3.1. Dust aggregation process in the early solar nebula
Weidenschilling and Cuzzi  developed a model of dust aggregation in which the relative velocities between grains embedded in the solar nebula gas are determined by their sizes. A crucial point in this model is the question under which conditions a collision will lead to sticking or not. Based on the collision velocities given in  for 1 AU solar distance, our results indicate that micron-sized grains always stick to objects up to cm to dm size and can stick to objects of dm to m size due to effects of irregular grain shape or collisional grain charging. The latter effect can directly contribute to the efficiency of the preplanetary dust aggregation because rebounding grains can be trapped in the collision-induced electrostatic fields. Particle sticking in the velocity regime of several 10 m s_1 due to effects of irregular grain shape or collisional charging is important in the frame of the model because the authors identified the growth in the cm to m range as the "crucial gap". Both for smaller and for larger bodies, the relative velocities in collisions are smaller than for this size range and can thus more easily explain particle growth. Also for the outcome of a more recent modelling by Weidenschilling  which is more related to comet formation but still based on the same model as used before in , the stickiness in the velocity regime of several 10 m s-1 is critical.
Electrostatic forces are not the only long-range interactions which support the dust aggregation process. Niibold and Glassmeier  theoretically investigated the aggregation of magnetic particles in an astrophysical context and additional experimental  and numerical work on this topic is under way.
3.2. Influence of magnetic fields on charged particle motion?
Weidenschilling and Cuzzi  assumed that the motion of particles in the solar nebula was exclusively caused by gravitation and aerodynamical drag forces. However, our results show that the particles or a fraction of them could be highly charged which rises the question about influences of magnetic fields. In  we demonstrated that, according to presently discussed magnetic conditions in the solar nebula, magnetic forces on micron-sized particles could dominate aerodynamical ones. However, we also pointed out that assumptions about the magnetic field and its motion are highly uncertain today. Further work will be necessary to investigate the possible action of magnetic forces on particles which could influence the spatial dust distribution in the solar nebula, the relative velocities in collisions. Concerning the idea that, in case that magnetic forces cause fast enough collisions, further collisional charging could lead to a self-sustained collisional grain charging process.
Meteoritic chondrules are stony spheroids of mm-size which underwent a melting by a short-duration heating in the time of the solar system formation. Chondrules are common in meteorites suggesting that they are important for understanding physical conditions in the solar nebula. Collisional dust grain electrification, subsequent large-scale electric field generation by separation and accumulation of oppositely charged objects, and, finally, electrical breakdown in the neutral gas of the early solar nebula has long been discussed to lead to lightning capable of melting meteoritic chondrule precursors. Although this explanation is, compared to others, not favored today , it is still seriously under discussion. Three points of recent work show that a detailed treatment of this topic might lead to new insights which support the idea of chondrule formation by lightning. (1) Grain charging is, according to our experimental results, by orders of magnitude stronger than in former models  . The work of Desch and Cuzzi  showed that a numerical model involving stronger charge transfers in grain-grain collisions could explain chondrule formation by lightning. (2) Based on experimental work, it was pointed out that the dust aggregates are less compact than assumed in former work resulting in larger surface-to-mass ratios . With the larger surface, a larger surface charge can be carried per particle mass. This effect is comparable to an effect investigated in  who treated the role of a fine dust component. In the frame of this model, the efficient transport of electric charges due to a large surface-to-mass ratio would support the the chondrule formation by lightning if such a dust component existed. Our experiments help to quantify the charge transport because surface charge densities resulting from collisional charging were determined, and they indicate a high charge transport efficiency. (3) The awareness of and the basis for treating the large-scale separation of oppositely charged objects due to interactions with the turbulent nebular gas has improved. E.g. Cuzzi et al.  reviewed this topic with respect to chondrule formation, and Klahr and Henning  investigated the role of gas eddies in trapping and concentrating solid particles depending on their sizes and aerodynamical properties. Based on the results by Poppe et a.l.  summarized in this contribution, we propose to focus the interest on magnetic interactions with charged particles which could play an important role in determining the particle motion and the spatial distribution of the particles. This suggests that an additional separation mechanism directly sensitive to the sign of charged particles could be viable.
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