Temperature Relaxation Near the Interface of Two Semi‐Infinite Plasmas

• Published in: The Physics of fluids (1958) 1969-01, Vol.12 (1), p.172-182
• Main Authors: Lin, Shao‐Chi, Wei, Hsin Yi
• Format: Article
• Language: English
• ISSN: 0031-9171; 2163-4998
• DOI: 10.1063/1.1692260

The problem of electron‐ion temperature relaxation when two semi‐infinite, nonmagnetized plasmas at different initial temperatures were suddenly brought into thermal contact under constant pressure is investigated using the two‐fluid model. No current is assumed to flow across the interface, and charge separation is considered only to the extent of a simple correction on effective thermal conductivity (i.e., no plasma oscillation). Viscous stresses associated with induced fluid motion are also neglected. The asymptotic solution for long time after thermal contact is shown to be identical to that in a single‐temperature plasma, with effective thermal conductivity equal to approximately [1 + (3m e /m i ) 1 2 ] times the local electron thermal conductivity. For a time scale shorter than or comparable to the mean electron‐ion collisional energy transfer time t ei a self‐similar solution is obtained in the form of a double series in ascending powers of the nondimensional time τ = t/t ei and of the initial temperature difference parameter ε ≡ (T 2 −T 1 )/(T 2 +T 1 ) . It is found that the induced pressure is quite large at early times, suggesting that thermal shock could be a significant source of plasma wave excitation in certain non‐steady problems.