Nonlinear Dynamics of a 2-D Model of Corotating Plasma in a Dipole Magnetic Field with Application to Jupiter

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The two-dimensional dynamics of plasma motion in an idealized form of the corotating convection system of the jovian magnetosphere is investigated. Plasma pressure is ignored, and a dipole magnetic field is assumed, with the magnetic axis and spin axis aligned. The effects of microdiffusion are incorporated into an otherwise macroscopic magnetohydrodynamic model. By applying the mathematical technique (of Galerkin truncation) that was used to derive the famous Lorenz equations for convection in Earth's atmosphere, we reduce the governing partial differential equations to simple, low-order, ordinary differential form. On the basis of this extreme simplification, the plasma dynamics of the jovian magnetosphere is found to be controlled by the height-integrated Pedersen ionospheric conductivity Sigma viz., if Sigma is greater than a critical value Sigma_c then plasma motion is steady-state convection, whereas if Sigma is less than Sigma_c then plasma motion is expected to be chaotic. The value Sigma_c is found to lie in the approximate range 0.7 mho <= Sigma_c <= 1.8 mho, which is within the accepted range of values of Sigma for Jupiter. This predicted form of control of magnetospheric plasma motion by the height-integrated Pedersen ionospheric conductivity is testable if sufficiently refined data become available. Lyapunov (fractal) dimensions of typical strange attractors are found to be in the range D_L ~ 2.03-2.3. Whether a low-dimensional strange attractor does exist at certain times in the jovian magnetosphere can be reliably tested only by analyzing a sufficiently long time series constructed from plasma velocity data.

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