Textbooks rarely give time−domain solutions to antenna problems. For the case of a finite linear antenna along which a fixed current waveform propagates, we present analytical time−domain solutions for the electric and magnetic radiation (far) fields. We also give computer solutions for the total (near and far) fields. The current waveform used as an example in the computer calculations approximates that of a lightning return−stroke, a common geophysical example of the type of radiation source under consideration.

The magnetic flux density due to first and to subsequent lightning return strokes is calculated for distances from the strokes of 0.5 to 200 kin. The basis of the calculations is various assumed forms for the channel current as a function of time and of channel height. Two new channel-current models are introduced for first strokes and one new model for subsequent strokes, in addition to the use of the models of Bruce and Golde and of Dennis and Pierce. The new models provide a better approximation to the real lightning channel current than do the previous models, but all models considered yield radiation fields far from the channel that are consistent with experiment. It is shown that, contrary to the claims of Norinder and co-workers, the magnetic-field rise time for a stroke within a distance of about 20 km is essentially unrelated to the current rise time in the stroke channel base. For subsequent strokes, field rise times of many tens of microseconds can be due to current rise times shorter than a microsecond. On the other hand, field rise times for subsequent strokes may be strongly influenced by current fall times. The analysis of Norinder and co-workers which relates peak channel-base current to peak magnetic field yields values of current that can be considered accurate to about a factor of 2. :. spatial properties of the return-stroke current are known. A number of investigators (Bruce and Golde, 1941; E. L. Hill, 1957; Dennis and Pierce, 1964; •R. D. Hill, 1966) have assumed models for th e return stroke in order to compute the radiation fields far (order of 100 km) from the discharge. Other investigators (Norinder and I)ahle, 1945; Papet-L•pine, 1961, 1964 Miiller-Hillebrand, 1962) have attempted to determine the return-stroke current from close measurements (within 10 km of the discharge) of the magnetic field and application of theory. In the present paper we present calculations of the magnetic field due to the return stroke at distances of 0.5 to 200 km from the discharge channel for various assumed returnstroke models. We consider only the usual type of return stroke, the return stroke between cloud and ground which lowers negative charge from cloud to ground.Before considering the return-stroke models used previously and those to be considered in this-paper, it is appropriate to examine the available experimental data on the return stroke. 'According to Schonland [1956], as a Copyright ¸ 1969 by the AmeriCan Geophysical Union. first return stroke propagates from ground to cloud its luminosity decreases abruptly in intensity at each branch point, luminous decreases being accompanied by decreases in the velocity of the return-stroke wavefront. Both luminosity and velocity are roughly constant between branches. Schonland [1956] gives I X 108 m/see as a typical initial velocity for a return-stroke wavefront and 4 X 107 m/see as a most frequent value near the top of the channel. Schonland ei al. [1935] and Schonland and Collens [1934] state that, in addition to the luminosity and velocity changes ...

Over the past 60 years, ground-based remote sensing measurements of the Earth's mesospheric temperature have been performed using the nighttime hydroxyl (OH) emission, which originates at an altitude of ∼87  km. Several types of instruments have been employed to date: spectrometers, Fabry-Perot or Michelson interferometers, scanning-radiometers, and more recently temperature mappers. Most of them measure the mesospheric temperature in a few sample directions and/or with a limited temporal resolution, restricting their research capabilities to the investigation of larger-scale perturbations such as inertial waves, tides, or planetary waves. The Advanced Mesospheric Temperature Mapper (AMTM) is a novel infrared digital imaging system that measures selected emission lines in the mesospheric OH (3,1) band (at ∼1.5  μm) to create intensity and temperature maps of the mesosphere around 87 km. The data are obtained with an unprecedented spatial (∼0.5  km) and temporal (typically 30″) resolution over a large 120° field of view, allowing detailed measurements of wave propagation and dissipation at the ∼87  km level, even in the presence of strong aurora or under full moon conditions. This paper describes the AMTM characteristics, compares measured temperatures with values obtained by a collocated Na lidar instrument, and presents several examples of temperature maps and nightly keogram representations to illustrate the excellent capabilities of this new instrument.

Expressions are derived that allow the current in a lightning return stroke to be calculated from a measurement of either the magnetic flux density or the radiation field (electric field intensity or magnetic flux density) of the discharge. Published magnetic field and radiation field data are of insufficient time resolution to allow an adequate current determination to be made.Most lightning current measurements have been made on strokes to tall buildings or towers and represent the current flowing at the lightning channel base . In an effort to determine the properties of lightning strokes not influenced by tall structures, Norinder and his co-workers [e.g., Norinder and Dahle, 1945] measured the magnetic fields from distant strokes to earth and from theory derived lightning currents. Urnan and McLain [1969], by assuming a range of channel currents and computing the resultant magnetic fields, have shown that the theory used by Norinder and coworkers is erroneous. As a result, the current rise times Norinder and his co-workers derived are invalid, whereas the peak currents they derived are probably within a factor of 2 of the actual peak currents.In this paper we derive expressions that allow the current in a lightning return stroke to be calculated from a measurement of either the magnetic flux density or the radiation field Copyright (•) 1970 by the American Geophysical Union.(electric field intensity or magnetic flux density) of the discharge. THEORY We assume that each point on the lightning channel is the same distance r from an observation point P on the earth's surface and that the earth is a perfectly conducting plane. Thus, we treat the channel as if it were composed of a circular arc above the earth's surface centered at P and its 'image' arc below the earth's surface. The 'arc' approximation to a vertical lightning channel is roughly valid for distances from the channel greater than about two or three times the return stroke height. For example, suppose one is solely interested in obtaining values for the rate of rise of current and the peak current. These occur in the first several microseconds of the return stroke so that the maximum return stroke height of interest is'a few hundred meters (corresponding to a typical initial return stroke velocity of about one-third the speed of light), and the theory can be aplied for measurements made at any distance 5143

Expressions are derived relating the stepped leader radiation field to the leader current and current propagation velocity. These expressions are also applicable to the return stroke. The waveforms of the stepped leader radiation field measured by Pierce, Appleton, and Chapman can be reproduced by the sum of the effects of two current waves: (1) a slow current wave with a current width at half‐maximum of about 14 μsec and a propagation time of about 12 μsec, which produces the wings of the radiation field curve, and (2) a fast current wave with a current width at half‐maximum of 4 to 5 μsec and a propagation time of about 1 μsec, which produces the positive and negative peaks of the radiation field. The fast current is associated with the luminous leader step; the slow current is most reasonably associated either with the leader step or with the leader channel above the step. The peak current for the typical stepped leader waveform described by Pierce is calculated to be between about 800 amps and 5 ka; the maximum rate of change of current between about 0.25 and 1.5 ka/μsec. Alternatively, the maximum rate of change of leader current is derived from Hodges's data on the ratio of peak leader radiation field to peak return stroke radiation field. For a modal type α stepped leader the maximum rate of change of current is found to be about 2 ka/μsec; for a modal type β leader, about 10 ka/μsec. The currents calculated to flow in the stepped leader provide a charge transfer of between about 2×10−3 and 10−2 coul per leader step, an insufficient amount of charge to account for the 10−3 coul/m found on a typical fully developed stepped leader. Relatively steady currents must therefore flow in the leader channel to account for the charge transfer. Since the significant light output from a stepped leader has considerably shorter time duration than the significant current, it is probable that the photographed luminosity of the leader is due to the electrical breakdown at the propagating current fronts, rather than to the larger currents that subsequently flow.