Figure 6 illustrates the behavior of the electron concentration for the
\(z\)-branch of frequencies at \({V_{0}=0}\) (the dipole is oriented along the \(OZ\) axis). The
spatial distribution of the electron concentration calculated for the time moment
\({\tau_{x}={3\pi}/{2}}\) (see Fig. 6,\(a\)) has a maximum, which is located under
the dipole and is symmetric with respect to the substitutions \({x\rightarrow-x}\) and \({y\rightarrow-y}\). Figure 6,\(b\) demonstrates the behavior of
a perturbation in time, which is close to periodic. Figure 7 exhibits the same
as in Fig. 6, but provided that electrons drift with the velocity
\({V_{0}\approx 0.94}\). In this case, the dipole is also oriented in the plane
\(y=0\), but the wave dynamics is somewhat more complicated than that obtained
above for the \(x\)-branch. Perturbations located near the dipole move against the
electron stream, whereas the remote perturbations move along the stream. At
\({X\approx 3.5}\), the character of perturbations changes, and the role of the wave
propagation becomes dominant.
Consider the solution of the integral equation (LABEL:integal_equation) for the
dipole \(y\)-orientation. The real part of an electron concentration perturbation
looks like
\begin{equation}
\label{nrokRe_y}{n^{\prime(y)}(\mathbf{r},\tau_{y})=e^{\frac{\omega_{y}^{\prime\prime}}{\omega_{y}^{\prime}}\tau_{y}}\left[J_{y}^{\prime}(\mathbf{r})\cos{\tau_{y}}+J_{y}^{\prime\prime}(\mathbf{r})\sin{\tau_{y}}\right]},\\
\end{equation}