Vortices in nonuniform upper-hybrid field

The equations describing the interaction of an upper-hybrid pump wave with small low-frequency density perturbations are discussed under assumption that the pump is spatially nonuniform. The conditions for the modulational instability are investigated. Instead of a dispersion relation, describing the growth of perturbations in the case of an uniform pump, in our case of nonuniform pump a differential equation is obtained and from its eigenvalues are found the instability criteria. Taking into account the slow-frequency self-interaction terms some localized solutions similar to dipole vortices are found, but described by analytic functions in all space. It is shown that their characteristic size and speed are determined by the pump intensity and its spatial structure. (au)