Quantum Two-Stream Instability with Exchange Interaction

Quantum plasmas can be described in the framework of the self-consistent field approach by a set of time-dependent Schrodinger equations (TDSE) for the electrons in a self consistent potential. This approach is also well-known as the multistream model of quantum plasmas. The self-consistent field is commonly calculated in the Vlasov approximation from the average charge density of all electrons thereby neglecting the quantum-mechanical exchange interaction. In the present work, we consider a linear Hartree-Fock model with screened Coulomb interactions to examine the role of the exchange interaction. The two-stream instability is analysed and results for the Vlasov, Hartree and Hartree-Fock approximations are compared in detail. It is found that the exchange interaction considerably modifies the stability behavior for weakly screened Coulomb interactions. In particular, crossings of the two branches of the dispersion relation lead to oscillating unstable solutions that are not present in the absence of the exchange interaction.