A new theory has been developed which gives the distribution of density with altitude for a planetary exosphere in the absence of thennodynamic equilibrium. The results differ considerably from those calculated on the basis of a hydrostatic equation. To apply this theory to the earth's exosphere, we first fix the temperature of the base of the exosphere, which is located at 530 km, by using satellite drag data between 500 and 1000 km. A temperature of 1500° gives a reasonable fit to the rather sparse data and allows us to calculate the atomic oxygen distribution with altitude. From the cosmic ray neutron albedo theory of the inner (cosmic ray) radiation belt, we can set an upper limit of about 10 6 hydrogen atoms per cm 3 at an altitude of 1000 km, but their concentration could be less. However, the total density including the ionized component must be of the order of 10 −19 g/cm 3 at 1000 km. The existence of a minimum between the two observed radiation belts, the so-called “slot”, is accounted for in terms of the breakdown of the adiabaticity of the magnetic moment of trapped particles. This same theory also allows one to make statements concerning the mean energy of the trapped protons in the inner radiation belt. It should become progressively softer with increasing altitude. The outer (auroral) radiation belt, which is centered at 3 earth radii, has a lifetime which is controlled primarily by the presence of a scattering atmosphere. From a theory which takes into account both energy loss and scattering, one can calculate the intensity contours for the quasi-equilibrium state. Special techniques give the transient case following the injection of particles into this region. The initial injection of solar corpuscular radiation consists mainly of protons and electrons with velocities of 2 × 10 8 cm/ sec. These 20 keV protons form a third and rather transient ( $ ̃ 1 day) radiation belt at 4–8 earth radii; they account for most of the effects observed during magnetic storms. Their initial diamagnetie effects produce the “reverse sudden commencement” ( SC ∗ ). Their increase of upper atmosphere ionization accounts for the sudden commencement currents while their drift in longitude accounts well for the main phase of magnetic storms. In comparing various removal processes for the injected protons, we find that charge exchange is about 100 times more effective than atmospheric scattering. Using our theoretical distribution for the hydrogen exosphere, we can therefore calculate the complete development of a magnetic storm as a function of time, including the distribution around the earth of trapped protons as well as their magnetic effects.
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