The experiments with Z-pinches show the appearance of "hot sports", where neutrons and x-ray emission are produced. In the first stage of the hot-spot evolution the x-ray hardness reaches the values up to 10-12 keV,and in the second more long stage the x-ray hardness can reach the values up to 100 keV and even much higher. If the x-ray hardness in the first stage of the Z-pinch evolution can be explained by the plasma temperature,then in the second stage of the Z-pinch evolution the x-ray hardness, with the quantum energy about 100 keV and more, hardly can be explained in this manner.Therefore, some another mechanisms of the x-ray emission should be drawn. Up to now, there are various mechanisms of the generation of the x-ray emission with such a high x-ray hardness had been proposed: the forming of non-Maxwell electron distribution functions,a rapid increase of the Z-pinch resistance and the subsequent increase of the Z-pinch voltage, the generation of relativistic electron beams and maybe some others. The suggested theory includes in some sense all the enumerated features in the framework of the model,based on the violation of the plasma quasineutrality condition connected with Hall effect. This results in the generation of the current filaments with a very high potential difference across the filament. In addition, the electron current filaments are considered at the stage when the time of their evolution is smaller than the characteristic skin time. In this case, the total filament current must be equal to zero, so that the direct current along the filament axis must be accompanied by the retum current at the periphery of the filament. The intercurrent repulsion results in the increase of the electron density at the axis of the inner current, where the electron velocity has a maximum value which corresponds to a high value of the transverse potential difference. One must stress that according to the recent measurements the filament currents represent only a small part of the Z-pinch current.
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