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AlfvéN: It is difficult to see how your mechanism works. You assume that the current is given by the conductivity of the body. Instead, would not the lack of charged particles transferring the current to and from the body be the limiting factor? If so, the energy released by ohmic heating must be small compared to the heating due to direct solar-wind impact on the body.

SINGER: Have you investigated the torque produced in the parent body by the interaction of the induced magnetic moments and the external field?

SONETT: This calculation has not been carried out. It was suggested earlier (Sonett et al., 1970) that fields of the magnitude indicated would have completely despun parent bodies. Then if the asteroids are their residues, they should not be spinning today. Repeated collisions, however, could cause spin up where the total ensemble spin angular momentum is zero but both prograde and retrograde spins are present. SINGER: For one of your modes of heating, it is necessary for currents to flow between the solar wind and the body. Will photoelectrons suffice? SONETT: It seems most likely that photoelectron emission from the negative hemisphere and positive ion collection on the other hemisphere would suffice for the steady-state TM mode that I discussed. A value of nearly 10-3 A/m2 is given for peak photocurrent (Sonett et al., 1970). The use of the photocurrent mechanism to supply current carriers means, however, that the mechanism is restricted to the sunlit hemisphere, whereas the calculations are for cylindrical symmetry. However, I do not think that the error introduced by the restriction to the sunlit hemisphere is severe.


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R. T. G/UL/
WASA Manned Spacecraft Center

Alfvén and Arrhenius (1970) have considered the development and stability of jetstreams by collisional interactions among grains; and they propose that in a jetstream environment, grains may collect and adhere to form self-gravitating embryos. Gravitational attraction of smaller particles by these embryos may then lead to a net accretion because high relative approach speeds, which could erode or break up embryos, have been minimized during the formation of the jetstream.

As an embryo grows, the synodic orbital frequencies between it and the particles it attracts become greater than the collision frequencies among these particles and between these particles and the rest of the jetstream. At this point, the embryo rather than the primordial jetstream will determine both the orbital parameters a, e, and i that the particles near the embryo adopt and the distribution of the particles among these orbits. The question is, will the redistribution of particle orbits by embryos remove particles from the jetstream?

Figure 1 illustrates schematically how streams of particles are attracted to impact an embryo in a two-dimensional model developed by Giuli (1968a,b). Calculations for a three-dimensional model have been made, and they qualitatively support the results for the two-dimensional model. The dotted lines represent elliptical particle orbits as seen in a rotating coordinate system centered on a massless embryo. The coordinates rotate with the same period as the embryo's orbital period. As mass is added to the embryo, it attracts some of the particles of given a and e to impact, and it gravitationally scatters other particles from their former (a, e) orbits and places them in different (a’, e') ones. The impact cross section of the embryo is greatest for those orbits that provide impacting particles with impact speeds vi at or near the embryo escape speed ve. There is a well-defined relation between a and e for impacting orbits with visve = const = 1, say, such that, if the dotted lines in figure 1 represent (amax, emax) for these orbits, then all impacting orbits with vi = we are contained within the two regions defined by the inner and outer extremes of the dotted lines.

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Figure 1.—Schematic illustration of particle streams gravitationally attracted to an embryo in the two-dimensional model developed by Giuli (1968a,b).

Calculations show that particles on impacting orbits with given visve that do not impact on a given “pass” by the embryo will be scattered back into orbits with different (a’, e') that are also impacting orbits with the same value of v/ve, or else will be scattered into orbits with greater (a", e") that will eventually become impacting orbits with the same visve as soon as the embryo becomes massive enough to reach them. In other words, if a particle is ever on an impacting orbit with given visve, it remains on some orbit with the same visve until it impacts, no matter how many times it is scattered before impact occurs. Spatially this means that, as the embryo grows, the particles that it does not capture on a given pass are shoved outward into more distant locations in the primordial jetstream, where they may be captured on succeeding passes. In two dimensions, the two “scattering jetstreams” (denoted by the inner and outer extremes of the two dotted lines in fig. 1) recede into the surrounding “viscous jetstream.” The region between the scattering jetstreams is mostly devoid of particles; the regions outside are populated by the primordial jetstream particles; and the regions in the scattering jetstreams contain both primordial particles and particles relocated from the inner regions. Therefore, we expect the scattering jetstreams to have higher particle density than the viscous jetstream. In three dimensions, we expect the scattering jetstream to be a toroidal annulus of enhanced particle density, enclosing a tube of diminished particle density. In the center of the tube is the embryo.

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