Creation of Magnetic Fields by Electrostatic and Thermal Fluctuations

It is pointed out that the unmagnetized inhomogeneous plasmas can support a low frequency electromagnetic ion wave as a normal mode like Alfven wave of magnetized plasmas. But this is a coupled mode produced by the mixing of longitudinal and transverse components of perturbed electric field due to density inhomogeneity. The ion acoustic wave does not remain electrostatic in non-uniform plasmas. On the other hand, a low frequency electrostatic wave can also exist in the pure electron plasmas. But the magnetic field fluctuations in both electron as well as in electron-ion plasmas are coupled with the electrostatic perturbations in unmagnetized case. The main instability condition for these low frequency electrostatic and electromagnetic modes is the same ${2/3}\kappa_n < \kappa_T$ (where $\kappa_n$ and $\kappa_T$ are inverse of the scale lengths of density and electron temperature, respectively).