Self-organization in a two-fluid plasma has been studied by nonlinear 3D simulation. The theory[1] predicts creation of the "double Beltrami (DB) field" described by an alignment of a pair of generalized vorticities and the corresponding flows. The Hall term in the two-fluid model leads to a singular perturbation that enables the formation of an equilibrium given by a pair of two different Beltrami fields (eigenfunctions of the curl operator). The DB states can span a richer set of plasma conditions than the single Beltrami states (the Taylor states).
The compressible Hall-MHD equations are solved by the finite difference and the Runge-Kutta-Gill methods in a 3 dimensional rectangular domain. The quasi-neutrality n=n_i=n_e, and p_e=0 are assumed. In order to compare with the single-fluid MHD simulations done by Horiuchi et. al.[2], we assume a 2D force-free equilibrium as an initial condition. Simulation results show that a relaxed two-fluid plasma flows due to perpendicular components of lows, which do not exist in the Taylor states, and has small scale structures of an order of the ion collisionless skin depth (an intrinsic scale in the Hall-MHD). A variational principle in the two-fluid system will be discussed.

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