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We estimated the brightness temperature of radio zebras (zebra pattern --ZP), considering that ZPs are generated in loops having an exponential densityprofile in their cross-section. We took into account that when in plasma thereis a source emitting in all directions, then in the escape process from theplasma the emission obtains a directional character nearly perpendicular to theconstant-density profile. Owing to the high directivity of the plasma emissionthe region from which the emission escapes can be very small. We estimated thebrightness temperature of three observed ZPs for two values of the densityscale height (1 and 0.21 Mm) and two values of the loop width (1 and 2 arcsec).In all cases high brightness temperatures were obtained. For the higher valueof the density scale height, the brightness temperature was estimated as 1.1$\times$ 10$^{15}$ - 1.3 $\times$ 10$^{17}$ K, and for the lower value as 4.7$\times$ 10$^{13}$ - 5.6 $\times$ 10$^{15}$ K. We also computed the saturationenergy density of the upper-hybrid waves (which according to the double plasmaresonance model are generated in the zebra source) using a 3D particle-in-cellmodel with the loss-cone type of distribution of hot electrons. We found thatthis saturated energy is proportional to the ratio of hot electron andbackground plasma densities. Thus, comparing the growth rate and collisionaldamping of the upper-hybrid waves, we estimated minimal densities of hotelectrons as well as the minimal value of the saturation energy density of theupper-hybrid waves. Finally, we compared the computed energy density of theupper-hybrid waves with the energy density of the electromagnetic waves in thezebra source and thus estimated the efficiency of the wave transformation.

Brightness Temperature of Radio Zebras and Wave Energy Densities in Their Sources