  A one-dimensional model for thinning of the Earth's plasma sheet [J. K. Chao
et al., Planet. Space Sci. 25, 703 (1977)] according to the Current Disruption
(CD) model of auroral breakup is extended to two dimensions. A rarefaction
wave, which is a signature component of the CD model, is generated with an
initial disturbance. In the 1D gas model, the rarefaction wave propagates
tailward at sound velocity and is assumed to cause thinning. Extending to a 2D
gas model of a simplified plasma sheet configuration, the rarefaction wave is
weakened, and the thinning ceases to propagate. Extending further to a 2D
plasma model by adding magnetic field into the lobes, the rarefaction wave is
quickly lost in the plasma sheet recompression, but the plasma sheet thinning
is still present and propagates independently at a slower velocity than a 1D
model suggests. This shows that the dynamics of plasma sheet thinning may be
dominated by sheet-lobe interactions that are absent from the 1D model and may
not support the behaviour assumed by the CD model.
