The Kinetic Theory of the Solar Wind and its Interaction with the Moon

Citation

Griffel, David Henry (1968) The Kinetic Theory of the Solar Wind and its Interaction with the Moon. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DH61-ZQ91. https://resolver.caltech.edu/CaltechETD:etd-09202008-111601

Abstract

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Beyond about .1 A.U. from the sun, fluid mechanics is not a good approximation for the solar wind, because the collision frequency is low. Analysis of the particle dynamics shows that if there are no collisions beyond .1 A.U., then at the earth T[...]/T[...] = 35; this is much greater than is observed. We study the effects of interactions by means of the Boltzmann equation. Solving it with Krook's collision term, we find that the temperature anisotropy observed by the Vela satellite requires each particle to make an average of 2 or 3 collisions between .1 and 1 A.U. The temperature averaged over direction roughly follows an adiabatic law, with γ = 3/2; γ tends to increase with distance. The theory predicts an excess of high-velocity particles, as is observed by Vela, even when the collision frequency is independent of velocity; but to produce an effect as strong as that observed requires a fairly strong velocity-dependence of the collision frequency.

We proceed to study the interaction of the wind with the moon, treated as a solid body, with neither magnetic field nor atmosphere, absorbing and neutralizing all incident particles. We construct an exact theory of the boundary layer between such a body and a plasma with a magnetic field parallel to the surface, valid when the plasma has no velocity towards the surface. The thickness of the layer is about two gyroradii, and the magnetic field rises across it according to the equation of pressure balance.

We then consider two-dimensional models of the complete wind-planet interaction, and show that in any steady two-dimensional flow, the plasma velocity must be tangential to the body. Then, using the model of the sheath constructed above, we show that there can be no steady flow at all around a finitely conducting cylinder.

Finally, we consider the magnetic fields induced by the interplanetary field inside the moon, taking account of its rotation. If the applied field is uniform, then in the steady state there is a constant axial field inside the sphere; near the surface there is a complex toroidal field, dying away to zero in the interior if the sphere is spinning rapidly. If the external field is non-uniform, there is a residual toroidal field throughout the sphere. If the diffusion time is longer than the time between reversals of the inter-planetary field, then the moon will contain concentric shells of toroidal and axial fields, independently diffusing inwards.

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