Upper-hybrid solitons and oscillating-two-stream instabilities

A warm two-fluid theory of soliton formation near the upper-hybrid frequency is developed. Several forms of the nonlinear Schrödinger equation are obtained, depending on whether the electric field is completely perpendicular to the dc magnetic field or whether it has an additional small component parallel to the magnetic field. For the perpendicular case, the character of the soliton depends on its scale length, L, and on β. For low β, when L<c/ωpe, stationary envelope and hole solitons are found, whereas in the limit L≳c/ωpi the super-Alvénic solitons described magnetohydromagnetically by Kaufman and Stenflo are obtained. However, the case E∥≠0 may be of more interest, since it couples the pump to the excited waves more efficiently. In the limit of linearization about an infinite wavelength pump, the nonlinear Schrödinger equations yield purely growing (oscillating-two-stream) instabilities in both cases.