Electromagnetic linear dispersion relation for plasma with a drift across magnetic field revisited

A current across the magnetic field is formed in various situations in plasma. The relative drift between ions and electrons due to the cross-field current becomes a source of various microscopic instabilities. A fully electromagnetic and kinetic linear dispersion relation for plasma with a drift across magnetic field is derived by assuming a uniform background plasma. The dielectric permittivity tensor for shifted Maxwellian velocity distributions is also presented. Linear dispersion relations obtained by using the new dielectric permittivity tensor were confirmed by comparison with the previous studies and with particle-in-cell simulation results.