Flux-tube model for ultrarelativistic heavy-ion collisions: Electrohydrodynamics of a quark-gluon plasma

The mechanism of energy deposition and matter formation in the central rapidity region of ultra- relativistic nucleus-nucleus collisions is studied in terms of the flux-tube model. This model assumes that two Lorentz-contracted nuclei are color charged at the instant of collision by a random color exchange. The strong color-electric field confined between the two capacitor plates will immediately begin to polarize the vacuum making qq\ifmmode\bar\else\textasciimacron\fi{} and gluon pairs and the quanta excited in the system may form a rapidly expanding plasma. We examine the transverse evolution of the plasma within the framework of nonviscous relativistic hydrodynamics, incorporating the matter formation from an expanding background color field and also taking into account the interaction of the plasma with the remaining field. The hydrodynamic equations with a source term for the matter, which is due to the pair creation and Joule heating, are derived from a semiclassical transport equation. We solve these hydrodynamic equations coupled to Abelian equations for the expanding background field, and examine the generation of a transverse flow as well as entropy production at the early stage of the matter evolution. It is shown that only a small portion of the initial field energy can be converted into transverse-collective-flow energy of the plasma fluid and transverse-flow energy never becomes significant in comparison with internal thermal excitation energy of the plasma fluid before the hadronization transition sets in. As expected, most of the deposited energy goes into longitudinal motion.