MHD waves within Noncommutative Maxwell theory
  In the presence of a strong uniform magnetic field, we study the influence of space noncommutativity on the electromagnetic waves propagating through a quasi-static homogeneous plasma. In this treatment, we have adopted a physical model which considers plasma as quasi-neutral single fluid. By using noncommutative Maxwell theory, the ideal magnetohydrodynamics (MHD) equations are established, in which new equilibrium conditions are extracted. As an empirical study, some attractive features of MHD waves behavior are investigated. Furthermore, it is shown that the presence of space noncommutativity enhances slightly the phase velocity of the incompressive shear Alfv\'{e}n waves. In a compressible plasma, the noncommutativity plays the role of an additional compression on the medium, in which its relevant effect on the fast mode occurs for highly oblique branchs, while the low effect appears when the propagations are nearly parallel or anti-parallel. In addition, it turned out that the influence of space deformation on the slow modes is $\sim 10^{3}$ times smaller than that on the fast modes. The space noncommutativity effect on the slow waves is negligible in low plasma $\beta $ value, and could appear when $\beta $ is higher than $0.1,$ thus the extreme modification occurs for oblique slow waves propagating with angles between $30^{\circ}$ and $60^{\circ}$. Finally, we comment on the possible effect of such waves on CMB spectrum in photon-baryon plasma. 
S. Bourouaine and A. Benslama