Modulational instability of magnetosonic waves in a spin 1∕2 quantum plasma

Abstract

The modulational instability (MI) of magnetosonic waves (MSWs) is analyzed, by using a two-fluid quantum magnetohydrodynamic model that includes the effects of the electron-1∕2 spin and the plasma resistivity. The envelope modulation is then studied by deriving the corresponding nonlinear Schrödinger equation from the governing equations. The plasma resistivity is shown to play a dissipative role for the onset of MI. In the absence of resistivity, the microscopic spin properties of electrons can also lead to MI. In such a situation, the dominant spin contribution corresponds to a dense quantum plasma with the particle number density, n0≳1028m−3. Also, in such a dissipative (absorbing) medium, where the group velocity vector is usually complex for real values of the wave vector, the role of the real group velocity in the propagation of one-dimensional MSW packets in a homogeneous absorbing medium is reported. The effects of quantum spin on the stability/instability conditions of the magnetosonic envelope are obtained and examined numerically. From the nonlinear dispersion relation of the modulated wave packet it is found that the effect of the spin (plasma resistivity) is to decrease (increase) the instability growth rate provided the normalized Zeeman energy does not exceed a critical value. The theoretical results may have relevance to astrophysical (e.g., magnetars) as well as to ultracold laboratory plasmas (e.g., Rydberg plasmas).