rate, which is also associated with an important qualitative change in the process, which becomes a periodic function of the distance to the quark star surface.

The present paper is organized as follows. In Section 2 we review the basic properties of the electrosphere of quark stars. The electron-positron rate production in the electric field of the electrosphere is obtained in Section 3. The boundary effects are considered in Section 4. In Section 5 we calculate the electron-positron pair flux of the electrosphere and compare our results with those obtained by @Us98a [@Us98b; @Us01]. A brief summary of our results is given in Section 6.

Structure of the electrosphere of strange stars
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In the electrosphere, electrons are held to the strange quark matter (SQM) surface by an extremely strong electric field. The thickness of the electrosphere is much smaller than the stellar radius $R\simeq 10^6$ cm, and a plane-parallel approximation may be used to study its structure [@Us05]. In this approximation all values depend only on the coordinate $z$, where the axis $z$ is perpendicular to the SQM surface ($z=0$) and directed outward. To find the distributions of electrons and electric fields in the vicinity of the SQM surface, 