SHALLOW-WATER AND DEEP-WATER APPROXIMATIONS IN THE THEORY OF THE DISRUPTIVE INSTABILITY OF THIN CURRENT-CARRYING LAYERS

Within the framework of the two-fluid hydrodynamics of plasmas it is s hown that the problem of instability of a thin current-carrying layer admits two limiting cases which allow analytic solutions and complemen t one another. These limits are analogous to the well-known shallow-wa ter and deep-water approximations in the fluid mechanical ''wave-break ing'' instability. In this case, the long-wave limit coincides with th e ''quasi-Chaplygin'' dynamic system of Bulanov and Sasorov, Fit Plazm y 4, 746 (1978) [Sov. J. Plasma Phys. 4, 418 (1978)], while the short- wavelength limit corresponds to the phenomenological model of Trubniko v, Usp. Fit. Nauk 160, 167 (1990) [Sov. Phys. Usp. 33, 87 (1990)], for the clumping of ''elementary'' currents. In the latter case, strong c ollapse is unavoidable with the appearance nf current filaments that t rap a finite current. (C) 1998 American Institute of Physics.