural network (NN) modeling of aircraft operation may be changed.

Garud, Sumedha↗
NASA NTRS1990

A statistical study of merging galaxies: Theory and observations

A study of the expected frequency of merging galaxies is conducted, using the impulsive approximation. Results indicate that if we consider mergers involving galaxy pairs without halos in a single crossing time or orbital period, the expected frequency of mergers is two orders of magnitude below the observed value for the present epoch. If we consider mergers involving several orbital periods or crossing times, the expected frequency goes up by an order of magnitude. Preliminary calculation indicate that if we consider galaxy mergers between pairs with massive halos, the merger is very much hastened.

Chatterjee, Tapan K.↗
NASA NTRS1990

Electrochemical impedance spectroscopy of metal alloys in the space transportation system launch environment

AC impedance measurements were performed to investigate the corrosion resistance of 18 alloys under conditions similar to the Space Transportation System (STS) launch environment. The alloys were: (1) zirconium 702; (2) Hastelloy C-22, C-276, C-4, and B-2; (3) Inconel 600 and 825; (4) Ferralium 255; (5) Inco Alloy G-3; (6) 20Cb-3; (7) SS 904L, 304LN, 316L, 317L, and 304L; (8) ES 2205; and (9) Monel 400. AC impedance data were gathered for each alloy at various immersion times in 3.55 percent NaCl-0.1N HCl. Polarization resistance values were obtained for the Nyguist plots at each immersion time using the EQUIVALENT CIRCUIT software package available with the 388 electrochemical impedance software. Hastelloy C-22 showed the highest overall values for polarization resistance while Monel 400 and Inconel 600 had the lowest overall values. There was good general correlation between the corrosion performance of the alloys at the beach corrosion testing site, and the expected rate of corrosion as predicted based on the polarization resistance values obtained. The data indicate that electrochemical impedance spectroscopy can be used to predict the corrosion performance of metal alloys.

Calle, Luz↗
NASA NTRS2000

The Life Cycle Application of Intelligent Software Modeling for the First Materials Science Research Rack

Marshall Space Flight Center (MSFC) has been funding development of intelligent software models to benefit payload ground operations for nearly a decade. Experience gained from simulator development and real-time monitoring and control is being applied to engineering design, testing, and operation of the First Material Science Research Rack (MSRR-1). MSRR-1 is the first rack in a suite of three racks comprising the Materials Science Research Facility (MSRF) which will operate on the International Space Station (ISS). The MSRF will accommodate advanced microgravity investigations in areas such as the fields of solidification of metals and alloys, thermo-physical properties of polymers, crystal growth studies of semiconductor materials, and research in ceramics and glasses. The MSRR-1 is a joint venture between NASA and the European Space Agency (ESA) to study the behavior of different materials during high temperature processing in a low gravity environment. The planned MSRR-1 mission duration is five (5) years on-orbit and the total design life is ten (IO) years. The MSRR-1 launch is scheduled on the third Utilization Flight (UF-3) to ISS, currently in February of 2003). The objective of MSRR-1 is to provide an early capability on the ISS to conduct material science, materials technology, and space product research investigations in microgravity. It will provide a modular, multi-user facility for microgravity research in materials crystal growth and solidification. An intelligent software model of MSRR-1 is under development and will serve multiple purposes to support the engineering analysis, testing, training, and operational phases of the MSRR-1 life cycle development. The G2 real-time expert system software environment developed by Gensym Corporation was selected as the intelligent system shell for this development work based on past experience gained and the effectiveness of the programming environment. Our approach of multi- uses of the simulation model and its intuitive graphics capabilities is providing a concurrent engineering environment for rapid prototyping and development. Operational schematics of the MSRR-1 electrical, thermal control, vacuum access, and gas supply systems, and furnace inserts are represented graphically in the environment. Logic to represent first order engineering calculations is coded into the knowledge base to simulate the operational behavior of the MSRR-1 systems. An example of engineering data provided includes electrical currents, voltages, operational power, temperatures, thermal fluid flow rates. pressures, and component status indications. These type of data are calculated and displayed at appropriate instrumentation points, and the schematics are animated to reflect the simulated operational status of the MSRR-1. The software control functions are also simulated to represent appropriate operational behavior based on automated control and response to commands received by the crew or ground controllers. The first benefit of this simulation environment is being realized in the high fidelity engineering analysis results from the electrical power system G2 model. Secondly, the MSRR-1 simulation model will be embedded with a hardware mock-up of the MSRR-1 to provide crew training on MSRR-1 integrated payload operations. G2 gateway code will output the simulated instrumentation values, termed as telemetry, in a flight-like data stream so that the crew has realistic and accurate simulated MSRR-1 data on the flight displays which will be designed for crew use. The simulation will also respond appropriately to crew or ground initiated commands, which will be part of normal facility operations. A third use of the G2 model is being planned; the MSRR-1 simulation will be integrated with additional software code as part of the test configuration of the primary onboard computer, or Master Controller, for MSRR-1. We will take advantage of the G2 capability to simulate the flight like data stream to test flight software responses and behavior. A fourth use of the G2 model will be to train the Ground Support Personnel that will monitor the MSRR-1 systems and payloads while they are operating aboard the ISS. The intuitive, schematic based environment will provide an excellent foundation for personnel to understand the integrated configuration and operation of the MSRR-1, and the anticipated telemetry feedback based on operational modes of the equipment. Expert monitoring features will be enhanced to provide a smart monitoring environment for the operators. These features include: (1) Animated, intuitive schematic-based displays which reflect telemetry values, (1) Real-time plotting of simulated or incoming sensor values, (3) High/Low exception monitoring for analog data, (4) Expected state monitoring for discrete data, (5) Data trending, (6) Automated malfunction procedure execution to diagnose problems, (7) Look ahead capability to planned MSRR-1 activities in the onboard timeline. And finally, the logic to calculate telemetry values will be deactivated, and the same environment will interface to the incoming data for the real-time telemetry stream to schematically represent the onboard hardware configuration. G2 will be the foundation for the real-time monitoring and control environment. In summary, our MSRR-1 simulation model spans many elements of the life cycle development of this project: Engineering Analysis, Test and Checkout, Training of Crew and Ground Personnel, and Real-time monitoring and control. By utilizing the unique features afforded by an expert system development environment, we have been able to synergize a powerful tool capable of addressing our project needs at every phase of project development.

Rice, Amanda↗
NASA NTRS1990

Spectral absorption of marine stratocumulus clouds derived from in situ cloud radiation measurements

A multiwavelength scanning radiometer was used to measure the angular distribution of scattered radiation deep within a cloud layer at discrete wavelengths between 0.5 and 2.3 microns. The relative angular distribution of the intensity field at each wavelength is used to determine the similarity parameter, and hence single scattering albedo, of the cloud at that wavelength using the diffusion domain method. In addition to the spectral similarity parameter, the analysis provides a good estimate of the optical thickness of the cloud beneath the aircraft. In addition to the radiation measurements, microphysical and thermodynamic measurements were obtained from which the expected similarity parameter spectrum was calculated using accepted values of the refractive index of liquid water and the transmission function of water vapor. An analysis is presented for the results obtained for a 50 km section of clean marine stratocumulus clouds on 10 July 1987. These observations were obtained off the coast of California from the University of Washington Convair C-131A aircraft as part of the First ISCCP Regional Experiment (FIRE). A comparison of the experimentally-derived similarity parameter spectrum with that expected theoretically from the cloud droplet size distribution measured simultaneously from the aircraft is presented. The measurements and theory are in very close agreement for this case of clean maritime clouds.

King, Michael D.↗
NASA NTRS1994

Concurrent X-ray and optical observations of two dwarf novae during eruption

The dwarf novae SU UMa and RU Peg were each observed with the ROSAT Observatory during outburst. SU UMa was also observed twice between outbursts. The spectrum of SU UMa during quiescence is well fitted by a 2.1 keV thermal bremsstrahlung model with a Gaussian line at 0.97 keV absorbed by a column density of 1.4 x 10(exp 20)/sq cm. During the outburst the X-ray count rate dropped by a factor of 3. The outburst spectrum is well fitted to a similar spectrum with a significantly larger absorption. In outburst the mass transfer rate, dot-M, approaches the critical value for the optically thin/thick transition predicted by theoretical models of the boundary layer while the X-ray emission remains optically thin. The best-fit model to the outburst spectrum of RU Peg is a 4.9 keV thermal bremsstrahlung plus a line at 0.89 keV absorbed by a column density of 2.8 x 10(exp 20)/sq cm. The column density is consistent with the upper limit determined for interstellar absorption. The boundary layer at outburst is expected to be optically thick based on the value of dot-M determined from the IUE spectra. There are no ROSAT observations of RU Peg between outbursts, but the flux detected by ROSAT is a factor of 10 lower than that seen with the Einstein Observatory, probably during quiescence. For both CVs the X-ray flux from the boundary layer significantly decreases at the same time that the optical-UV flux greatly increases. We suggest that during outburst most of the boundary layer energy is carried away as kinetic energy of the wind.

Silber, A.↗
NASA NTRS1987

Theoretical determination of the radiative lifetime of the A 2Sigma(+) state of OH

The present theoretical potentials and transition moment-based computation of the radiative lifetime of the A 2Sigma(+)(v-prime = 0, N-prime = 1) state of OH yields a value of 673 ns, in excellent agreement with two of the experimental values obtained through laser excitation fluorescence. The theoretical radiative lifetimes, which are expected to be lower bounds and accurate to 2 percent, are accurate enough to preclude both the slightly lower value determined by Hanle effect studies and the higher values obtained by the high frequency deflection technique.

Bauschlicher, Charles W., Jr.↗
NASA NTRS2021

Reflection Modeling of the Black Hole Binary 4U 1630–47: The Disk Density and Returning Radiation

We present the analysis of X-ray observations of the black hole binary 4U 1630−47 using relativistic reflection spectroscopy. We use archival data from the Rossi X-ray Timing Explorer, Neil Gehrels Swift Observatory, and Nuclear Spectroscopic Telescope Array observatories, taken during different outbursts of the source between 1998 and 2015. Our modeling includes two relatively new advances in modern reflection codes: high-density disks, and returning thermal disk radiation. Accretion disks around stellar-mass black holes are expected to have densities well above the standard value assumed in traditional reflection models (i.e., n(e) ∼ 10^(15) per cu. cm). New high-density reflection models have important implications in the determination of disk truncation (i.e., the disk inner radius). This is because one must retain self-consistency in the irradiating flux and corresponding disk ionization state, which is a function of disk density and system geometry. We find that the disk density is n(e) ≥ 10^(20) per cu. cm across all spectral states. This density, combined with our constraints on the ionization state of the material, implies an irradiating flux impinging on the disk that is consistent with the expected theoretical estimates. Returning thermal disk radiation—the fraction of disk photons that bend back to the disk producing additional reflection components—is expected predominantly in the soft state. We show that returning radiation models indeed provide a better fit to the soft-state data, reinforcing previous results that show that in the soft state, the irradiating continuum may be blackbody emission from the disk itself.

Riley M. T. Connors↗
NASA NTRS2016

Applied Time Domain Stability Margin Assessment for Nonlinear Time-Varying Systems

The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.

Kiefer, J. M.↗
NASA NTRS1972

Structure of coronal neutral sheets

A qualitative model for the structure of the neutral sheet lying along the axis of coronal streamers is developed. The internal topology of the sheet is that of extremely thin magnetic tongues greatly distended outward by the solar wind expansion inside the sheet. Due to finite conductivity effects, expansion is taking place across the field lines but is retarded relative to the external flow by the reverse jxB force. The sheet thickness is determined by three considerations: the electrical conductivity that specifies the magnitude of the gradients in field strength, the expansion velocity that stretches the field lines outward decreasing the sheet thickness, and finally, the lateral pressure balance that limits the approach of the oppositely directed external field toward the neutral plane. If sigma is the electrical conductivity, the sheet thickness is shown to be proportional to sigma-1/3. For an electron conductivity evaluated perpendicular to the internal field in the sheet, the thickness is of the order of 100 km in the inner corona and 10,000 km at 1 AU. Microturbulence and instabilities are expected to yield dimensions greater than these theoretical values since these effects tend to reduce the effective conductivity.

Pneuman, G. W.↗
NASA NTRS1972

Solar cosmic ray, solar wind, solar flare, and neutron albedo measurements, part C

All mineral detectors exposed on Apollo 16 had high surface track densities probably produced by a solar flare that occurred during the mission. The heavy ions followed a power law spectrum with exponent approximately 3 down to approximately 200 KeV/nucleon. The abundance of low-energy particle tracks observed in this flare may explain the high track densities observed in lunar dust grains. Pristine heavy-particle tracks in feldspar give long tracks. Shallow pits similar to those expected from extremely heavy solar wind ions were observed in about the expected number. Initial results give a low apparent value of neutron albedo relative to theory.

Burnett, D.↗
NASA NTRS1981

Impulsive phase of solar flares. 1: Characteristics of high energy electrons

The variation along a magnetic field line of the energy and pitch angle distribution of high energy electrons injected into a cold hydrogen plasma containing either an open or closed magnetic field structure was investigated. The problem is formulated as a time independent Fokker-Planck Equation for the electron number distribution as a function of the electron energy, electron pitch angle, and the structure of the global magnetic field. Simple analytic solution valid in the small pitch angle regime and for slowly varying magnetic field is presented. For the more general situation a numerical code for solving the Fokker-Planck Equation was used and it was found that the analytic expression agrees well with the numerical results to values of the pitch angle much larger than expected. For most practical applications, one many confidently use the analytic expression instead of having to resort to lengthy numerical computations. These results are useful in the study of the nonthermal models of the impulsive phase of solar flares.

Leach, J.↗
NASA NTRS1986

Studies of dynamo field structure and related effects: DE satellite project guest investigator program

The establishment of the latitudinal and longitudinal structure of the low latitude dynamo electric (DE) field was initiated using data primarily from the Unified Abstract (UA) files of the Atmosphere Explorer E (AE-E) satellite. Mass plots of the vertical ion drift values were made for 1977, 1978, and 1979. The average diurnal variation of V sub v within 20 degrees of the dip equator is remarkably similar to that obtained at Jicamarca in the same years. The average meridional ion drift velocity vectors, obtained as a function of latitude by combining the average vertical and horizontal (nearly north-south) ion drift values from the AE-E, showed the expected variations with local time and season based on the well known equatorial fountain effect theory. The average diurnal variation of the vertical drift was found for four different ranges of dip latitude for a northern solstice season. The effect of the transequatorial neutral winds was as evident in this plotting format as in the meridional or fountain effect format. Finally, the average vertical drift velocity V sub v, not the east-west electric field E sub ew, was found to be approximately independent of longitude, as expected from the dynamo theory.

Coley, W. R.↗
NASA NTRS1989

Infrared focal plane performance in the South Atlantic anomaly

Proton-induced pulse height distributions (PHD's) in Si:XX detectors were studied analytically and experimentally. In addition, a preliminary design for a flight experiment to characterize the response of Si:XX detectors to the trapped proton environment and verify PHD models was developed. PHD's were computed for two orbit altitudes for a variety of shielding configurations. Most of the proton-induced pulses have amplitudes less that about 3.5 x 10(exp 5) e-h pairs. Shielding has a small effect on the shape of the PHD's. The primary effect of shielding is to reduce the total number of pulses produced. Proton-induced PHD's in a Si:Sb focal plane array bombarded by a unidirectional 67-MeV beam were measured. The maximum pulse height recorded was 6 x 10(exp 5) pairs. The distribution had two peaks: the larger peak corresponded to 3.8 x 10(exp 5) pairs and the smaller peak to 1.2 x 10(exp 5) pairs. The maximum pulse height and the larger peak are within a factor of two of predicted values. The low-energy peak was not expected, but is believed to be an artifact of inefficient charge collection in the detector. The planned flight experiment will be conducted on a Space Shuttle flight. Lockheed's helium extended life dewar (HELD) will be used to provide the required cryogenic environment for the detector. Two bulk Si:Sb arrays and two Si:As impurity band conduction arrays will be tested. The tests will be conducted while the Space Shuttle passes through the South Atlantic Anomaly. PHD's will be recorded and responsivity changes tracked. This experiment will provide a new database on proton-induced PHD's, compare two infrared detector technologies in a space environment, and provide the data necessary to validate PHD modeling.

Junga, Frank A.↗
NASA NTRS1995

Heating of the solar middle chromosphere by large-scale electric currents

A global resistive, two-dimensional, time-dependent magnetohydrodynamic (MHD) model is used to introduce and support the hypothesis that the quiet solar middle chromosphere is heated by resistive dissipation of large-scale electric currents which fill most of its volume. The scale height and maximum magnitude of the current density are 400 km and 31.3 m/sq m, respectively. The associated magnetic field is almost horizontal, has the same scale height as the current density, and has a maximum magnitude of 153 G. The current is carried by electrons flowing across magnetic field lines at 1 m/s. The resistivity is the electron contribution to the Pedersen resitivity for a weakly ionized, strongly magnetized, hydrogen gas. The model does not include a driving mechanism. Most of the physical quantities in the model decrease exponentially with time on a resistive timescale of 41.3 minutes. However, the initial values and spatial; dependence of these quantities are expected to be essentially the same as they would be if the correct driving mechanism were included in a more general model. The heating rate per unit mass is found to be 4.5 x 10(exp 9) ergs/g/s, independent of height and latitude. The electron density scale height is found to be 800 km. The model predicts that 90% of the thermal energy required to heat the middle chromosphere is deposited in the height range 300-760 km above the temperature minimum. It is shown to be consistent to assume that the radiation rate per unit volume is proportional to the magnetic energy density, and then it follows that the heating rate per unit volume is also proportional to the energy from the photosphere into the overlying chromosphere are briefly discussed as possible driving mechanisms for establishing and maintaining the current system. The case in which part of or all of the current is carried by protons and metal ions, and the contribution of electron-proton scattering to the current are also considered, with the conclusion that these effects do not change the qualitative prediction of the model, but probably change the quantitative predictions slightly, mainly by increasing the maximum magntiude of the current density and magnetic field to at most approximately 100 mA/m and approximately 484 G, respectively. The heating rate per unit mass, current density scale height, magnetic field scale height, temperatures, and pressures are unchanged or are only slightly changed by including these additional effects due to protons and ions.

Goodman, M. L.↗