| Numerical analysis of the model for cyclotron instability in the Earth's
magnetosphere is performed.
This model, based on the self-consistent set of equations of
quasi-linear plasma theory, describes different regimes of wave generation and related
energetic particle precipitation. As the source of free energy the injection of energetic
electrons with transverse anisotropic distribution function to the interaction region is
considered.
A parametric study of the model is performed. The
main attention is paid to the analysis of generation regimes for different characteristics
of energetic electron source, such as the shape of pitch angle distributions and its
intensity.
Two mechanisms of removal of energetic electrons from a
generation region are considered, one is due to the particle
precipitation through the loss cone and another one is
related to the magnetic drift of energetic particles.
It was confirmed that two main regimes occur in this system in the presence
of a constant particle source, in the case of precipitation losses.
At small source intensity relaxation oscillations were found, whose
parameters are in good agreement with simplified analytical theory
developed earlier. At a larger source intensity, transition to a
periodic generation occurs.
In the case of drift losses the regime of self-sustained periodic
generation regime is realized for source intensity higher than some
threshold.
The dependencies of repetition period and dynamic
spectrum shape on the source parameters were studied in detail.
In addition to simple periodic regimes, those with more complex
spectral forms were found.
In particular, alteration of spikes with different spectral shape can
take place. It was also shown that
quasi-stationary generation at the low-frequency band
can coexist with periodic modulation at higher frequencies.
On the basis of the results obtained, the model
for explanation of quasi-periodic whistler wave emissions is verified. |