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260 P. Dyal and C. W. Parkin, Induction in the Moon 2.5 POINT where: / DIPOLE - AXIAL ~SENSORiii g~(r)= exp(—k~ri /R) — exp [_k~(~~ + 2)] (27) o.A DATA ____________ 2.0 RT~’~ andk~are roots of the zero-order Bessel function. The A A A A TRANSXERSE L~?) axial components of the confined and unconfmed fields 3 4 are respectively —ai TRANSVERSE’ 1~iac/arand —a~,/u/ar;the ratio of 1.0 the /Bc\ radial component 1 ~ r of confined field tounconfmed 3k, 7g~(r) (28) field along the cylinder axis is: 0 I 2 3 4 ~ n1 4(kn) r/R Fig.9. Confmementof apoint dipole magnetic field, shown theoretically and experimentally. Theinserts schematically This axial confined-to-unconfmed field ratio is also show lunar confmement by the solar wind, approximated by plottedin Fig.9. a capped-cylinder superconductor enclosing a point dipole A laboratory experiment has been devised to exfield. The theoretical curves showratios of confined to unconfined dipolar field versus distance along the cylinder axis, amine the “axial” and “transverse” solutions (eq.25 Data are results of a laboratoryexperiment in which confine- and 28). The highly conducting solar wind plasma ment of a small dipole magnet’s field by acylindrical super- cavity is modeled by a thin lead superconducting conductor is measured experimentally, capped cylinder and the instantaneous induced polo. idal field is modeled by a small dipolar samarium- - The scalar potential which describes the field due cobalt magnet placed equidistant from the closed end to an unconfined point dipole is: and the side walls of the cylinder. The measured ratios mx = —i-r (24) of confined fields to unconfmed fields are shown in Fig. 9 along with the theoretical value expressed in eq.25 and 28. The transverse component of magnetic field due to The theory and laboratory data presented in Fig. 9 either of the potentials (eq.22 or 23) canbe calculated represent to first order the effects of solar wind comas a function of distancer along the cylinder axis, using pression on a poloidal induced lunar field, as measured B~(r) = —ail,/ax. The ratio of the transverse component. by a lunar surface magnetometer positioned at the of confined field to unconfmed field on the cylinder antisolar point. This compressive phenomenon, which axis is then: has a measurable geometrical effect on the poloidal i Bc\ 2 ~ r field,does notsignificantly change the time dependence 3N~f trans. 3 n1 = R 1(0)f~(r) (N,~— 1)4(Nn) (25) of puted the poloidal internal electrical-conductivity eddy-current field. Therefore, profile a(r), the corn- which is a function only of the poloidal time-dependence, where fn(r) is expressed in eq.23; 4(0) 0.5. This will not be modified by solar wind compression to the transverse conflned.’to-unconfined field ratio is plotted in Fig~9. order of approximation used here. Now we considerthe effect of confinement field 3.2. Compression ofthe permanent lunar fieldsby the due to a dipole lying on the cavity axis and directed along the cavity axis (see Fig.9, insert). The potential solar wind plasma of the confined dipole (P. Cassen, personal communi- Remanent magnetic fields have been measured by cation, 1972) is: Apollo magnetometers emplaced at nine sites on the Moon. Magnitudes and locations of these steady fields = m ~ J 0(k~x)g~(r) (26) are listed in Table I. ac ~ n=1 J~(k~) Simultaneous solar wind plasma properties have been measured at the Apollo 12 and 15 landing sites. - To first order, a compression of the Apollo 12 rema-
TABLE I Lunar surface remanent magnetic fields P. Dyaland C. W. Parkin, Induction in theMoon 261 Site Coordinates Measured magnetic fields (‘y) Apollo 12 3.2°S 23.4°W 387 Apollo 14 37°S 17.5°W 1037 and 43~(separated by 1.1 km) Apollo 15 26.1°N 3.7°E 37 Apollol6 8.9’S 15.5°E 1l27,113’y,1897,232~r,and3277 (separated by 0.5 —7.1 km) nent field in direct proportion to the solar wind pres. sure has been measured. For one-hour averages ofmeawind pressure increase of 7’ l0~8dyn/cm 2. The ratio of plasma pressure to total magnetic pressure is suTements, the increase in magnetic field pressure = 8ir nm V2/B~r= 5.9, where BST = + ~B, ~2I8,i., where L?ILR ~A — (BE +B 2 5), asshown is directly in Fig. corre! io. during stagnation maximum condition plasma ((3 ~ pressure, 1) is notindicating reaëhed and thata the local lated The magnetic to the plasma field pressure increasesnm fromV 38 to 547 for a solar shock is probably not formed at the Apollo 12 site. Modulation of the remanent magnetic field by time variations in the solar wind pressure should add noise 10 to induction measurements made on the daytime side of the Moon (Dyal et al., 1972a), as was discussed in 2 section 2.3. b 8 N I E I 6 4. Magnetization field induction and permeability cal- lIo~ N 6 k ~ k ~ ~ 1’-~ culationstion interaction immersed can Referring be mode written in B~.For modes the again steady to can times eq. be geomagnetic 1, when neglected we consider all other (e.g., tailthe induction field), formagnetiza theeq. Moon and 8A = BE + B~.For a sphere of permea- 1 bility p. immersed in a static magnetic field 8E’ the surface components of total magnetic field are ex- ~ pressed (Jackson, 1962; Dyal and Parkin, 1972) as: BAX=(l+2F)BEX (29) E 4 BAYZ = (1— F) BEyz (30) C 3 where: E = - 2 (2km+1)(km_l)[1_(_~)] I - F= R’3 km+1)~km+2)_2~~)(km_i)2 (31) ~30 331 332 333 334 335 YEAR 969 TIME, day Fig. 10. Simultaneous plots of the magnetic field pressuredif- Here km is the relativepermeability p/p 0, R is the radius ference &8~/8irand solar wind dynamic-pressureat the Apollo of the sphere, and Rc is the radius below which the 12 surface site, showing acorrelationbetween the pressures. planetary temperature is above the Curie point.
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 13 and 14: TABLE II Inductiveresponse times of
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