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NASA NTRS1998

Aerothermal Heating Predictions for Mars Microprobe

A combination of computational predictions and experimental measurements of the aerothermal heating expected on the two Mars Microprobes during their entry to Mars are presented. The maximum, non-ablating, heating rate at the vehicle's stagnation point (at alpha = 0 degrees) is predicted for an undershoot trajectory to be 194 Watts per square centimeters with associated stagnation point pressure of 0.064 atm. Maximum stagnation point pressure occurs later during the undershoot trajectory and is 0.094 atm. From computations at seven overshoot-trajectory points, the maximum heat load expected at the stagnation point is near 8800 Joules per square centimeter. Heat rates and heat loads on the vehicle's afterbody are much lower than the forebody. At zero degree angle-of-attack, heating over much of the hemi-spherical afterbody is predicted to be less than 2 percent of the stagnation point value. Good qualitative agreement is demonstrated for forebody and afterbody heating between CFD calculations at Mars entry conditions and experimental thermographic phosphor measurements from the Langley 20-Inch Mach 6 Air Tunnel. A novel approach which incorporates six degree-of-freedom trajectory simulations to perform a statistical estimate of the effect of angle-of-attack, and other off-nominal conditions, on heating is included.

Mitcheltree, R. A.↗

NASA NTRS2017

Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points

Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.

compressor↗

NASA NTRSDate not supplied

Assessment of Crew Time for Maintenance and Repair Activities for Lunar Surface Missions

NASA is currently evaluating different methods to predict how much time crewmembers will spend conducting repair and maintenance activities on future space missions. As mission scope and spacecraft architectures change, understanding how crew repair and maintenance timelines are impacted by mission operations and technology changes is vital for future mission planning. Past work has been done using historical International Space Station (ISS) data to accurately predict crew habitation and operation timelines, resulting in the development of NASA’s Exploration Crew Time Model (ECTM). However, understanding crew maintenance and repair requirements has posed a unique challenge due to the complexity of available datasets, the probabilistic nature of sub-system failures, and the impacts of reliability growth on failure rates. This paper presents a methodology to collect and condition empirical repair and maintenance time data from available datasets, to extrapolate from that data to estimate projected maintenance and repair times for a lunar Surface Habitat (SH), and to assess how uncertainty in repair time could impact utilization time on the lunar surface. NASA ISS maintenance and crew time data are logged into two central databases: the Maintenance Data Collection (MDC) and the Operations Planning Timeline Integration System (OPTimIS). Separately, each of these two datasets capture only portions of the complete set of data required to generate an accurate assessment of crew time spent on maintenance activities at a sub-system level. To create a more useful crew time estimate for maintenance timelines, the authors developed a methodology to capture relevant data from each set and combine and utilize that data by linking crew time requirements to specific components. The authors compare the failure logs in the MDC to crew activity logs pulled from OPTimIS and then process the data to estimate required repair time for each failure and repair event. The entire maintenance activity dataset is then categorized based on the class of failed component to ensure a significant sample size for each class and accurate crew time estimates for any components lacking relevant data. This resultant component repair time data can be used in the future to generate Mean Time to Repair (MTTR) estimates and confidence intervals for each class of component based on a probabilistic distribution of documented maintenance events. These improved MTTR values can then be applied to candidate element sub-system architectures, along with component Mean Time Between Failure (MTBF) data to generate distributions for potential required system crew repair time estimates for a given mission. The authors applied these modeling methods to a case study of a crewed mission to the planned SH and produced expected corrective maintenance crew time distributions. The results produced an expected corrective maintenance crew time at over 24 hours per mission, and a maintenance crew time distribution that reflects the importance of planning for sufficient maintenance requirements each mission. Repair time distributions can then be used to develop more accurate crew schedules and to assess potential available utilization time.

Crew Time↗

NASA NTRS2024

A Low Density Ocean Inside Titan Inferred From Cassini Data

The Cassini mission has provided measurements of the gravity of several moons of Saturn, as well as an estimate of the tidal response, expressed as the degree 2 Love number k 2 , of its largest moon, Titan. The first estimates of Titan’s Love number were larger than pre-Cassini expectations. Interior modeling suggested it may be explained with a dense ocean, but interpretation remained unclear. We have analyzed Cassini tracking data to determine Titan’s gravity field and its Love number. Our gravity results are consistent with earlier studies, but we find a lower Love number for Titan of k 2 =0.375±0.06. This lower value follows from an elaborate investigation of the tidal effects. We show that a dense ocean is not implied by the obtained Love number; instead, a water or ammonia ocean is more likely. A lower density ocean can increase the likeliness of contact between the silicate core and ocean, which can leach minerals into the ocean and could promote its habitability.

Sander Goossens↗

NASA NTRS1985

Plasma measurements of the Pioneer Venus Orbiter in the Venus ionosheath - Evidence for plasma heating near the ionopause

A study of the angular spread of plasma fluxes detected in the Venus ionosheath is presented. It is shown that in the inner regions of the ionosheath, where the flux intensity is severely decreased with respect to solar wind values, the width of the azimuthal distribution of the local plasma is comparable to, or even larger than, that of the stronger fluxes measured in the outer ionospheath. The observed variation of the angular width suggests the existence of a source of heating near the ionopause but is not consistent with the overall cooling that would be expected if mass loading and charge exchange collisions were solely responsible for the interaction process at that boundary. Dissipative phenomene associated with local plasma turbulence processes seem to be required to account for the broad angular distributions seen near the ionopause.

Perez-De-tejada, H.↗

NASA NTRS1987

Deuterium in the daytime thermosphere

Ion concentration measurements for H(+) and D(+) from the magnetic ion mass spectrometer on the Atmosphere Explorer C satellite are used, in conjunction with other atmospheric data, to determine the concentrations of H and D in the nonpolar daytime thermosphere. The ratio of the observed D(+) to H(+) concentrations has essentially the same height dependence in the 300 to 800-km region as expected for their neutral counterparts, even in the presence of ion temperature gradients and probable large vertical ion fluxes. Rapid charge exchange with atomic oxygen ensures that D/H is about equal to D(+)/H(+) at the lower altitudes where the derived D to H concentration ratio is a factor of about 6 larger than its sea level value, for an exospheric temperature of 930 K. This relative enhancement of deuterium arises from the fact that hydrogen more readily escapes the earth, and a large vertical gradient in the H concentration relative to its diffusive equilibrium value is necessary to drive this upward flux through the lower thermosphere. If these planetary losses of hydrogen are much greater than those associated with evaporative escape, as is the current view, then correspondingly larger deuterium loss rates are also likely in order that the thermospheric D/H ratio not increase well above the observed value. The absolute winter daytime concentration of deuterium at 300 km is found to be 210 + or - 50 atoms/cu cm.

Breig, E. L.↗

NASA NTRS1991

SAM 2 measurements of the polar stratospheric aerosol. Volume 9: October 1982 - April 1983

The Stratospheric Aerosol Measurement (SAM) II sensor aboard Nimbus 7 is providing 1.0 micron extinction measurements of Antarctic and Arctic stratospheric aerosols with a vertical resolution of 1 km. Representative examples and weekly averages including corresponding temperature profiles provided by NOAA for the time and place of each SAM II measurement are presented. Contours of aerosol extinction as a function of altitude and longitude or time are plotted, and aerosol optical depths are calculated for each week. Typical values of aerosol extinction and stratospheric optical depth in the Arctic are unusually large due to the presence of material from the El Chichon volcano eruption in the Spring of 1982. For example, the optical depth peaked at 0.068, more than 50 times background values. Typical values of aerosol extinction and stratospheric optical depth in the Antarctic varied considerably during this period due to the transport and arrival of the material from the El Chichon eruption. For example, the stratospheric optical depth varied from 0.002 in October 1982, to 0.021 in January 1983. Polar stratospheric clouds were observed during the Arctic winter, as expected. A representative sample is provided of the ninth 6-month period of data to be used in atmospheric and climatic studies.

Mcmaster, L. R.↗

NASA NTRS1991

Neutrino-heated stars and broad-line emission from active galactic nuclei

Nonthermal radiation from active galactic nuclei indicates the presence of highly relativistic particles. The interaction of these high-energy particles with matter and photons gives rise to a flux of high-energy neutrinos. In this paper, the influence of the expected high neutrino fluxes on the structure and evolution of single, main-sequence stars is investigated. Sequences of models of neutrino-heated stars in thermal equilibrium are presented for masses 0.25, 0.5, 0.8, and 1.0 solar mass. In addition, a set of evolutionary sequences for mass 0.5 solar mass have been computed for different assumed values for the incident neutrino energy flux. It is found that winds driven by the heating due to high-energy particles and hard electromagnetic radiation of the outer layers of neutrino-bloated stars may satisfy the requirements of the model of Kazanas (1989) for the broad-line emission clouds in active galactic nuclei.

Macdonald, James↗

NASA NTRS1993

Possible dust contamination of the early solar system

Measurements carried out over more than twenty years indicate a deficiency of neutrinos emitted from the deep interior of the Sun in conjunction with the neutrino flux expected from canonical solar models. The early measurements were sensitive only to high-energy neutrinos emitted from B-8 on a minor branch of the energy-producing nuclear reactions in the solar interior. Thus these measurements were not widely considered to be a definitive test of solar physics. However the more recent measurements, which are sensitive to lower energy neutrinos, produced primarily by the p-p reaction on the main energy-producing branch of the solar nuclear reactions, pose a far more significant mystery in physics. One possibility is that the Sun's interior opacity is lower than expected due to a paucity of elements. This paper discusses that the Sun formed from material less abundant in heavy elements than usually believed, and the subsequent contamination due to the settling of surrounding dust brought the abundance of heavy elements - in the protoplanetary nebula, and in the Sun's convective envelope - up to the currently observed value.

Levy, E. H.↗

NASA NTRS1995

Hopkins Ultraviolet Telescope observations of H2 toward the planetary nebula NGC 1535

We have observed the far-ultraviolet spectrum (912-1860 A) of the bright high-excitation planetary nebula NGC 1535 with approximately 3 A resolution using the Hopkins Ultraviolet Telescope (HUT) aboard the Astro-1 space shuttle pmission in 1990 December. We see strong continuum emission down to the Lyman limit and strong P Cygni profiles from high-excitation lines such as C IV wavelength 1549, N V wavelength 1240, O V wavelength 1371, and O VI wavelength 1035. Below 1150 A strong absorption bands of H2 are seen, which were unanticipated by us because of the low reddening and high galactic latitude of the object and the absence of detected H2 emission in the infrared. We construct model H2 spectra and convolve them to the HUT resolution for comparison with the NGC 1535 data. We find good agreement with a population distribution characterized by a single temperature (T = 300 K) or a two-temperature model (T = 144/500 K), and determine limits on the H2 column density. While both inter-stellar and circumstellar origins for the observed H2 absorption are plausible, we ascribe the material to the planetary nebula in order to estimate the conditions of excitation and place upper limits on the mass of both H2 and H1 in this system. Because the UV transitions are ground-state connected, we determine a stringent upper limit of 0.03 d(sup 2)(sub 1.6) solar mass on the mass of H2, where d(sub 1.6) is the distance relative to an assumed distance of 1.6 kpc. This value is less model-dependent than IR estimates. Along with the central star and nebular masses, these estimates allow us to limit the main-sequence mass of the progenitor star to less than 1.8 solar mass. This upper limit is consistent with a relatively low-mass extended thick disk or Population II progenitor, as expected for an object approximately 1 kpc off the galactic plane.

Bowers, Charles W.↗

NASA NTRS1997

Biweekly Maps of Wind Stress for the North Pacific from the ERS-1 Scatterometer

The European Remote-sensing Satellite (ERS-1) was launched in July 1991 and contained several instruments for observing the Earth's ocean including a wind scatterometer. The scatterometer measurements were processed by the European Space Agency (ESA) and the Jet Propulsion Laboratory (JPL). JPL reprocessed (Freilich and Dunbar, 1992) the ERS-1 backscatter measurements to produced a 'value added' data set that contained the ESA wind vector as well as a set of up to four ambiguities. These ambiguities were further processed using a maximum-likelihood estimation (MLE) and a median filter to produce a 'selected vector.' This report describes a technique developed to produce time-averaged wind field estimates with their expected errors using only scatterometer wind vectors. The processing described in this report involved extracting regions of interest from the data tapes, checking the quality and creating the wind field estimate. This analysis also includes the derivation of biweekly average wind vectors over the North Pacific Ocean at a resolution of 0.50 x 0.50. This was done with an optimal average algorithm temporally and an over-determined biharmonic spline spatially. There have been other attempts at creating gridded wind files from ERS-1 winds, e.g., kriging techniques (Bentamy et al., 1996) and successive corrections schemes (Tang and Liu, 1996). There are several inherent problems with the ERS-1 scatterometer. Since this is a multidisciplinary mission, the satellite is flown in different orbits optimized for each phase of the mission. The scatterometer also shares several sub-systems with the Synthetic Aperture Radar (SAR) and cannot be operated while the SAR is in operation. The scatterometer is also a single-sided instrument and only measures backscatter along the right side of the satellite. The processing described here generates biweekly wind maps during the wktwo years analysis period regardless of the satellite orbit or missing data.

SYNTHETIC APERTURE RADAR↗

NASA NTRS2001

Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.

Brandt, Achi↗

NASA NTRS2001

Resonance Scattering of Fe XVII X-Ray and EUV Lines

Over the years a number of calculations have been carried out to derive intensities of various X-ray and EUV lines in Fe XVII to compare with observed spectra. The predicted intensities have not agreed with solar observations, particularly for the line at 15.02 Angstroms; resonance scattering has been suggested as the source for much of the disagreement. The atomic data calculated earlier used seven configurations, 2s(sup 2) 2p(sup 6),2s(sup 2) 2p(sup 5)3s, 2s(sup 2) 2p(sup 5)3p, 2s(sup 2)2p(sup 5)3d, 2s2 p(sup 6)3s, 2s2p(sup 6)3p, and 2s2p(sup 6)3d, having n=3 orbitals and the scattering calculations in the distorted wave approximation were carried out only for incident energies above the threshold of the highest fine-structure level. These calculations have now been extended to thirteen configurations by adding six more configurations having n=4 orbitals, namely 2s(sup 2) 2p(sup 5)4s, 2s(sup 2) 2p(sup 5)4p, 2s(sup 2) 2p(sup 5)4d, 2s2p(sup 6)4s, 2s2p(sup 6)4p, and 2s2p(sup 6)4d, giving rise to 73 fine structure levels. The scattering calculations are carried out below as well as above the threshold of the highest fine-structure level. The incident energies below the threshold are 55.8, 65, 70, and 76 Ry and those above are 85, 127.5, 170, 212.5, 255, 340, and 425 Ry. The collision strengths are calculated up to total angular momentum L(sup T) = 33. Level populations and intensity ratios are calculated at various electron temperatures and densities. It is not possible to predict how the ratios would change when configurations with n=5 and 6 orbitals are added but some estimates have been made for a few transitions by Liedhal, who indicates an asymptotic convergence when n=5 and 6 orbitals are added. These improved calculations of Fe XVII change the intensity ratios compared to those obtained earlier, bringing the optically thin F(15.02)/F(16.78) ratio and several other ratios closer to the observed values: However, some disagreement with the solar observations still persists, even though the agreement of the presently calculated optically thin F(15.02)/F(15.26) ratio with the experimental results of Brown et al. and Laming et al. has improved. Some of the remaining discrepancy is still thought to be the effect of opacity, which is consistent with expected physical conditions for solar sources. EUV intensity ratios are also calculated and compared with observations. Level populations and intensity ratios are calculated, as a function of column density of Fe XVII, in the slab and cylindrical geometries. As found previously, the predicted intensities for the resonance lines at 15.02 and 15.26 Angstroms exhibit initial increases in flux relative to the forbidden line at 17.10 Angstroms and the resonance line at 16.78 Angstroms as optical thickness increases. The same behavior is predicted for the lines at 12.262 and 12.122 Angstroms. Predicted intensities for some of the allowed EUV lines are also affected by opacity.

Bhatia, A. K.↗

NASA NTRS2009

Multimodal Friction Ignition Tester

The multimodal friction ignition tester (MFIT) is a testbed for experiments on the thermal and mechanical effects of friction on material specimens in pressurized, oxygen-rich atmospheres. In simplest terms, a test involves recording sensory data while rubbing two specimens against each other at a controlled normal force, with either a random stroke or a sinusoidal stroke having controlled amplitude and frequency. The term multimodal in the full name of the apparatus refers to a capability for imposing any combination of widely ranging values of the atmospheric pressure, atmospheric oxygen content, stroke length, stroke frequency, and normal force. The MFIT was designed especially for studying the tendency toward heating and combustion of nonmetallic composite materials and the fretting of metals subjected to dynamic (vibrational) friction forces in the presence of liquid oxygen or pressurized gaseous oxygen test conditions approximating conditions expected to be encountered in proposed composite material oxygen tanks aboard aircraft and spacecraft in flight. The MFIT includes a stainless-steel pressure vessel capable of retaining the required test atmosphere. Mounted atop the vessel is a pneumatic cylinder containing a piston for exerting the specified normal force between the two specimens. Through a shaft seal, the piston shaft extends downward into the vessel. One of the specimens is mounted on a block, denoted the pressure block, at the lower end of the piston shaft. This specimen is pressed down against the other specimen, which is mounted in a recess in another block, denoted the slip block, that can be moved horizontally but not vertically. The slip block is driven in reciprocating horizontal motion by an electrodynamic vibration exciter outside the pressure vessel. The armature of the electrodynamic exciter is connected to the slip block via a horizontal shaft that extends into the pressure vessel via a second shaft seal. The reciprocating horizontal motion can be chosen to be random with a flat spectrum over the frequency range of 10 Hz to 1 kHz, or to be sinusoidal at any peak-to-peak amplitude up to 0.8 in. (.2 cm) and fixed or varying frequency up to 1 kHz. The temperatures of the specimen and of the vessel are measured by thermocouples. A digital video camera mounted outside the pressure vessel is aimed into the vessel through a sapphire window, with its focus fixed on the interface between the two specimens. A position transducer monitors the displacement of the pneumatic-cylinder shaft. The pressure in the vessel is also monitored. During a test, the output of the video camera, the temperatures, and the pneumatic-shaft displacement are monitored and recorded. The test is continued for a predetermined amount of time (typically, 10 minutes) or until either (1) the output of the position transducer shows a sudden change indicative of degradation of either or both specimens, (2) ignition or another significant reaction is observed, or (3) pressure in the vessel increases beyond a pre-set level that triggers an automatic shutdown.

Davis, Eddie↗

NASA NTRS2012

Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

Ono, Masahiro↗

NASA NTRSDate not supplied

Design for Reliability (DfR) in Space Life Support

The engineering process of Design for Reliability (DfR) is well established in the automotive and aerospace industries. DfR should be useful in the future development of space life support systems. DfR is a sequence of tasks that develop system requirements and plan reliability analysis and testing. First and fundamentally, the reliability requirement is defined. Next the system reliability model is developed, often using a reliability block diagram. The overall system reliability requirement is allocated to the subsystems and an estimate of the attainable reliability is made. This expected reliability can be improved by simplifying the design by removing components or by replacing less reliable components. Improving reliability can require difficult compromises, such as reducing performance requirements, increasing budget, or extending testing. The actual system reliability can be determined only by testing, which should continue long enough to provide the required confidence in the measured value. New systems often have unexpected design errors that cause failures in early testing. The usual reliability improvement process of testing, finding the failure modes, and redesigning to remove them reduces the failure rate and is referred to as “reliability growth.” After redesign has been completed, the system should be further tested to determine the actual achieved reliability more accurately. If the final system failure rate is too high, redundant systems can be used to improve overall operational reliability. Adding redundancy simply to increase the one- or two-fault tolerance metric may sometimes reduce reliability. Reliability can be improved in three ways: redesigning the system to include more reliable subsystems and components, reliability growth testing and failure mode removal, and by using parallel redundant systems. DfR should combine these approaches to achieve the required reliability while managing performance, cost, and schedule.

Reliability↗

NASA NTRSDate not supplied

Design for Reliability (DfR) in Space Life Support

Reliability↗

NASA NTRS1981

On the role of the magnetic field in the solar wind interaction with Venus - Expectations versus observations

Observations of the magnetic field near Venus suggest that elements of three different models (direct interaction, tangential discontinuity, magnetic barrier) are present. A bow shock is found to occur at an altitude of about 0.3 Venus radii at the subsolar point. The compression of the decelerated solar wind plasma behind the bow shock causes interplanetary field lines to 'pile up'. The magnetic field inside the bow shock increases from approximately twice the IMF strength at the bow shock to values in the range of approximately 40-100 gammas at altitudes between about 200 and 1,200 km. The maximum value of the piled up field, which is correlated with the dynamic pressure of the solar wind outside the bow shock, is found at lower altitudes for larger field strengths. Just Venus-ward of the maximum field, the pressure of the cold plasma increases to a level balancing the pressure of the external magnetic field. Hence, to a first approximation, the ionosphere has a diamagnetic response excluding the magnetosheath field. However, strong magnetic fields are found at times throughout the ionosphere.

Luhmann, J. G.↗