A specific type, of longitudinal wave instability in a plasma due entirely to an external quasi-static electric field Eo is considered for the oases of ion-acoustic and Langmuir waves. The quasi-static time variation of the field leads to a relal ively simple mechanism for the development, of instability. For frequency ranges typical.of ion-acoustic, and Langrauirwaves dispersion relations are obtained, with Landau damping and pair Coulomb collisions taken into account in addition to E(). The model integral of Bhatnagar, Gross & Krook is used to describe collisions. Two methods for taking account of the influence of the electric field on development of the instability are compared: that of Pines & Hchrieffer and that of Brinca and Dysthe. Expressions are obtained for the growth rates in the framework of linear theory. Numerical .simulations of both types of instabilities.are peiforined for specific values of the phisma parameters.
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