Physics of Plasmas, Volume 28, Issue 4, April 2021. An exact solution of two fluid ideal classical plasma equations is presented which shows that the one-dimensional jet-like axial outflow and two-dimensional magnetic field are generated simultaneously by the density and temperature gradients of both electrons and ions in cylindrical geometry. Particular profiles of density function [math] (where [math] is normalized by some constant density N0) and temperatures Tj (for [math] have to be chosen to obtain an exact solution of the complicated nonlinear partial differential equations. But this is a natural analytical exact solution of the ideal two fluid plasma equations. The basic mechanism presented here explains the creation of plasma jet-like flows along with magnetic fields in astrophysical environments such as young stellar objects, active galactic nuclei, solar spicules, flares, and coronal loops. The theoretical model is also applicable to laser induced plasma where magnetic field and plasma ablation are produced simultaneously. An exact analytical solution of ideal neutral fluid equations is also presented which shows that the jet-like outflows can be generated by the density and temperature gradients in such systems.

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