global electromagnetic induction in the moon and planets - MTNet

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.