# 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?

• Temperatures in the middle of stars can exceed 5 keV, and in some stars strong magnetic fields can be present. But whether you'd call those plasmas magnetized or not is problem dependent; for example should depend on how the Larmor radius compares to other spatial scales of interest. – Maxim Umansky Jan 8 at 21:53
• On a larger scale, when the kinetic energy of the fluid is sufficiently greater than the magnetic pressure, you can probably ignore the magnetic fields. On smaller scale, you probably can't. – Kyle Kanos Jan 10 at 20:34
• There are definitely circumstances where the magnetic field is very small compared to other plasma parameters (e.g., very high plasma beta). There are no situations where the magnetic field is completely zero, but whether it's relevant to the situation depends upon the problem at hand. – honeste_vivere Jan 12 at 21:08
• Yes, precisely I am trying to know examples of environments where the magnetic field is very weak (very high plasma beta). – Betatron Jan 13 at 9:09

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 $${\bf B}$$
$$\begin{array}{c|cccc} \hline \mbox{Plasma}& T_e \mbox{ in eV} & n_e \mbox{ in}\ \mathrm{m}^{-3} & B \mbox{ in T} & \beta\\ \hline \mbox{solar core} & 10^3 & 10^{30} & 1 & 10^8\\ \mbox{ionosphere} & 0.1 & 10^{12} & 10^{-5} & 5\cdot10^{-8}\\ \mbox{interstellar medium} & 1 & 10^{6} & 10^{-6} & 50\\ \mbox{intergalactic medium} & 10 & 10 & 10^{-7} & 5\\ \mbox{accretion disk Sgr A*} & 10^6 & 10^{12} & 10^{-3} & 0.5\\ \hline \end{array}$$