A preliminary investigation of the pseudo-spectral method numerical solution of the Perkins instability equations in the homogeneous TEC case

A pseudo-spectral method code is developed to simulate the electrodynamic instability (spread-F) behavior of the mid-latitude ionosphere by numerically solving two of the Perkins (J. Geophys. Res. 78 (1973) 218) equations. This work follows that of Miller (On gravity waves and the electrodynamics of the mid-latitude ionosphere, Ph.D. Thesis, Cornell University, 1996) and provides extensions in both the solution method-resulting in more precise, efficient and robust solutions-and in the range of solutions investigated. In the linear instability-development stage, the simulation result is consistent with the Perkins (1973) predictions, yielding relative differences of less than 0.6%. A random initial condition case like that of Miller (1996) is carried out with the result agreeing with Miller's result obtained in a different manner. In addition, the effect of non-linearity of the equation system is observed. The range of initial conditions investigated indicates that over a large wavelength range, self-similar ionospheric instability structures (Geophys. Res. Lett. 28 (2001) 4167) can be generated in conductivity and potential (the field-line integrated electron concentration is constant). Further, by using dual-wave-mode excitation with suitable parameters, saturation of the instability process is observed. Some dual-mode excitation processes are very different from the single-mode excitation case in many respects-especially in wavelength dependence. The turbulent saturation is observed in simulation to be caused by the E×B instability that requires a sharp conductivity gradient at the backside of the drift movement. On the other hand, other dual-mode excitation processes do not display a saturation state. In this case, the process converges to and then follows the path of the corresponding single-mode excitation example.