A new'' approach to the quantitative statistical dynamics of plasma turbulence: The optimum theory of rigorous bounds on steady-state transport
- Princeton Univ., NJ (USA). Plasma Physics Lab.
- Texas Univ., Austin, TX (USA). Inst. for Fusion Studies
The fundamental problem in the theory of turbulent transport is to find the flux {Gamma} of a quantity such as heat. Methods based on statistical closures are mired in conceptual controversies and practical difficulties. However, it is possible to bound {Gamma} by employing constraints derived rigorously from the equations of motion. Brief reviews of the general theory and its application to passive advection are given. Then, a detailed application is made to anomalous resistivity generated by self-consistent turbulence in a reversed-field pinch. A nonlinear variational principle for an upper bound on the turbulence electromotive force for fixed current is formulated from the magnetohydrodynamic equations in cylindrical geometry. Numerical solution of a case constrained solely by energy balance leads to a reasonable bound and nonlinear eigenfunctions that share intriguing features with experimental data: the dominant mode numbers appear to be correct, and field reversal is predicted at reasonable values of the pinch parameter. Although open questions remain upon considering all bounding calculations to date one can conclude, remarkably, that global energy balance constrains transport sufficiently so that bounds derived therefrom are not unreasonable and that bounding calculations are feasible even for involved practical problems. The potential of the method has hardly been tapped; it provides a fertile area for future research. 29 refs.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 6765264
- Report Number(s):
- PPPL-2704; ON: DE90013499; TRN: 90-020191
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
REVERSE-FIELD PINCH
TRANSPORT THEORY
ADVECTION
ENERGY BALANCE
EQUATIONS OF MOTION
MAXWELL EQUATIONS
MHD EQUILIBRIUM
TURBULENCE
VARIATIONAL METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUILIBRIUM
MASS TRANSFER
PARTIAL DIFFERENTIAL EQUATIONS
PINCH EFFECT
700103* - Fusion Energy- Plasma Research- Kinetics