Roal’d Z. Sagdeev

Nonlinear oscillations of rarified plasma

The paper basically is a review of a number of studies devoted to the theory of nonlinear motions of plasma under conditions where collisions between particles do not play a determining role.The problem is formulated in the introduction. It concerns the evolution in time of an initial perturbation of finite amplitude. The resulting physical picture will depend on these competing processes: nonlinear increase of wave steepness, dispersion, absorption and instability. In a number of cases where adsorption and instability are insignificant, it is possible to obtain an idea of the character of the nonlinear motions by applying the appropriate linear dispersion law.The second Section presents certain specific types of nonstationary nonlinear motions permitting exact mathematical solution, namely: nonlinear oscillations of electrons at zero temperature, nonlinear motion of plasma across a strong magnetic field, and ion waves of finite amplitude in non-isothermal plasma where pi pe. In a number of instances, evolution of the initial perturbation leads to the formation of a multi-component current, some peculiarities of which are discussed in the third Section. In the next Section stationary nonlinear waves are described, i.e. waves not changing their form with time. In a particular case they are the so-called solitary waves, similar to waves on the surface of heavy liquid in a channel of finite depth. The possibility of the existence of such waves requires linear laws of dispersion of a specific character. The possibility of solitary waves of rarefaction is pointed out.The question of absorption of waves in rarified plasma is then discussed. An approximate quasi-linear method is developed which permits the kinetic considerations in the absorption of waves of finite amplitude to be simplified. The method consists in the representation of the distribution function f(r, v, t) as a sum of rapidly and slowly varying terms. In the equation for the slowly varying term a quadratic average effect of fast oscillations is taken into consideration. This method is applied to two particular problems: the absorption of Langmuir electronic oscillations (in the limit of very small amplitude the equation for wave-damping goes over into the well-known formula for the so-called Landau-damping), and the cyclotronic absorption of transversely polarized waves which propagate along the constant magnetic field.In the last section some types of instabilities of non-linear motions are shown. In addition to the instabilities associated with the multi-component motion, it is shown that waves in a magnetic field (in particular, solitary waves) are unstable if their amplitude exceeds a certain critical value which decreases as the plasma temperature decreases.

An infinitely expandable space radiotelescope

Abstract Great rewards for radio astronomy lie in increasing antenna collecting areas and the distance between them. Both these possibilities, which determine sensitivity and angular resolution, can be developed essentially without limit if radiotelescopes can be built in space. Radio interferometers, with base lines up to 10 AU, assembled from large reflectors 1 to 10 km in diameter, could operate in the 1 mm to 1 m range with a sensitivity of 3 × 10 −37 W m −2 Hz −1 and an angular resolution of 1.5 × 10 −10 sec of arc. These parameters are a million times better than those of modern radio astronomical systems. Such instruments could solve many urgent problems: the search for artificial radio signals and other evidence of extraterrestrial civilizations; detection and study, within the RF range, of solar-like stars and planets; and holography of astronomical sources and direct measurements of their distance. The maximum distances of objects which could be studied would be comparable with the radius of curvature of the Universe. A possible space radiotelescope (SRT) configuration, with a modular spherical reflector and feeds providing multibeam operation, is analyzed here. An extendable reflector capable of operating at any intermediate stage is assembled from 200-m modules. These consist of a three-dimensional spar framework on which flat hexagonal subreflectors of about 4 m are mounted. The precise geometry required of such a reflector is provided by automatic adjustment of subreflector position relative to the framework and by adjustment of connections between modules. In this way, radiotelescopes for the 1 mm to 1 m range may be built with diameters up to 10 km. The problems of system delivery and assembly in orbit are assessed. Preliminary estimates for developing and constructing an SRT that is more than 1 km in diameter are lower than for a similar collecting area on Earth. State-of-the-art technology already allows the development and construction of a 200-m space module.