A Linear Technique to Understand Non-Normal Turbulence Applied to a Magnetized Plasma

Abstract

In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal structures makes quantitative understanding and prediction difficult. We present a technique to overcome this difficulty by modeling the effect that the advective nonlinearities have on spatial turbulent structures. The nonlinearities are taken as a periodic randomizing force with time scale consistent with critical balance arguments. We apply this technique to a model of drift wave turbulence in the Large Plasma Device (LAPD) [W. Gekelman \emph{et al.}, Rev. Sci. Inst. {\bf 62}, 2875 (1991)], where non-modal effects dominate the turbulence. We compare the resulting growth rate spectra to that obtained from a nonlinear simulation, showing good qualitative agreement, especially in comparison to the eigenmode growth rate spectra.