SumnnaryThe joule heating and motion of uniform ionized gas is discussed, on the assumption that uniform electric and mechanical force fields are orthogonal to the (homogeneous) magnetic field. Application to the ionosphere during geomagnetic disturbance reveals (i) Joule heating at a rate of order 10-5 erg cm-3 sec-1 in the region 100 to 200 km altitude at the auroral zone is common during geomagnetic disturbance.(ii) Scale heights and temperatures at altitudes above about 100 km increase with geomagnetic disturbance. (iii) The energy of the process causing geomagnetic disturbance is in general not measureable by the energy of geomagnetic disturbance. (iv) A horizontal gradient of pressure of size 10-10 dyne cm-3 may be maintained at heights above 150 km in the auroral zone during geomagnetic disturbance. (v) Wind speeds in the polar ionosphere increase with geomagnetic disturbance.

SummaryA model of an aurora regarded as a plane slab of highly ionized air parallel to the geomagnetic field within the ionosphere is examined. The model is stable in the presence of a wind of neutral molecules which, blowing the slab across the geomagnetic field, generates an electric polarization field perpendicular to its faces and a current along its length. This current is concentrated in a small height range and is chiefly due to electron drift.The aurora moves normal to itself with a speed of the same order as the wind speed, while the drift carries its luminosity and ionization pattern along its length at a speed an order of magnitude greater. Measurement of these speeds will permit determinations of collision frequencies of ions and electrons within the aurora.Assuming, in the equatorial vicinity of the auroral zone, an equatorwards wind in the evening and a polewards wind in the night and morning hours it is possible to explain the major movements of the aurora and associated bay type magnetic disturbances. It is suggested that the magnetic disturbance indices K and Kp are indicators of wind speed. A likely mechanism of maintenance of luminosity and ionization in the aurora is outlined. The general features of magnetic disturbance current systems within the auroral zone are briefly considered in relation to the theory and it is suggested that auroras are visible manifestations of the current flow.Qualitative speculation on a possible source of energy for winds in the polar dynamo region leads to a unified account of the Van Allen radiation belts, auroras, and some (low latitude) airglow.

Recently, Bond and Jacka (1962) sought to order the average frequency of occurrence of visible auroras in eccentric dipole latitude. It is considered that eccentric dipole co-latitudes (II'), longitudes (cp'), and times for places on the surface of the Earth (here assumed spherical) may be of interest to workers in various fields.Mapped grids of II' and cpt are reproduced here. The Working Data and Formulae (a) The coordinate transformationsOne approximation to the magnetic field of the Earth is that of the eccentric dipole. It is defined so that the direction of its axis is that of the centred dipole approximation to the geomagnetic field (Chapman and Bartels 1951) and in which all but the sectorial terms of second order in the magnetic potential vanish (Bartels 1936).Working data for the present computations were taken from Parkinson and Cleary (1958). They find the geographic co-latitude (II) and longitude (cp) of the poles (a' for austral, b' for boreal) of the eccentric dipole to be lIa' = 165·0, CPa' = 120,4,whilst the location (D) of the eccentric dipole is 0·0685 Earth radii from the centre For present purposes the transformation from geographic to eccentric dipole coordinates is effected in stages as follows.(1) A right-handed system of geographic coordinates (x, y, z) is selected so that the origin is the centre of the Earth, the z axis points to the north geographic pole, and the x axis is in the meridian plane of Greenwich.

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SummaryThe geometry of the radiation point of an auroral corona is examined. The radiation point of two rays is the antidirection of the point within the Earth at which the rays meet or appear to meet. It is therefore incorrect to identify the radiant point of a corona with local auroral zenith. Their difference in direction is commonly 0.5° of zenith distance. The importance of rays as magnetic disturbance indicators in the height range 100-1000 km is stressed, particularly in view of possible deformations of the magnetosphere whose full effects may not be estimated from groundbased observations of the geomagnetic field.

Using the concept of steady nozzle flow along a narrow tube, the effect a variable temperature has on achieving one or two critical points is considered for a neutral gas in a locally heated region of the outer atmosphere of a planet or star. An implicit finite-difference formula, which does not require restrictions on the temperature variation for convergence, is used to solve the general nozzle flow equation. The direct dependence on temperature variation of a single critical point at which the flow becomes supersonic is shown for a model in which the gravitational force component is almost constant. The mathematical possibility of achieving a solution that passes through two critical points, such that in the intermediate region a reversal occurs and the velocity is supersonic, is demonstrated and an example is given.

The concept of steady nozzle flow along a narrow tube is applied to the motion of neutral gas constituents in a locally heated isothermal region of the outer atmosphere of a planet or star. The artificial nozzle throat at which the flow becomes supersonic is achieved by using one of two streamline functions within a vertical plane suggested by the possible shapes of convection cells. One streamline spirals above the surface of the planet at constant elevation, and the other 'bends over' asymptotically towards the horizontal. The former achieves the nozzle throat by the gravitational force decreasing with distance from the centre of the planet, while the latter relies on the gravitational component along the streamline decreasing as the streamline approaches the horizontal. Conditions under which the effects of viscosity and frictional interactions in the Earth's atmosphere may be neglected from the assumed hydrodynamic description are considered. For the proposed models and boundary conditions appropriate to an intensely heated region of the Earth's atmosphere, the dependences of the critical distance, temperature boundary values, and velocity and heating profiles on variations in the parameters are shown.