Suppose we have a plasma with corresponding plasma frequency $\omega_{\text{pl}}$. Next, assume that there is some scattering inside the plasma, due to which photons can be created. Is it possible to create a photon with the energy $E < \omega_{\text{pl}}$? Or such process is impossible?
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The short answer is yes. I wrote some more general responses at https://physics.stackexchange.com/a/138460/59023 and https://physics.stackexchange.com/a/264526/59023.
The longer answer is yes as well, but then one is concerned with whether the photons to which you refer exist as a freely propagating electromagnetic wave (i.e., the oscillating fields effectively do not interact with the charged particles) or as coupled plasma mode (i.e., the oscillating fields affect the charged particles).
A plasma is just an ionized gas and can be weakly ionized or strongly ionized. An example of the former is the Earth's ionosphere (at certain altitudes and times of day).
In the latter case (e.g., the solar wind), the charged particles (i.e., negatively charged electrons and positively charged ions) are allowed to oscillate. If we only examine things larger than the Debye length, then for most purposes the plasma is effectively charge neutral. However, this does not mean that electric and/or magnetic fields due to oscillating charges cannot exist. It just means that in a quasi-steady state, the gas is neutral over distances larger than the Debye length
There are a whole zoo of plasma waves that exist in both weakly and strongly ionized plasma and even more instabilities – the mechanism through which a plasma dissipates free energy by radiating an electromagnetic or electrostatic wave.
If you are asking about quark-gluon plasmas, then I am guessing somewhat similar rules apply but that is beyond my expertise.
honeste_vivere
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