Electrostatic mode envelope excitations in e-p-i plasmas - application in warm pair ion plasmas with a small fraction of stationary ions

The nonlinear propagation of amplitude-modulated electrostatic wavepackets in an electron-positron-ion (e-p-i) plasma is considered, by employing a two-fluid plasma model. Considering propagation parallel to the external magnetic field, two distinct electrostatic modes are obtained, namely a quasi-thermal acoustic-like lower mode and a Langmuir-like optic-type upper one. These results equally apply in warm pair ion ( e. g. fullerene) plasmas contaminated by a small fraction of stationary ions ( or dust), in agreement with experimental observations and theoretical predictions in pair plasmas. Considering small yet weakly nonlinear deviations from equilibrium, and adopting a multiple-scales perturbation technique, the basic set of model equations is reduced to a nonlinear Schrodinger (NLS) equation for the slowly varying electric field perturbation amplitude. The analysis reveals that the lower ( acoustic) mode is mostly stable for large wavelengths, and may propagate in the form of a dark-type envelope soliton ( a void) modulating a carrier wavepacket, while the upper linear mode is intrinsically unstable, and thus favours the formation of bright-type envelope soliton ( pulse) modulated wavepackets. The stability ( instability) range for the acoustic ( Langmuir-like optic) mode shifts to larger wavenumbers as the positive-to-negative ion temperature ( density) ratio increases. These results may be of relevance in astrophysical contexts, where e-p-i plasmas are encountered, and may also serve as prediction of the behaviour of doped ( or dust-contaminated) fullerene plasmas, in the laboratory.