Two-dimensional self-modulation of lower hybrid waves in inhomogeneous plasmas

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Abstract
For lower hybrid waves in an inhomogeneous plasma, the two‐dimensional self‐modulation effects due to ponderomotive force are studied under the assumption that the field is electrostatic and has a narrow k spectrum. For a locally linear temperature profile and a broad class of density profiles, exact nonlinear solutions (solitons) are obtained by the inverse scattering method. The solitons decay and spread as they propagate. In addition to the usual area condition on the potential F φ dξ⩾π/2, inhomogeneity introduces a second condition for solitons to occur. It is shown that this second condition is not satisfied in typical tokamak plasmas, i.e., there is no soliton formation, in contrast to the homogeneous case. Furthermore, the scaling of the threshold conditions with density and temperature makes them more difficult to satisfy in larger machines.