Linear stability of exponential density profiles

The problem of the linear stability of a plasma with density profiles

in a homogeneous magnetic field B = î_zB₀ has been solved exactly. The dispersion relation leads to stability criteria less severe than those obtained in the local approximation. As examples, we consider Bernstein waves and the low-frequency drift instability. In the second example the marginal stability curve

is given for different values of the parameters k_x, R_i, R_i n‧/n, with T_i = T_e. Further, the same method is applied to a plasma with equilibrium distribution function in a linear electric potential φ = αx and a homogeneous magnetic field B = î_xB₀.