Statistical theory and transition in multiple-scale-lengthturbulence in plasmas

Abstract

The statistical theory of strong turbulence in inhomogeneous plasmas isdeveloped for the cases where fluctuations with different scale lengthscoexist. Nonlinear interactions in the same kind of fluctuations as well asnonlinear interplay between different classes of fluctuations are kept in theanalysis. Nonlinear interactions are modelled as turbulent drag, nonlinearnoise and nonlinear drive, and a set of Langevin equations is formulated. Withthe help of an Ansatz of a large number of degrees of freedom with positiveLyapunov number, Langevin equations are solved and the fluctuation dissipationtheorem in the presence of strong plasma turbulence has been derived. A casewhere two driving mechanisms (one for the micro mode and the other forsemi-micro mode) coexist is investigated. It is found that there are severalstates of fluctuations: in one state, the micro mode is excited and thesemi-micro mode is quenched; in the other state, the semi-micro mode isexcited, and the micro mode remains at finite but at a suppressed level. A newtype of turbulence transition is obtained, and a cusp-type catastrophe isrevealed. A phase diagram is drawn for turbulence which is composed ofmultiple classes of fluctuations. The influence of the inhomogeneous globalradial electric field is discussed. A new insight is given for the physics ofthe internal transport barrier. Finally, the non-local heat transport due tothe long-wavelength fluctuations, which are noise-pumped by shorter-wavelengthfluctuations, is analysed and its impact on transient transport problems isdiscussed.