  The double plasma resonance (DPR) instability plays a basic role in the
generation of solar radio zebras. In the plasma, consisting of the loss-cone
type distribution of hot electrons and much denser and colder background
plasma, this instability generates the upper-hybrid waves, which are then
transformed into the electromagnetic waves and observed as radio zebras. In the
present paper we numerically study the double plasma resonance instability from
the point of view of the zebra interpretation. We use a 3-dimensional
electromagnetic particle-in-cell (3-D PIC) relativistic model. First using the
multi-mode model, we study details of the double plasma resonance instability.
We show how the distribution function of hot electrons changes during this
instability. Then we show that there is a very good agreement between results
obtained by the multi-mode and specific-mode models, which is caused by a
dominance of the wave with the maximal growth rate. Therefore, for computations
in a broad range of model parameters, we use the specific-mode model. We
compute the maximal growth rates of the double plasma resonance instability.
The results are compared with the analytical ones. We find a very good
agreement between numerical and analytical growth rates. We also compute
saturation energies of the upper-hybrid waves in a very broad range of
parameters. We find that the saturation energies of the upper-hybrid waves show
maxima and minima at almost the same values of
$\omega_\mathrm{UH}/\omega_\mathrm{ce}$ as the growth rates. Furthermore, we
find that the saturation energy of the upper-hybrid waves is proportional to
the density of hot electrons. The maximum saturated energy can be up to one
percent of the kinetic energy of hot electrons. All these findings can be used
in the interpretation of solar radio zebras.
