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Author(s):
S.-I. Itoh, K. Itoh, M. Yagi, M. Kawasaki and A. Kitazawa
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Title:
Transition in Multiple-scale lengths Turbulence in Plasmas
Date of publication:
Feb. 2002
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Key words:
statistical theory, strong turbulence, renormalization, multiple scale lengths, bifurcation, cusp catastrophe, butterfly catastrophe, subcritical excitation, probability density function, transition probability
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Abstract:
The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale-lengths coexist. Statistical nonlinear interactions between semi-micro and micro modes are first kept in the analysis as the drag, noise and drive. The nonlinear dynamics determines both the fluctuation levels and the cross field turbulent transport for the fixed global parameters. A quenching or suppressing effect is induced by their nonlinear interplay, even if both modes are unstable when analyzed independently. Influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of internal transport barrier. The thermal fluctuation of the scale length of lambda_D is assumed to be statistically independent. The hierarchical structure is constructed according to the scale lengths. Transitions in turbulence are found and phase diagrams with cusp type catastrophe are obtained. Dynamics is followed. Statistical properties of the subcritical excitation are discussed. The probability density function (PDF) and transition probability are obtained. Power-laws are obtained in the PDF as well as in the transition probability. Generalization for the case where turbulence is composed of three-classes of modes is also developed. A new catastrophe of turbulent states is obtained.
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