Modulation instability of low-frequency electrostatic ion waves in magnetized electron-positron-ion plasma

The nonlinear amplitude modulation of low-frequency electrostatic ion waves propagating in collisionless magnetized electron-positron-ion plasma are studied. The Krylov-Bogoliubov-Mitropolsky perturbation method is employed to derive the nonlinear Schroedinger equation. Modulation instability of both ion-acoustic and ion-cyclotronlike modes is examined. We found that the ion-acoustic mode, which propagates below the ion-cyclotron frequency, is stable if the strength of the external magnetic field is small. However, as the strength of the magnetic field increases, this mode becomes modulationally unstable for a range of wave numbers and angles of propagation. This range increases as the strength of the magnetic field and/or positron density increases. For the ion-cyclotronlike mode, which propagates above the ion-cyclotron frequency, a number of stability/instability regions appear in the (kc,θ) plane even for a very small value of the magnetic field. It is found that, for both modes, critical wave number kc separating the stability and instability regions, shifts towards higher values as the density of the positron increases.