A model is introduced of an ionospheric plasma cloud (deformable dielectric) with a piecewise-constant ion density and a diffusive ^regularized boundary. The linear stability of a single-contour circular cloud is studied and a new evolution equation for modal amplitudes is obtained which has the property that the wave number of maximum amplitude decreases with time (downward cascade). Analytic expressions show that large clouds evolve more slowly and appear more dissipative. PACS numbers: 52.35.Py, 02.70.+d, 41.10.Dq, Ionospheric, collision-dominated, low-jS plasma clouds, driven by ambient, uniform electric fields or winds are being studied for two main reasons. First, they are probes of properties of the natural and disturbed ionosphere. Second, they evolve nonlinearly and yield magnetic field-aligned finescale structures (irregularities or striations) that can degrade radio-wave propagation. 1 Past analytic studies of the evolution of ion densities have been almost entirely confined to the linear stability of one-dimensional (ID) stationary states. Linson and Workman, 2 Shiau and Simon, 3 and Volk and Haerendel 4 attributed the cause of striations to the EXB gradient-drift instability. 5 Presently there are no 2D stationary states of continuous density variation and no 2D stability analyses exist.In recent computational studies, finite-difference algorithms were used to study the evolution of ID and 2D ion density clouds with small-amplitude 2D perturbations. 6 ' 7 It has been found that the growth of sinusoidal perturbations on ID clouds agrees with linear theories. 6 These perturbations evolve into fingerlike striations that emanate from the cloud's "backside" (the direction opposite to the drift velocity EXB"/|.£| 2 ). The results obtained are in qualitative agreement with field experiments. 8 We now investigate the linear stability of a twodimensional model of an idealized cloud, namely a piecewise-constant distribution of ions:where D is a simply connected, bounded region in i? 2 with boundary r. The contour, r, deforms with a velocity V d = E. x B/|B| 2 , where EL is the self-consistent electric field on the inside of r and § = B 0 e z is Earth's magnetic field, assumed to be constant. In the rest of this paper we set .B 0 = l. Our contributions are twofold: (1) We in-troduce a contour dynamical model of the piecewise-constant cloud which generalizes the "waterbag" method. The evolution equations include a physically motivated diffusive regularization procedure 9 which inhibits the formation of contour singularities and makes the system well posed.(2) We analyze the linear stability of a circular region and demonstrate a new linear phenomenon, "downward cascade," namely, the wave number of maximum amplitude decreases with time. Our work is a combined analytical-numerical study.We also use our results to validate a numerical algorithm which solves the nonlinear contour evolution model. The equations of motion of the continuum ionospheric plasma system of Fig. 1 (inset) have been given as 6 V-(iVV$) = 0,...