Effect of an electron current along the magnetic field on the development of ionization instability in a low temperature plasma

In deriving the dispersion equation of ionization waves in a (low temperature) seeded MHD plasma, allowance is made for an electron current along the impressed magnetic field. This leads to a critical value of the Hall which depends on the angle ( alpha ) between current and magnetic field by a factor 1/sin alpha . The most unstable waves no longer travel at right angles relative to the magnetic field direction; their increment and direction are given in terms of alpha and magnetic field strength.