Three-dimensional electrostatic waves in a nonuniform quantum electron-positron magnetoplasma

The dispersion properties of three-dimensional electrostatic waves in a nonuniform quantum electron-positron magnetoplasma are examined. A new dispersion relation is derived using the electron and positron densities response arising from the balance between the quantum Bohm and electrostatic forces, and from the electron and positron continuity and Poisson equations. In the local approximation regime, the dispersion relation admits both oscillatory and purely growing instabilities those depend on the quantum parameters as well as the density, velocity and magnetic field inhomogeneities.