In the nighttime equatorial F region, zonal neutral air winds and gravity waves propagating across the magnetic field tend to drive the ionization as if there were no field. When the phase trace speed of a gravity wave equals the drift speed of the ionization, strong ionization perturbations may occur (Whitehead's spatial resonance effect). The resonance effect is described by a parametric differential equation. Without diffusion, it yields perturbations in the form of periodic δ functions. Therefore a coefficient of turbulent diffusion is introduced to limit the perturbation amplitude. Then the equation can be solved in terms of partial Fourier sums. Numerical calculations with reasonable F region parameters indicate that under spatial resonance conditions, gravity waves cause considerable secondary flows of ionization as a result of nonlinear effects. The contours of constant ionization density show steep or even breaking wave fronts similar to those observed by HF radar and radio propagation experiments in the large-scale structure of the equatorial spread F. The spatial resonance mechanism produces field-aligned tubes of decreased ionization density which may be the primary cause of ‘plasma bubbles’ detected by satellite and rocket probes.
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