variation of the transmission probability $\left| \mathcal
T\right| ^{2}=\exp
\left( -2\sigma \right) $ is represented, as a function of the parameter $\zeta =\sqrt{m_{e}^{2}+k_{\perp }^{2}}/\omega $ and for different values of the temperature and particle energy ratio $2\pi
^{2}T^{2}/\omega ^{2}$ in Fig. 2. For large values of the particle energy, $\omega >>\sqrt{m_{e}^{2}+k_{\perp }^{2}}$, $\zeta \rightarrow 0$ and the transmission probability is equal to $1$, $\left| \mathcal
T\right| ^{2}\rightarrow 1$. The transmission probability also increases with the temperature of the electrosphere.

In the process of particle production in the electrosphere of quark stars due to the tunnelling from the negative energy state, a positive energy particle (an electron) is created, leaving a hole in the negative energy continuum, which can be taken to be an anti-particle (a positron) moving in a direction opposite to the direction of the created particle. The created pair of particles is characterized by the energy (frequency) $\omega $. For such a pair, one cannot, strictly speaking, specify a particular point as the location where the pair is produced [@Wa88]. One can only say that the pair of particles begins to emerge between the point $z_{-}$ and $z_{+}$. Nevertheless, one can associate the point $z$, which is the 