Physical significance of growth rate in plasma Let us say that we have a dispersion relation curve and associated instability curve as shown below for a magnetised plasma, which have been formulated through kinetic theory. The frequencies and growth rate have been normalized w.r.t. cyclotron frequency of proton.

My question is: what does this both plot physically signifies?
 A: The top panel shows the real part of the frequency, $\omega_{r}$, and the bottom the imaginary part, $\gamma$, versus the projection of the wave vector orthogonal to the quasi-static magnetic field, $k_{\perp}$, normalized to what I assume is the proton thermal gyroradii.
The point of the top panel is to illustrate at what $\omega_{r}$ one would observe a fluctuation for a corresponding perpendendicular wavelength.  The bottom panel informs you of the most likely value of $k_{\perp}$ to use, which then determines the value of $\omega_{r}$.  The latter part here assumes that the most likely observed fluctuation corresponds to the fastest growning mode, i.e., at the peak value of $\gamma$, sometimes called $\gamma_{max}$.  The corresponding wavenumber is then sometimes referred to as $k_{\perp, max}$, i.e., the value of $k_{\perp}$ at $\gamma_{max}$.
As an aside, these types of graphs tend to start from the assumption that the wavenumber is entirely real while the frequency has both a real and imaginary part.  A finite imaginary frequency physically implies a temporal growth, i.e., the fluctuation will grow in time regardless of location.  Conversely, a finite imaginary wavenumber physically implies a spatial growth, i.e., the fluctuation will grow based upon location or as it propagates (if the real part of the frequency is finite) regardless of time.  In some cases the two scenarios are interchangeable so it is kind of a matter of choice.  In other situations, there are physical boundary conditions that prevent the freedom of choosing whether the frequency and/or the wavenumber have finite imaginary parts.
Update
As a practical application, consider the following.
In a stationary fluid frame, one would expect to see a fluctuation with frequencies satisfying $1.5 \lesssim \omega_{r}/\Omega_{cp} \lesssim 2$ assuming the mode with the maximum value for $\gamma$ is also the largest amplitude mode (sometimes the largest growth rate mode saturates at a really low amplitude, but most of the time this is not true).  The above frequency range is determined by looking at the range of $k_{\perp}$ values in the growth rate plot.
If the fluid is flowing relative to the probe/instrument at velocity, $\mathbf{V}_{bulk}$, then the observed frequency will experience a Doppler shift given by:
$$
\omega_{sc} = \omega_{r} + \mathbf{k} \cdot \mathbf{V}_{bulk}
$$
where $\omega_{sc}$ is the spacecraft frame frequency, $\omega_{r}$ is the plasma rest frame frequency (same as the $\omega_{r}$ from the plot), and $\mathbf{k}$ is the wave vector.
