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258 P. Dyal and C. W. Parkin, Induction in theMoon i = x, y, z, where A, are transfer functions of compo- lunar center. Other conductivity profiles have been nents of frequency-dependent magnetic fields, ex- calculated using the Sonett et al. (1971) transfer funcpressedin the orthogonal coordinate system with tion, showing that the spike profile is not unique but origin on the surface of the sphere (~is radial and j) that the frontside transfer function can be fitted by and ~ are tangent to the surface); bEj(f) is the simpler two- and three-layer models (Kuckes, 1971; Fourier transform of the external driving magnetic Sill, 1972; Reisz et al., 1972). field; bpj(f) andbr,(f) are Fourier transforms of the induced global poloidal and toroidal magnetic 2.3. Comparison of transient and harmonic-analysis fields, respectively, techniques The harmonic data analysis approach involves Fourier-analyzing simultaneous data from the Apollo Since transient and harmonic techniques yield dif- 12 lunar surface magnetometer, taken during lunar ferent conductivity profiles (compare Fig. 6 and 8) daytime, and the lunar orbiting Explorer35 magneto- using data from the same magnetometers, it is useful meter. Then ratios of the surface data to orbital data to discuss the assumptions involved in both analyses. are used to calculate a transfer function of the form First we consider two basic assumptions of the harof eq.21. It is assumed that the toroidal induction monic technique: (a) only the poloidal induction and mode is neglected such that the Fourier-transformed external driving fields are measured on the daytime surface magnetometer data represent the sum lunar side; and (b)the induced poloidal field is perbEj(f) + bpi(f), while the transformed orbiting mag- fectly confmed by a spherically symmetric current netometer data represent the driving field bE,(f) layer. The first assumption considers that the total alone, field measured by the lunar surface magnetometer is The form of the transfer function is determined by composed of onlythe external solar wind driving field the internal conductivity distribution in the Moon; BE and the poloidal lunar response field Bp. By reftherefore, a “best fit” conductivity profile can be ob- erence to eq. 1, we recognize that various other fields tamed by numerically fitting to the transfer function. may be contributing to the surface magnetometer data, Fig. 8 shows the “best fit” radial conductivity profile e.g.,interaction fields (BF) due to such effects as cornof Sonett et al. (1971) obtained in this manner. The pression of lunar remanent fields by the solar wind conductivity profile is characterized by a large “spike” plasma and generation of plasma wave modes on the of maximum conductivity about 1500 km from the sunlit side. Referring to Fig. 8, we note an asymmetry effect which isnot predicted by simple harmonic-analysis theory: the harmonic analysis yields two different i02 I I I conductivity profiles, one calculated from y-axis (east— west) data alone and the other from z-axis (north— south) data alone. Thisy—z asymmetry can be ex- \ plained as being in part due to the daytime compression \ \ of the local rernanent field at the Apollo 12 magnetoio 4 meter surface site by the solar wind (Dyal et al., 1972a). o-, mho/meter - ~ Thus, when lunar daytime magnetometer data are used - -- -to study global lunar properties, knowledge of simultaneous solar wind propertiesis important a. The second assumption considers that the induced l0”6 poloidal field is confined in the lunar sphere by the COSOUCTIVIIY mRflI* RM solar wind plasma. Experimentally the solar wind plasma I I I spectrometer (Snyder et al., 1970) does not measure a 4 8 2 6 20 confining plasma on the dark side lunar hemisphere, and LUNAR RADIUS kmx 102 the transient magnetic field data show to first order a Fig. 8. Electrical conductivity profiles from Fourier harmonic vacuum poloidal response on the lunar dark side (Dyal analysisof lunar daytime data (from Sonett et at., 1971). and Parkin, 1971). It is questionable whether confme-
P. Dyal and C. W. Parkin, Induction in theMoon 259 ment is complete even on the sunlit side: a subsatel- resulting poloidal-induction field and any permanent lite magnetometer has measured evidence of induced fields originating in the lunar crust. Both of these interlunar fields at distances greater than 100 km above actions have beenmeasured by Apollo magnetometers the lunar sunlit surface (Coleman et al., 1972), mdicating that confinement isnot complete over dis- and solar wind spectrometers. tancesgreater than a proton gyroradius (‘~100 km). 3.1. Confinement of induced poloidal fieldsby the For these reasons, the spherically symmetric plasma confinement assumption should be modified. solar wind plasma In summary, it is seen that magnetic fields meas- Fig. 3 schematically portraysthe effects of the highly ured on the lunar day side quite possibly involve a conducting solar wind on the lunar induced poloidal very complicated set of magnetic phenomena which field; in this case the induced field geometrical con-figcan contribute varying magnetic field amplitudes at uration is altered such that the poloidal field is cornvarying frequencies over the entire measured spectrum, pressed onto the lunar surface on the sunlit side and is and that these contributions cannot be adequately extended back into the cylindrical “cavity” region on treated using the above-mentioned assumptions the dark side. This compression has been experlinen- (a) and (b). A recent harmonic paper (Sonett et al., tally confirmed by measurements from magnetometers 1972) has considered effects such as that due to on the lunar surface. For the uncompressed (vacuum) remanent field compression and responsevariations case the ratio of tangential components of surface as a function of solar wind k-vector direction with total field (BAY,Z) to external driving field (BEy,z) will respect to the Moon. As a result, the conductivity have a maximum value of 1.5 (see eq.8). Daytime “spike”, which was emphasized earlier, is now recog- ratios, however, are considerably higher than 1.5; for nized as only one of a larger set of possible conduc- example, at 0.01 Hz the z-component amplication has tivity proffles, some of which are much more in agree- been measured to be 3.7 (Dyal et al., 1970). Nighttime ment withthe transient-response three-layer models data show a smaller compressive effect in the tangential published earlier (Dyal and Parkin, 1971, 1972). components; examples in Fig. 4B show a y-axis ratio of Furthermore, the recent harmonic papers state that 2.0 and az-axis ratio of 1.75. resolution of data restricts conductivity models to The confinement of the induced poloidal field by three or four layers rather than the eight layers used the highly conducting solar wind is theoretically studied for the “spike” model, by considering a pOint dipole field inside a supercon-~ Though of an apparently less complicated nature, ducting cylinder. Two geometrical orientations of the there are also problems associated with the assump. point dipole are considered: along the cylinder axis tions of the darkside transient analysis technique. and transverse to the cylinder axis. (See inserts in Fig.9 The main problems involve: (a) the finite time re- for an illustration of these orientations.) The field of quired for a “step” transient to cross the lunar sphere; the dipole orisnted transverse to the cylinder axis has (b) the field increase along the antisolar line due to been determinedby Parker (1962). For a dipole on diamagnetic currents at the solar wind cavity bound- the axis of a capped superconducting cylinder (of ary; and (c) deviations from sphere-in-a-vacuumtheory radius R), lying a distance R from the cap, the scalar due to partial confinement of induced fields by the potential of the confined dipole is: solar wind. These problems are considered in section 2 2.13; the partial-confinement problem (c) is considered in more detail in the following section. — —2m cos ~, 2 n=1 “~c— R Np~J 1 (N~x/R)f~(r) (N2—DJ2(N 22 ‘ n / 1’ n where: f (r) = exp (—N Jr I /R) + exp (—N (r + 2R)/R) (23) 3, Interaction of the solar wind withlunar mduced ~1 fl fl - and remanent fields and 4 is the azimuthal angle measured around the axis of the cylinder, from the dipole axis;m is the The solar wind plasma transports the inducing mag- dipole moment;r is the distance along the cylinder netic field past the Moon and also interactswith the axis; N~is the n-th root off 1 (Nn) = 0.
Page 1 and 2: Physics of theEarth and Planetary I
Page 3 and 4: P. Dyal and C. W. Parkin, Induction
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Page 11 and 12: TABLE I Lunar surface remanent magn
Page 13 and 14: TABLE II Inductiveresponse times of
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