In MRTI are received and investigated the microwave discharges of average and high gas pressure, developing in the field of radiation with amplitude, significantly smaller critical value, exclusively along a surface of dielectric. The discharges initiated by means of passive electromagnetic vibrators, located on a surface of dielectric, look like a net of thin channels pressed to a surface of dielectric. Experiments with dielectric plates from quartz, textolite, glass-reinforced textolite,

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... and quartz glass, ceramics and polyethylene have specified in independence of discharge properties on a kind of dielectric material. Special interest was presented by experiments with thin dielectric films. At a thickness of films even 100мкм discharges have the same properties, as discharges on a surface of unlimitedly thick plates. Experiments were spent on installations with wavelength of MW radiation 8.9 cm and 2.5 cm. As the reasons, causing primary propagation of streamer discharge over a surface of dielectric, the electrostatic effects and physical-chemical surface processes in presence of the discharge were considered. But the second factor was classified as a factor, which is not defining the reason of indifference of phenomena to a material of dielectric testifies. However, attraction to the phenomena theory of first factor, the processes of electrostatic effect, changing distribution of MW field in a vicinity of the head of the growing streamer, has appeared uneasy because the calculations have shown, that the increase in amplitude of a field at a head of a streamer near surface of dielectric with dielectric permeability ε ~ 2-4 (typical values for used materials) does not exceed 10-15 % for thick dielectric layers and very small for thin films, that is obviously not enough for maintenance of primary propagation along a surface. But more detailed calculations at both electrostatic and electrodynamic approach have shown, that presence of a dielectric layer with ε ~ 2-4 displaces a maximum of amplitude of a field in a streamer head towards a surface (not changing essentially its amplitudes) if the thickness of a dielectric layer is more than distance from the streamer head to a surface. By earlier numerical modeling it has been shown, that the streamer develops towards a maximum of amplitude of a field defined by the sum of a primary field and field generated by currents induced in discharge channels and forgoing to a head of streamer. At presence of dielectric the charges, induced in dielectric, displaces a field maximum nearer to surface so a streamer, keeping the tendency to extend in direction of field maximum, continuously slides over a surface. It is possible to assert, that the electrostatic factor is the defining factor for the surface streamer MW discharges.