Hele-Shaw Cell Experiments for Simulation of Structures in High-Altitude Plasmas

摘要

The magnetohydrodynamic (MHD) equations that describe the motion of a tenuous plasma in a uniform magnetic field are mathematically analogous to the hydrodynamic equations describing two-dimensional flow of an incompressible fluid. As a consequence, one can construct a laboratory analogue of MHD phenomena involved in the structuring of high-altitude plasma clouds on scales that lead to radiowave scintillation. A simple laboratory tool for visualizing the relevant dynamics is the Hele-Shaw cell, which consists of two pieces of plate glass between which appropriate fluids are constrained to undergo two-dimensional flow. Two fluids of different density but equal kinematic viscosity are placed in a Hele-Shaw cell with a uniform boundary between them, and the cell is oriented vertically with gravity acting across the boundary. Within a few seconds, the boundary becomes structured under the influence of the Rayleigh-Taylor instability, which then may be studied well into its nonlinear regime. In the dynamic analogue that ensues, the fluid density and velocity represent respectively the plasma density and convective velocity (in the E x B regime), the fluid stream function represents the electrostatic potential, and the gravitationally driven free-fall velocity in the cell represents the gravitationally assisted neutral-wind velocity in the ionosphere. In this report, the mathematical underpinnings of the analogue are reviewed; they are found quite firm for scales in excess of about 100 meters in the nighttime equatorial F layer, subject to one untested assumption.