A rigorous theory of small disturbances in a weakly ionized nonuniform
plasma in crossed electric and magnetic fields is developed. Regular
inhomogeneities both of plasma density and collision frequency are tak
en into account. The analysis of eigenvalues and eigenmodes is perform
ed in the electrostatic approximation. It is shown that the inhomogene
ity of collision frequency is of fundamental significance, is responsi
ble for the creation of boundary conditions, and determines the range
of existence and spatial structure of eigenmodes. It is also shown tha
t there is no localized mode associated with steep plasma density grad
ients. The dispersion relation and altitude behavior of eigenmodes are
investigated in the WKB approximation in the case of the exponential
profile of collision frequencies, which is natural for the ionospheric
E-region. (C) 1997 American Institute of Physics. [S1070-664X(97)0411
1-6].