Amplitude and size scaling for interchange motions of plasma filaments

The interchange dynamics and velocity scaling of blob-like plasma filaments are investigated using a two-field reduced fluid model. For incompressible flows due to buoyancy the maximum velocity is proportional to the square root of the relative amplitude and the square root of its cross-field size. For compressible flows in a non-uniform magnetic field this square root scaling only holds for ratios of amplitudes to cross-field sizes above a certain threshold value. For small amplitudes and large sizes, the maximum velocity is proportional to the filament amplitude. The acceleration is proportional to the amplitude and independent of the cross-field size in all regimes. This is demonstrated by means of numerical simulations and explained by the energy integrals satisfied by the model.