Where does non-relativistic and semi-relativistic bi-maxwellean plasma naturally occur in universe? I also need the numerical values of electron number density, magnetic field, and temperature of such environment.
Mostly non-Maxwellian distribution like bi-Maxwellian distribution exists in the space plasmas. In this regard, you can study non-Maxwellian plasmas. The parameters can also be found from attached type of research articles.
You can also find non-Maxwellian distributions in equilibrium when inelastic processes are important. These can be stronger for lower-energy electrons (say) than for high-energy electrons, while the energy input is through the high-energy electrons. One result can be a dip in the electron energy distribution function where they lose energy preferentially. It happens in gas discharges, for example; one is known as the Druyvestein distribution (which is not a bi-Maxwellian).