High-frequency instabilities in an explosion-generated relativistic plasma

A realistic problem of an explosion-generated relativistic plasma is talked about with respect to the instabilities developed in such systems. For this, the dispersion equation is derived analytically and solved numerically for typical values of physical quantities. Our calculations reveal that two types of instabilities occur in the said plasma if the dust particles and relativistic effects of ions and electrons are considered. Both types of the instabilities are high-frequency instabilities, which carry growth rates of different magnitudes. In view of the magnitudes, the instability having higher/lower growth rate is called as high-frequency higher/lower growth rate instability. The relativistic effects of ions support the growth of these instabilities, whereas those of electrons suppress the growth of the instabilities. The waves propagating with larger phase velocity are found to grow at higher rates. There exists a critical value of the drift velocity of dust particles, above which another instability starts growing but with significantly lower growth rate.