Stability test for strongly inhomogeneous plasmas through Nyquist diagrams

The stability of inhomogeneous plasma equilibria in the water bag approximation is discussed by means of Nyquist diagrams. A function suitable for a Nyquist diagram is constructed, and the method is applied to demonstrate the instability of the electron sheath configuration. The behavior of the Nyquist diagram shows directly that instabilities occur near multiples of the bounce frequency of the innermost sheath contour in phase space.