  The phase space of driftons (drift-wave quanta) is studied within the
generalized Hasegawa--Mima collisionless-plasma model in the presence of zonal
flows. This phase space is made intricate by the corrections to the drifton ray
equations that were recently proposed by Parker [J. Plasma Phys. $\textbf{82}$,
95820602 (2016)] and Ruiz $\textit{et al.}$ [Phys. Plasmas $\textbf{23}$,
122304 (2016)]. Contrary to the traditional geometrical-optics (GO) model of
the drifton dynamics, it is found that driftons can be not only trapped or
passing, but they can also accumulate spatially while experiencing indefinite
growth of their momenta. In particular, it is found that the Rayleigh--Kuo
threshold known from geophysics corresponds to the regime when such "runaway"
trajectories are the only ones possible. On one hand, this analysis helps
visualize the development of the zonostrophic instability, particularly its
nonlinear stage, which is studied here both analytically and through
wave-kinetic simulations. On the other hand, the GO theory predicts that zonal
flows above the Rayleigh--Kuo threshold can only grow; hence, the deterioration
of intense zonal flows cannot be captured within a GO model. In particular,
this means that the so-called tertiary instability of intense zonal flows
cannot be adequately described within the quasilinear wave kinetic equation,
contrary to some previous studies.
