## Appendix A: derivation of dispersion equation## A.1. Vertical propagation
This infinite set of equations completely defines the solution. A nontrivial solution exists if the infinite Hill determinant is zero: This condition is the dispersion equation for waves with spatial period and even eigenfunction. It is known that an infinite Hill determinant written in the above form is convergent. For the even solution with period the recurrence relation for the coefficients along with (A2) defines the coefficients of the solution (23). The dispersion equation is
Eq. (A7) again has the solutions (23) and (24). The even solution of period is defined by the recurrence relations The recurrence relations (A9) define the Hill determinant. The dispersion equation is
The mean flow is introduced to remove mean plasma flux from the model. It causes a Doppler shift, which is eliminated by replacing the phase velocity in (A10) by in (A13); the parameter is replaced by and the dispersion relation reads ## A.2. Oblique propagationThe coefficients of the solution (42) satisfy the recurrence relations where are defined by (A13). The recurrence relations define an infinite set of linear algebraic equations, which has a non-trivial solution if an infinite Hill determinant is zero. This defines the dispersion equation. For solutions with this equation is © European Southern Observatory (ESO) 1998 Online publication: March 10, 1998 |