1Research Laboratory of Electronics and Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Tóm tắt
It is well known that absolute instabilities can be located by prescribed mappings from the complex-frequency plane to the wavenumber plane through the dispersion relation D(ω,k)=0. However, in many systems of physical interest the dispersion relation is polynomial in ω while transcendental in k, and the implementation of this mapping procedure is particularly difficult. If one maps consecutive deformations of the Fourier integral path (originally along the real k axis) into the ω plane, points having (∂D/∂k)=0 are readily detected by the distinctive feature of their local maps. It is shown that a simple topological relationship between these points and the image of the real k axis determines the stability characteristics of the system, without mapping from the ω plane back into the k-plane.
