Unmagnetized plasmas in space Please, I need some information about high temperature plasmas in astrophysical environments.
To my knowledge, plasmas in astrophysical environments are  magnetized (is it true?). Are there  astrophysical environments where one can find plasmas with relativistic electron temperature $(k_B T_e>5keV)$ and also unmagnetized, in order to study them via  theories for unmagnetized plasmas?
 A: To answer your question, let's first clarify on the definition of the plasma $\beta$:
$$
\beta = \frac{p}{B^2/(2\mu_0)},
$$
with $p$ the kinetic plasma pressure (being the product of plasma temperature and density), $B$ the magnetic field, and $\mu_0$ the vacuum permeability. 
Then you distinguished between magnetized and unmagnetized plasmas, a proper definition in the context of your question might be:
\begin{eqnarray}
\beta \ll 1 &\Rightarrow& \mbox{magnetized plasma (magnetic field forces dominate)}\\
\beta \gg 1 &\Rightarrow& \mbox{unmagnetized plasma (hydrodynamics dominate)}
\end{eqnarray}
This is basically the same as the following definition, quoted from [1]:

A magnetized plasma is one in which the ambient magnetic field $\mathbf{B}$ is strong enough to significantly alter particle trajectories. In particular, magnetized plasmas are anisotropic, responding differently to forces which are parallel and perpendicular to the direction of ${\bf B}$

So, let's look at some astrophysical plasmas:
\begin{array}{c|cccc}
\hline
\mbox{Plasma}& T_e \mbox{ in eV}  & n_e \mbox{ in}\ \mathrm{m}^{-3} & B \mbox{ in T} & \beta\\ \hline
\mbox{solar core}            & 10^3 & 10^{30} & 1       & 10^8\\ 
\mbox{ionosphere}            & 0.1  & 10^{12} & 10^{-5} & 5\cdot10^{-8}\\ 
\mbox{interstellar medium}   & 1    & 10^{6}  & 10^{-6} & 50\\
\mbox{intergalactic medium}  & 10   & 10      & 10^{-7} & 5\\ 
\mbox{accretion disk Sgr A*} & 10^6 & 10^{12} & 10^{-3} & 0.5\\ \hline
\end{array}
Note that these are all to be understood as order of magnitude expressions. As you can see, there is some variety and there exists so much more, e.g. neutron stars and their environment. This small, very rough table should be enough though to give you some idea. The solar core might be what you are looking for.
[1] Richard Fitzpatrick: Plasma Physics
