Contains research objectives and reports on two research projects.National Aeronautics and Space Administration (Grant NsG-419

Bitter, F.

Fiocco, G.

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VI. GEOPHYSICSProf. F. Bitter Dr. J. F. Waymouth H. C. KoonsProf. G. Fiocco R. J. Breeding R. G. LittleDr. T. Fohl J. C. Chapman O. RediDr. H. C. Praddaude G. W. Grams C. J. Schuler, Jr.W. D. HalversonRESEARCH OBJECTIVESThis group will be concerned with a variety of problems of geophysical interest,including laboratory investigations of the properties of matter and radiation underextreme conditions. The initial program includes two principal projects.1. Planetary Radiation BeltsTheoretical and experimental studies will be undertaken to extend our knowledge ofthe interaction of charged particles in a magnetic field, especially to include conditionsunder which electric and magnetic forces are of comparable magnitude. These studiesshould have a bearing on scattering, recombination, and radiation processes in very lowdensity plasmas.Laboratory studies are planned for the investigation of the diffusion of charged par-ticles in the fields of magnetic dipoles.F. Bitter2. Scattering of Light in the Earth's AtmosphereStudies of the Earth's atmosphere by scattering of laser radiation will be pursued.An important part of this program will involve studying the dust layers existing at analtitude of 20 km and above. We are planning to take the apparatus to Sweden duringnext summer to observe noctilucent clouds.The possibility of using Raman scattering in order to obtain profiles of density andtemperature for various species in the lower atmosphere will be investigated.The scattering cross section in the vicinity of an absorption line will be investigatedexperimentally with a tunable laser.G. FioccoA. TRANSITION FROM PREDOMINANTLY ELECTRIC TO PREDOMINANTLYMAGNETIC BINDING IN THE HYDROGEN ATOM IN A MAGNETIC FIELDAttempts to obtain complete solutions for the hydrogen atom in a magnetic fieldthus far have been only partially successful, and will not be reported now. Thefollowing simple semiclassical calculation of the effect of combined magnetic andelectric forces acting on electrons in circular orbits in a hydrogen atom with thenucleus at rest indicates the kind of phenomena to be expected. For this case,for the forces, we have2m v ke + evB, (1)r 2rand for the canonical angular momentumQPR No. 72(VI. GEOPHYSICS)p = n =2 mr~ M(2)Upon eliminating the velocity, we obtain an expression for the radius4n =+ 4' (3)a bwhere a is the first Bohr orbith z  -10a kem =0.53 X 10 meter,and b is the lowest cyclotron orbit radius-83.62 X 10 meterb=This case is illustrated in Fig. VI-1. For small values of r and B, the radius isindependent of B. This is in accordance with the Larmor theorem, which states that,to a first approximation, magnetic fields do not distort atomic configurations, butmerely produce the Larmor precession. At high fields and in large orbits in which10910102106B ( w/m2 )106 -103106 10CONTOURS OF CONSTANTRADIUSFig. VI-1. Radius of circular Bohr orbits with magnetic quantumnumber m = ±n plotted as a function of n and B.QPR No. 72(VI. GEOPHYSICS)the electrostatic forces are negligible, the orbits approach the cyclotron orbits of freeelectrons.The total energy of the system,1 2 keE = - mv -2 rmay be put into the formE =±PBBn+ .n 2  ra  21 keFor small orbits in weak magnetic fields n2r 2field energy ±n tB B. For large fields- << nelPr , and the energy is simply the zero-aand the energy becomesE= n B Bwhen the magnetic moment is antiparallel (diamagnetic), or zero when it is parallel(paramagnetic) to the applied field. In the diamagnetic case, the energy levels approachthe cyclotron or Landau levels.2.0m0.-L-0.5Fig. VI-2.-210ss, orteslas, or1021w/m 2 )Magnetic moment of quantized circular orbitsin arbitrary magnetic fields.The magnetic moment of the atom in these states is plotted in Fig. VI-2 in units nor-malized to "n" Bohr magnetons. The density of energy levels, normalized to the corre-sponding density of Landau levels, is plotted in Fig. VI-3. Note that the usually accepteddensity of states of an atom in zero magnetic field, which rises to infinity as negativeQPR No. 72-1.0 8108 10- 6(VI. GEOPHYSICS)1.0-0.8-0.6IO0.4B=I0.2 10-30 -- 8 10:- 6-1 2 ev -0.5 x10 - 2  0 +0.5x10 -2  +10 evEFig. VI-3. Density of atomic-energy levels for circular diamagnetic orbitsin the vicinity of the ionization potential.energies approach the ionization potential and is zero for positive energies, is a"singular" or physically unachievable condition. In arbitrarily weak fields these par-ticular states have a very low density for negative energies, and a constant density equalto the density of Landau levels for free electrons for positive energies.This work was partly carried out at the Computation Center of the MassachusettsInstitute of Technology.F. BitterB. AN INTERPRETATION OF SOME OPTICAL RADAR RESULTS"Recent optical radar observations of echoes from the upper atmosphere have beenreported elsewhere by Fiocco and Smullin.l The results of several successive nightsof observations indicated, among other features, weak sporadic echoes at altitudesbetween 110 km and 140 km,; between 100 km and 110 km a noticeable reduction of thereturned signal was observed. The interpretation of the results reported here has beendeveloped in collaboration with Dr. Giusseppe Colombo, of the Smithsonian InstitutionAstrophysical Observatory, Cambridge, Massachusetts, and the University of Padua,Italy.The results that are of present interest are shown in Fig. VI-4. The diagram givesthe observed radar cross section per unit volume, averaged over 10-km range intervalsThis work was supported in part by the National Aeronautics and Space Adminis-tration (Grant NsG-419).QPR No. 72(VI. GEOPHYSICS)1.5x 0 - 12EE10 -12bzFig. VI-4. Average of observed radar crosssections per unit volume versusc range.OnCr AVERAGE OF 13 DAYSo 5x]0 - 135 x 10- 17 JULY - 16 AUGUST 1963O70 90 110 130 150RANGE (km)and over 13 nights during which observations were possible, from 17 July to 16 August1963. The radar's wavelength is 0.694 micron.We are concerned at present with an interpretation of the echoes obtained at heightsabove 100 km, that is, with the presence of maxima in the radar cross section above100 km, and of minima between 100 km and 110 km. The diagram results from averagingthe successive observations of each single night (several hundred pulses), and thenaveraging again the results of the 13 successive nights, giving to each night the sameweight. A few remarks have to be made with regard to the accuracy of these determina-tions. Some measure of accuracy is provided by the amplitude of the rms background-13 2 2 3fluctuations, which is equivalent to 1.5 X 10 (Z/100) cm /cm (Z = height in ki).Because of slow recovery and nonlinearity of the photodetector, the sensitivity of thereceiver decreases with decreasing height. The effect is noticeable at altitudes below90 km; the cross sections, as given in Fig. VI-4, are less accurate at this range. Nocorrection has been introduced, since the present discussion is limited to the results ofobservations at higher levels. We note, however, that the echoes observed between80 km and 90 km, at the mesopause, are indicative of cross sections much smaller thanthose that would be expected in noctilucent clouds,2 and are in agreement qualitativelywith the measurements of Mikirov. 3 The appearance of these echoes could be relatedQPR No. 72(VI. GEOPHYSICS)to the same process that is responsible for the formation of the noctilucent clouds.It seems reasonable to assume that these echoes at higher altitudes are produced bysmall particles, meteoroids. A knowledge of their shape and of the ratio of the size tothe wavelength is therefore essential in order to establish their individual cross sections.No- =Q37r ( )2 X x 7-a2Q - N 47ro33x 27raX 0.694 microns1 = 0.694 micronsFig. VI-5.Radar cross section No( of N totallyreflecting spheres of equal radius aand constant volume Q.0.01 0.1 a(microns)- IRADIUSFor a particle much larger than the wavelength the radar cross section, a-, is propor-tional to the geometrical cross section and independent of wavelength; for dimensionsmuch smaller than the wavelength X, the scattering cross section decreases with X- 4dependence. In the intermediate region of sizes, large fluctuations occur. Values ofthe ratio f/ira 2 for totally reflecting spheres are given by Van de Hulst 4 as a functionof x = Zra/. Suppose that a given volume Q is fragmented into N totally reflectingspheres of radius a, the density remaining constant. The total radar cross section ofthe N spheres, taken as independent scatterers, is3Tr 1 0-No = Q 2 x 2 (1)1 ifA plot of x 2 is shown in Fig. VI-5. As the wavelength of the radar is 0. 694 micron,wraQPR No. 72bIN-lX(VI. GEOPHYSICS)a reduction in size corresponds to a large increase in total cross section until an opti-mum size (xz 1, az 0. 11 micron) is reached beyond which the cross section decreasesvery rapidly. Thus one may conceive that on its flight through the atmosphere a meteor-oid undergoes progressive fragmentation in such a way that the collective radar crosssection of the fragments increases until an average optimum size is reached and thatfurther breakup, at lower heights, is responsible for a successive reduction of theobserved cross section.In the real case the particles will not behave as totally reflecting scatterers; thechoice of spherical shape is unfavorable because it minimizes the geometrical crosssection for a given mass and is probably far from reality, since published photographs5of "fluffy" particles by Hemenway and Soberman indicate very complex shapes. Forthese filamentary shapes the radar cross section is much larger than the geometricalcross section.Since we are interested in obtaining from the measure of the collective radar crosssection an order-of-magnitude estimate of mass density and influx, but do not have anymeasurement of individual radar cross sections, we shall assume that at some stagein the descent the meteoroid breaks up into fragments of optimum size for observationat the radar wavelength. We shall also assume that when the optimum size is reached,the average radar cross section r is 10 times larger than the average geometrical crosssection A.Witt, Hemenway, and Soberman2 have collected particles from the mesopause. Theyfound a large number of submicron particles of a size that would not be expected toscatter efficiently at wavelength X = 0. 69 micron, and that cannot exist in elliptical orbitin the solar system, because of radiation pressure.Some conditions of a purely mechanical character, which we have formulated but willnot present here, indicate that physically the following process is possible: A meteoroid,1with a radius of 10 microns or more, a density between 0. 1 and 0.5, and enteringvelocity of 30 km/sec, will begin to fragment in sizes of 0. 1-0.5 micron at a height of120-140 km (which is above the height Z previously defined) if it has a crushing strengthsomewhat higher than 10 dynes/cm2; these fragments of density close to one will keepbreaking up in flight downward into smaller crystals, typically of 0.02-0.05 micron, atan altitude of 110-120 km, having reached a speed of approximately 10 km/sec, if theyhave a crushing strength of the order of 100 dynes/cm . The size distribution shouldbe variable with height, and the atmosphere would be working as a "filter."On the bases of the radar observations and of the present model of fragmentation,an attempt can be made to estimate the influx on Earth of meteoric material that isundergoing fragmentation and is of a size suitable for observation.From the size population found by Hemenway and Soberman it can be established thatmost of the total mass is obtained in sizes smaller than 0. 1-micron radius. AccordingQPR No. 72(VI. GEOPHYSICS)to our model, all of this material is produced by fragmentation. Thus an estimate ofthe flux based on these particles of larger size that are observable by optical radar athigher altitudes accounts for most of the mass obtained at lower levels. Some of thelarger particles may well enter at lower speed in such a way that their contribution tothe total flux will be small.Since the experiments have been performed in a period of high meteoric activity andat night, a seasonal and diurnal rate factor affects the measurements. For the sake ofobtaining an order-of-magnitude estimate, we take the yearly average of the observeddifference in cross section between the maximum above 110 km and the minimum between-13 2 3100 km and 110 km to be of the order of 10 cm /cm . For particles of dimensionsclose to optimum, we shall assume an average radar cross section of the order of-9 2 -147 X 10 cm , an individual mass of the order of 2.5 X 10 gm, a density of 1.5, withan average radial velocity of 5 km/sec. A total influx of the order of 6 X 104 tons a dayon Earth is thus obtained. It is unnecessary to emphasize the great uncertainty attachedto this estimate, in view of the scarcity of experimental data and the variety of assump-tions. The number obtained is, however, in agreement with other published results. Forinstance, it is in fair agreement, within an order of magnitude, with evaluations obtainedfrom measurements of meteoric impact on satellites by Dubin and McCracken.6 Thehypothesis of fragmentation may account for the relatively low influxes obtained on thebasis of Volz and Goody's twilight experiments. 7 ' 8G. FioccoReferences1. G. Fiocco and L. D. Smullin, Nature 199, 1275-1276 (1963).2. G. Witt, C. L. Hemenway, and R. K. Soberman, COSPAR, 4th Space ScienceSymposium, Warsaw, Poland, 1963.3. A. Ye. Mikirov, Planet. Space Sci. 11, 417-426, 1963 (translated by H. S. M.Massey from Iskusstvennye Sputniki Zemli, No. 13, 97, 1962).4. E. C. Van de Hulst, Light Scattering from Particles (John Wiley and Sons, Inc.,New York, 1957).5. C. L. Hemenway and R. K. Soberman, Astron. J. 67, 256-266 (1962).6. M. Dubin and C. W. McCracken, Astron. J. 67, 248-256 (1962).7. F. E. Volz and R. M. Goody, J. Atmospheric Sci. 19, 385 (1962).8. N. P. Carleton, J. Atmospheric Sci. 19, 424 (1962).QPR No. 72

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