Suprathermal Component Research Articles

Arbitrary amplitude dust acoustic solitary waves in an electron-depleted dusty plasma with two high energy-tail ion distributions

Arbitrary amplitude dust acoustic waves (DAW’s) in two high energy-tail ion distributions are investigated. The electron number density has been assumed sufficiently depleted during the charging of the dust grains, on account of the attachment of the background plasma electrons on the surface of the dust grains. Our results reveal that under certain conditions, DA solitary waves with either negative or positive potential may be admitted. The high degree of suprathermalization of the relatively low temperature ion component favors the development of compressive localized structures. This behavior is preserved to a large extent in the small but finite amplitude regime. This means that the presence of additional relatively low temperature suprathermal ions does not only significantly modify the basic properties of DA structures, but also causes the existence of positive solitary potentials. This feature is completely new in a dusty plasma with two suprathermal ion components with widely disparate temperatures. Our results may be relevant to a number of space dusty plasma systems, particularly, the Saturn’s F-ring where electron depletion and suprathermality are thought to come into play.

Calculated neutron emission spectrum with knock-on effects for RF heated (3He)D plasmas

The neutron emission from (3He)D plasmas with RF heating is calculated using a model that includes supra-thermal (knock-on) components of the deuteron population. The RF generation of fast 3He ions is described and the knock-on components were determined with the help of newly derived 3He + d scattering cross sections. Results are presented on the neutron emission spectrum and its contributions from different deuteron velocity components. It is shown that knock-on leaves an observable feature in the spectrum with a clear dependence on absorbed RF power. The importance of the nuclear interaction in the elastic cross section is demonstrated. The results represent a step forward in the use of neutron emission spectroscopy to diagnose fusion plasmas with minority supra-thermal components in their fuel ion composition.

An extended hybrid magnetohydrodynamics gyrokinetic model for numerical simulation of shear Alfvén waves in burning plasmas

Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an extended version of hybrid magnetohydrodynamics gyrokinetic code (XHMGC) to study thermal ion kinetic effects on Alfvénic modes driven by energetic particles, such as kinetic beta induced Alfvén eigenmodes in tokamak fusion plasmas. The XHMGC nonlinear model can be used to address a number of problems, where kinetic treatments of both thermal and supra-thermal plasma components are necessary, as theoretically predicted, or where it is desirable to investigate the phenomena connected with the presence of two supra-thermal particle species with different radial profiles and velocity space distributions.

Hybrid simulations of the termination shock: Suprathermal ion velocity distributions in the heliosheath

The Los Alamos hybrid simulation code is used to examine kinetic properties of pickup ions at the heliospheric termination shock and in the downstream heliosheath. All simulations are one‐dimensional in spatial variations, represent the electrons as a zero‐mass fluid, and address only perpendicular shocks. Interpretation of measurements from the IBEX and Voyager spacecraft depend sensitively on the properties of the suprathermal ions downstream of the termination shock, so this research addresses three topics concerning such ions. First, a careful examination of pickup ion trajectories shows that their initial acceleration does not require specular reflection at the shock, as is sometimes assumed, but is the consequence of gyromotion by selected ions at the shock. The primary factor in this energy gain is a gyro‐phase‐dependent interaction with the motional electric field upstream of, and the magnetic field at, the shock. Second, shock simulations are carried out in which the upstream pickup ions are assumed to have four different types of velocity distributions. The downstream ion perpendicular velocity distributions f(v⊥) are similar in each of the runs and may be approximately characterized as a thermal Maxwellian and a suprathermal distribution. The only significant difference among the four downstream distributions is in the tails of the suprathermal component. Third, simulations are carried out for three different upstream Mach numbers; the results show that faster solar wind flows lead to increased fluxes of ions in the tails of the suprathermal component and are generally consistent with energetic neutral atom observations by the IBEX spacecraft.

Variation in lunar sodium exosphere measured from lunar orbiter SELENE (Kaguya)

Resonant scattering of the lunar sodium exosphere was measured from the lunar orbiter SELENE (Kaguya) from December 2008 to June 2009. Variations in line-of-sight integrated intensity measured on the night-side hemisphere of the Moon could be described as a spherical symmetric distribution of the sodium exosphere with a temperature of 2400–6000 K. Average surface density of sodium atoms in February is well above that in the other months by about 30%. A clear variation in surface density related to the Moon’s passage across the Earth’s magnetotail could not be seen, although sodium density gradually decreased (by 20±8%) during periods from the first through the last quarter of two lunar cycles. These results suggest that the supra-thermal components of the sodium exosphere are not mainly produced by classical sputtering of solar wind. The variation in sodium density (which depends on lunar-phase angle) is possibly explained by the presence of an inhomogeneous source distribution of photon-stimulated desorption (PSD) on the surface.

Influence of suprathermal background electrons on strong auroral double layers: Vlasov-simulation parameter study

Recent observations by the Fast Auroral SnapshoT (FAST) satellite [Andersson et al., Phys. Plasmas 15, 072901 (2008), this issue] suggest that characteristics of particles and waves on the high-potential side of strong double layers in Earth’s auroral downward current region are influenced by properties of the suprathermal electron component. Current-driven Vlasov simulations in one spatial dimension with suprathermal electrons differing in density and temperature were performed to study their influence on double-layer evolution. A sufficiently dense and hot suprathermal population is found to stabilize strong laminar double layers over long periods while regulating their strength and velocity. Synthetic electron energy-flux spectra from simulations with different suprathermal electron populations reveal certain similarities to the corresponding FAST observations.

Ion heat flux and energy transport near the magnetotail neutral sheet

Ten‐year averages of energy transport rates near the neutral sheet showed that the enthalpy flux density or thermal energy term QT = (5/2)PV was the largest, where P is the isotropic pressure and V is the bulk flow velocity. The ion heat flux, qi, was the next largest term. Sorting data using a magnetic flux transport parameter showed that qi could become dominant during periods of slow flow. Both qi and the ion bulk velocity Vi were duskward on the dusk side of the neutral sheet. This relationship is characteristic of cross‐tail drift and a heat flux that can be attributed to the energy dependent gradient and curvature drifts. The qi and Vi vectors often pointed in different directions on the dawn side. The x component of qi on the dawn side pointed tailward, suggesting entry through the magnetopause of a suprathermal ion component. On the dusk side the qix plots that were sorted using a magnetic flux transport parameter showed evidence of plasma sheet reconnection. The long‐term averaged x component of QT pointed earthward almost everywhere in the neutral sheet, and was attributed to periods of very fast plasma flow. The cross‐tail component of QT was separated into two contributions. One part of QTy involved a common drift away from midnight during both earthward and tailward fast flows. This feature suggests that thermal energy and plasma flow from the outer plasma sheet toward the neutral sheet near midnight, and then toward the flanks. The other part of QTy involved a differential duskward drift during fast earthward flows and a dawnward drift during fast tailward flows. The incremental E fields that would produce such convection point tailward during the fastest earthward flows and earthward during the fastest tailward flows. The dependencies of Vi, qi and QT on the interplanetary magnetic field (IMF) clock angle also were studied. Both Vi and QT were reduced when the IMF was northward and the neutral sheet plasma became cold and dense. However, no dependence of qi on the IMF direction was seen. This shows that the generation of a cold dense plasma sheet does not substantially change the distribution of the suprathermal ions that are most important in the production of qi.

Solar wind electron distribution functions inside magnetic clouds

This paper presents a study of the kinetic properties of the electron velocity distribution functions within interplanetary magnetic clouds, since they are the dominant thermal component and can contribute as much as 50% of the total electron pressure within the clouds. The study is based on high time resolution data from the Goddard Space Flight Center Wind Solar Wind Experiment vector electron and ion spectrometer. Studies on interplanetary magnetic clouds have shown observational evidence of anticorrelation between the total electron density and temperature, which suggests a polytrope law Pe = αneγ for electrons with the constant γ ≈ 0.5 < 1. This anticorrelation and small γ values are interpreted in the context of the presence of highly non‐Maxwellian electron distributions (i.e., nonthermal tails) within magnetic clouds. We have revisited some of the magnetic cloud events previously studied to quantify the nature of the nonthermal electrons by modeling the electron velocity distribution function using Maxwellian and kappa‐like distribution functions to characterize the kinetic nonthermal effects. The results show that the electron density‐temperature anticorrelation is not a unique feature of magnetic clouds. Within magnetic clouds, κ values are generally small, in the range of 1.6–5.4; however, such small values are also typical of regions outside the clouds. We have shown that the density‐temperature anticorrelation of the electron moments is persistently consistent with similar density‐temperature anticorrelation in the electron halo component of the velocity distribution function and essentially little or no correlation was obtained for the core component. This result clearly shows that the temperature and density of the suprathermal components play a significant role in the temperature‐density anticorrelation because of a relative enhancement of the halo component abundance to the total density.

Electron flat‐top distributions around the magnetic reconnection region

Cluster multisatellite observations provide snapshots of electron distributions around the magnetic neutral line. An isotropic flat‐top‐type electron distribution in phase space is frequently observed around the X line, together with large ion velocities and a Hall quadrupole‐like magnetic field inside the hot and tenuous plasma sheet in the magnetotail. The flat‐top distributions are also associated with a finite magnetic field in the direction normal to the neutral sheet, and the cross‐tail current density is sometimes very small. These results indicate that the flat‐top‐type distribution is mainly located near the outer boundary of the ion diffusion region in the plasma sheet outflow region, before reaching the pileup region with large normal component of the magnetic field. Simultaneously with the flat‐top distributions, strong field‐aligned electron beams mainly toward the X line are occasionally observed. This type of beam is mainly observed in the off‐equatorial plasma sheet and also appears well inside the plasma sheet. Typical energies of the beam are 4–10 keV, which is comparable to the upper edge of flat‐top energy. These highly accelerated electron distributions have a steep decrease in phase space density at the high‐energy end, and it is found that they are not correlated with the increase of the higher‐energy electrons related to suprathermal acceleration (>30 keV). This result indicates that the electron acceleration processes for the flat‐top‐type distributions are different from the suprathermal components, both of which are beyond the conventional MHD outflow acceleration and considered to be associated with some kinetic processes.

On the propagation of hydromagnetic waves in a plasma of thermal and suprathermal components

The propagation of MHD waves is studied when two ideal fluids, thermal and suprathermal gases, coupled by magnetic field are moving with the steady flow velocity. The fluids move independently in a direction perpendicular to the magnetic field but gets coupled along the field. Due to the presence of flow in suprathermal and thermal fluids there appears forward and backward waves. All the forward and backward modes propagate in such a way that their rate of change of phase speed with the thermal Mach number is same. It is also found that besides the usual hydromagnetic modes there appears a suprathermal mode which propagates with faster speed. Surface waves are also examined on an interface formed with composite plasma (suprathermal and thermal gases) on one side and the other is a non-magnetized plasma. In this case, the modes obtained are two or three depending on whether the sound velocity in thermal gas is equal to or greater than the sound velocity in suprathermal gas. The results lead to the conclusion that the interaction of thermal and suprathermal components may lead to the occurrence of an additional mode called suprathermal mode whose phase velocity is higher than all the other modes.

Cassini Ion and Neutral Mass Spectrometer data in Titan's upper atmosphere and exosphere: Observation of a suprathermal corona

The neutral nitrogen and methane measurements made by Ion and Neutral Mass Spectrometer during Cassini flybys TA, TB, and T5 in Titan's upper atmosphere and exosphere are presented. Large horizontal variations are observed in the total density, recorded to be twice as large during TA as during T5. Comparison between the atmospheric and exospheric data show evidence for the presence of a significant population of suprathermal molecules. Using a diffusion model to simultaneously fit the N2 and CH4 density profiles below 1500 km, the atmospheric structure parameters are determined, taking into account recent changes in the calibration parameters. The best fits are obtained for isothermal profiles with values 152.8 ± 4.6 K for TA, 149.0 ± 9.2 K for TB, and 157.4 ± 4.9 K for T5, suggesting a temperature ≃5 K warmer at night than at dusk, a trend opposite to that determined by solar‐driven models. Using standard exospheric theory and a Maxwellian exobase distribution, a temperature of 20 to 70 K higher would be necessary to fit the TA, TB, and egress‐T5 data above 1500 km. The suprathermal component of the corona was fit with various exobase energy distributions, using a method based on the Liouville theorem. This gave a density of suprathermals at the exobase of 4.4 ± 5.1 × 105 cm−3 and 1.1 ± 0.9 × 105 cm−3, and an energy deposition rate at the exobase of 1.1 ± 0.9 × 102 eV cm−3 s−1 and 3.9 ± 3.5 × 101 eV cm−3 s−1 for the hot N2 and CH4 populations, respectively. The energy deposition rate allowed us to roughly estimate escape rates for nitrogen of ≃7.7 ± 7.1 × 107 N cm−2 s−1 and for methane of ≃2.8 ± 2.1 × 107 CH4 cm−2 s−1. Interestingly, no suprathermal component was observed in the ingress‐T5 data.

Electromagnetic ion cyclotron waves instability threshold condition of suprathermal protons by kappa distribution

The well‐known generalized Lorentzian (kappa) distribution generally provides a good representation for the high‐energy tail population of natural cosmic suprathermal plasmas. In this study we examine the electromagnetic ion cyclotron waves (EMIC) instability driven by the temperature anisotropy condition (T⊥/T∥ > 1) of suprathermal protons modeled with a typical kappa distribution in a cold multispecies plasma (electron, H+, He+, and O+). Since the EMIC wave instability is found to be significant typically above the O+ band, we apply a linear theory to study the instability threshold condition for the He+ and H+ bands particularly around the geostationary orbit. The instability threshold condition, as in the case for a regular bi‐Maxwellian, is found to follow a typical form T⊥/T∥ − 1 = S/β∥α, with higher values in the He+ band than those in the H+ band in the case of the strong wave instability owing to a lower maximum wave growth in the He+ band. As the spectral index κ increases, the instability threshold condition generally decreases and tends to the lowest limiting values of the bi‐Maxwellian, since the evaluation by the bi‐Maxwellian generally overestimates the maximum wave growth. The densities of the cold components (particularly protons) have impacts on the threshold condition primarily in the H+ band, with a higher density of cold protons leading to a lower value of the threshold condition. The results above may further reveal the nature of this instability threshold condition for the EMIC waves in any other space plasmas where an anisotropic suprathermal ion component and cold multicomponents are present together.

Effect of He++ions on the propagation of low-frequency magnetohydrodynamic waves in the magnetosheath

[1] The paper investigates the role of suprathermal particles (He++) in the propagation of low-frequency waves in average magnetosheath plasma by utilizing a model which is a concatenation of two magnetohydrodynamic (MHD) fluids. The suprathermal component is described by a relativistic, collisionless anisotropic fluid while the background plasma is assumed to be a nonrelativistic, anisotropic MHD fluid. The pressure components of both the fluids are described by heuristic double-polytropic laws which are fairly well supported by observational data. The linearized analysis is carried out and dispersion relation is derived using normal mode technique. It is found that inclusion of the suprathermal component causes the excitation of an additional mode of propagation, besides reducing the phase speeds of slow, fast, and Alfvén modes. The additional mode, which can be characterized as a hybrid of the suprathermal and the fast modes in the direction perpendicular to the magnetic field, is the only mode which transports energy in the direction perpendicular to the magnetic field. Using appropriate polytropic indices obtained from AMPTE/IRM measurements in the magnetosheath leads to a new ordering of phase speeds and density-magnetic field correlation of the fast mode. The new suprathermal mode shows positive density-magnetic field correlation.

Diagnostic of the dayside ionosphere of Mars using the Total Electron Content measurement by the NEIGE/Netlander experiment: An assessment study

The NEtlander Ionosphere and Geodesy Experiment (NEIGE) of the Netlander mission to Mars will measure Doppler shifts affecting the radio links between ground stations and an orbiter. The experiment has two complementary scientific objectives which are the monitoring of the structure and dynamics of the ionosphere of Mars and the precise determination of Mars orientation parameters. The horizontal variation of the Total Electron Content (TEC) of the ionosphere will be derived from the so-called “geometric-free” combination of the Doppler shifts which affect radio links at two frequencies (in the UHF and S bands) between the Netlander microstations on the Mars surface and the data-relay orbiter. We describe a new method for retrieving the horizontal profile of the absolute value of the TEC. Simulations have allowed to evaluate the precision in the determination of the TEC using this method. We show that the daytime TEC can be retrieved with a precision of 5×10 13 m −2 for a nominal accuracy of 0,1 mm/ s on the orbital pseudo-velocity, which represents a relative precision of a few percent. A preliminary analysis of the sensitivity of the TEC to the physical parameters which control the ionosphere has been performed. For this purpose, we have used a new one-dimensional ionospheric model based on the solution of coupled kinetic, fluid and MHD equations. This model describes the suprathermal electron component, the thermal plasma component as well as the induced horizontal magnetic field. The code which provides the vertical electron density profile has been used to study the variation of the TEC with the solar zenith angle and with the induced magnetic field at the top of the ionosphere. In particular, we show that NEIGE will allow to diagnose the penetration into the daytime ionosphere of an induced magnetic field.

Extremely hard GRB spectra prune down the forest of emission models

We consider the evidence for very hard low energy spectra during the prompt phase of Gamma-Ray Bursts (GRB). In particular we examine the spectral evolution of GRB 980306 together with the detailed analysis of some other bursts already presented in the literature (GRB 911118, GRB 910807, GRB 910927 and GRB 970111), and check for the significance of their hardness (i.e. extremely steep spectral slopes below the EFE peak) by applying different tests. These bursts, detected by the Burst And Transient Source Experiment (BATSE) in the ∼30 keV–2 MeV energy range, are sufficiently bright to allow time resolved spectral studies on time intervals of the order of tenths of a second. We discuss the hard spectra of these bursts and their evolution in the context of several non-thermal emission models, which all appear inadequate to account for these cases. The extremely hard spectra, which are detected in the early part of the BATSE light curve, are also compared with a black body spectral model: the resulting fits are remarkably good, except for an excess at high energies (in several cases) which could be simply accounted for by the presence of a supra-thermal component. The findings on the possible thermal character of the evolving spectrum and the implications on the GRB physical scenario are considered in the frameworks of photospheric models for a fireball which is becoming optically thin, and of Compton drag models, in which the fireball boosts “ambient" seed photons by its own bulk motion. Both models, according to simple estimates, appear to be qualitatively and quantitatively consistent with the found spectral characteristics, although their possible caveats are discussed.

MHD spectroscopy

Experiments are conducted on the JET tokamak to demonstrate the diagnostic potential of Magneto-Hydro-Dynamics (MHD) spectroscopy, for the plasma bulk and its suprathermal components, using Alfvén eigenmodes (AEs) excited by external antennas and by energetic particles. The measurements of AE frequencies and mode numbers give information on the bulk plasma. Improved equilibrium reconstruction, in particular in terms of radial profiles of density and safety factor, is possible from the comparison between the antenna driven spectrum and that calculated theoretically. Details of the time evolution of the non-monotonic safety factor profile in advanced scenarios are reconstructed from the frequency behaviour of ICRH-driven energetic particle modes. The plasma effective mass is inferred from the resonant frequency of externally driven AEs in discharges with similar equilibrium profiles. The stability thresholds and the nonlinear development of the instabilities give clues on energy and spatial distribution of the fast particle population. The presence of unstable AEs provides lower limits in the energy of ICRH generated fast ion tails. Fast ion pressure gradients and their evolution are inferred from the stability of AEs at different plasma radial positions. Finally, the details of the AE spectrum in the nonlinear stage are used to obtain information about the fast particle velocity space diffusion.

High resolution observations of the sodium emission from the Moon

High resolution spectroscopy of the Moon's atmosphere allows to analyze the closest layers to the lunar surface giving the possibility to get information on the source and the evolution of the atmospheric atoms and their distribution with respect to the latitude. The sodium emission, that is one of the main components of the atmosphere, is easier to study thanks to the good efficiency of the solar resonant scattering. A long term program of observations of the Moon's sodium atmosphere has been performed at the 182cm telescope of the Astronomical Observatory of Padova, using an echelle spectrograph, allowing to get spectra in different periods of the year and lunar phases and at different latitudes. The slit was placed parallel to the lunar equator, with a spatial coverage of 150 km few tens of km above the surface, at the east and west sides (bright and dark limbs) and perpendicular to the equator at the north and south sides. In this way it has been studied the behaviour of the column densities, the scale heights and temperatures with respect to the latitude and the lunar phase. We report also one spectrum obtained during the total eclipse of April 1996. Moreover it has been possible to get spectra using the WHT-IAC Canarian telescope with a very high resolution spectrograph and a larger spatial coverage in order to discriminate better the thermal and suprathermal components assumed to characterize the sodium distribution in the atmosphere. Our data seem to emphasize the micrometeorite impacts mechanism that is not so neglible looking at the asimmetry of the emission intensities measured during one full Moon night, their high value agree with Potter and Morgan (1991). A further comparison with a spectrum obtained by Sprague et al. (1991) at about the same lunar phase shows an higher temperature for our spectrum that could be due to a competing release mechanism involving also the micrometeorite impacts.

Self-consistent description of L-H mode transition dynamics in tokamaks

A theoretical model of L-H transition in a tokamak, based on the self-consistent analysis of plasma transport and taking the suppression of anomalous transport by sheared poloidal plasma rotation and the establishment of a radial electric field due to non-ambipolar particle transport into account, is presented. The transition to an improved confinement regime for a plasma with or without suprathermal electron component is studied. A numerical simulation shows that this model adequately describes the main, experimentally observed features of L-H transition dynamics during electron cyclotron or lower hybrid heating. It is also shown that in certain conditions such a transition can be 'auto-oscillatory', which may be considered as an ELMs feature. The dependence of the localization region of the ELMs and their characteristics (frequency and magnitude) on the plasma parameters are investigated

Small Tokamaks for Fusion Technology Testing

Small steady-state tokamaks for testing divertors and fusion nuclear technologies are considered. Based on present physics and technology data and explanation to reduce R{sub 0}/a, H-D-fueled tokamaks with R{sub 0} {approximately} 0.6--0.75 m, R{sub 0}/a {approximately} 1.8--2.5, and B{sub t0} {approximately} 1.4--2.2 T can be driven with P{sub tot} {approximately} 4.5 MW to maintain I{sub p} {approximately} 0.5 MA and produce the ITER-level plasma edge and divertor conditions. Given an adequate steady-state divertor solution and Q{approximately}1 operation based on fusion through the suprathermal component, D-T-fueled tokamaks with R{sub 0} {approximately} 0.8 m, R{sub 0}/a {approximately} 2, and B{sub t0} {approximately} 4 T can be driven with P{sub tot} {approximately} 15 MW to maintain I{sub p} {approximately} 4.6 MA and produce an peak neutron wall load W{sub L} {approximately} 1 MW/m{sup 2}. Such devices appear possible if the plasma properties at the power R{sub 0}/a remain tokamak-like and, for the D-T case, can unshielded center core is feasible. The use of a single conductor as the inboard leg of the toroidal field coils for this purpose is discussed. The physics issues and the design features are identified for such tokamaks with a testing duty for factor goal of 10--20%.

The sodium and potassium atmosphere of the moon and its interaction with the surface

Observations of lunar atmospheric sodium and potassium from May 1988 to July 1991 are reported and analyzed. Densities at 80° north and south are less than equatorial ones by a factor of 2–3. For our observations, which do not reach above 800 km from the limb, the apparent scale heights for the intensity are 119–611 km for Na, and 85 and 154 km for K; most of these are much larger than would be expected for atoms thermalized to the surface temperature. However, the intensity drops off with increasing radius at a much greater rate than would be observed for an atmosphere that is mostly escaping. We interpret our data using both single- and two-component analyses. We amplify an earlier suggestion that source atoms are quickly redistributed into thermal and suprathermal populations by “competing release mechanisms” acting at the surface. The suprathermal distributions are produced by solar radiation releasing atoms adsorbed on the surface ( photodesorption). We present reasons why the energy distribution seems to mimic a Maxwellian. The competing release mechanisms explain an obvious trend of decreasing apparent scale heights toward the subsolar point, where the density in the lowest 100 km appears to be dominated by thermally desorbed atoms. The suprathermal component is expected to appear at greater altitudes, but the early subsolar data do not extend high enough to reveal it. Six of the data sets are tentatively resolved into thermal and suprathermal components. The variation with latitude is naturally explained if a larger fraction of the atoms at large solar zenith angles are adsorbed to the surface, rather than being visible in the atmosphere. Migration to the dark side may also play a role. It is shown that at most a very small fraction of the observed atoms below a few hundred km altitude can be on escape trajectories. We apply these ideas to the budget of atomic oxygen. We suggest that the inventory of oxygen atoms is greatly reduced because they stick to the surface with high efficiency similar to that of the alkalis, and subsequently recombine with each other or with partially reduced oxides of such atoms as Mg, Fe, Al, and Si.