Low frequency electrostatic waves propagating in plasmas with parameters varying along magnetic field lines

The analysis of low frequency electrostatic waves, drift waves in particular, is generalized to the case where the plasma parameters, the density in particular, have gradient also along magnetic field lines. A few related problems can be solved exactly, others approximately, but still beyond the accuracy of geometrical optics. A set of fully nonlinear basic equations are derived here and solved by a linearized analysis to give the appropriate dispersion relations. One conspicuous feature of such systems is a an amplitude increase that can be misinterpreted as an instability.