پلاسماي كوانتومي مغناطيسي

Magnetized Quantum Plasma

Introduction: Dynamics of quantum electron gas have a wide application in various physical systems, and it leads to importance of this subject. In Hartreeʹs approximation, each electron described by a mono particle wave function, and its electrostatics force can obtain from Poisson equation. Hartreeʹs model is useful for expression of quantum in phase-space. The Wigner-Poisson system can be reduced to an effective Schrodinger-Poisson system, for a large class of statistical mixtures, in which the Schrodinger equation contains a new nonlinearity. Aim: The present work devoted to study of two dimensional electron gas systems by using of Schrodinger-Poisson system. It needs to definition of a nonlinear potential for system. Also extraordinary waves studied as a special case of quantum magnetic plasma. Materials and Methods: In this work by using of nonlinear Schrodinger equation, and in present of an external magnetic field, the dispersion relation has calculated. The results in present and in absent of quantum effects and influence of magnetic field is investigated. Results: For the case of a zero-temperature two-dimensional electron gas, this additional nonlinearity is of the form H . In the long wave length limit, the results obtained from the effective Schrodinger-Poisson system are in agreement with those of the Wigner-Poisson system. Conclusion: The Wigner equation can reduce to nonlinear Schrodinger equation in phase space. The study of propagation of wave for special case k = ik, shows that dispersion relation is same as extraordinary dispersion relation. Also quantum modification obtained in the dispersion relation of extraordinary wave.