Microscopic instability and macroscopic flow pattern resulting from colliding plasmas are studied analytically in support of laboratory experiments. The plasma flows are assumed to stream radially from two separate centers. In a quasi-planar (2D) geometry, they may arise from an Ohmic explosion of two parallel wires, but similar configurations emerge from other outflows, e.g., colliding winds in binary star systems. One objective of this paper is to characterize the flow instabilities developing near the flow stagnation line. An exact solution for the Buneman-type dispersion equation is obtained without conventional simplifications. The unstable wave characteristics are key to anomalous resistivity that determines the reconnection rate of opposite magnetic fields transported with each flow toward the stagnation zone. The second objective of the paper is to calculate the stream function of the plasma shocked upon collision. We addressed this task by mapping the flow region to a hodograph plane and solving a Dirichlet problem for the stream function. By providing the instability growth rate, responsible for anomalous transport coefficients, and the overall flow configuration, these studies lay the ground for the next step. From there, we will examine the field reconnection scenarios and emerging mesoscopic structures, such as radial striata observed in the experiments.
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