Rigorous upper bounds for turbulent transport in bounded systems: Passive advection and reversed-field pinches

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1988

OSTI ID:6691417

Kim, Changbae

Upper bounds are considered for steady-state transport in turbulent bounded systems, for both passive advection and self-consistent cylindrical plasmas. Specifically, the work of Krommes and Smith on passive advection is extended in two directions: (1) For their reference model improved upper bounds are obtained by including the effects of cross-correlations up to fourth order. Numerical solutions of the model stochastic differential equation are also obtained; they show that the new bounds compare quite favorably with the exact results, even at large Reynolds and Kubo numbers; (2) The problem of particle transport due to statistically specified stochastic magnetic fields in a collisionless turbulent plasma is revisited to take account of a finite spatial autocorrelation length L{sub c}. A bound is obtained which reduces for small L{sub c} to the quasilinear limit and for large L{sub c} to the strong turbulence limit, and which provides a reasonable and rigorous interpolation for intermediate values of L{sub c}. Then, a self-consistent problem is treated by considering upper bounds for the turbulently generated electromotive force along the axial direction in a magnetized cylindrical plasma bounded by a perfectly conducting wall. One goal in particular is to obtain rigorous results about relaxation in reversed-field pinches. It is assumed that the plasma is driven by an external electric field and has reached a possibly turbulent steady state in which the total current is fixed and in which the conservation laws of energy and magnetic helicity are enforced. For simplicity, incompressible, resistive magnetohydrodynamic (MHD) equations are used. A bounding curve is obtained without the helicity constraint, used with the Hartmann number. Features of the maximal-emf state corresponding to the reversed-field state are discussed.

• Research Organization: Princeton Univ., NJ (USA)
• OSTI ID: 6691417
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700103* -- Fusion Energy-- Plasma Research-- Kinetics
ADVECTION
COLLISIONLESS PLASMA
CONSERVATION LAWS
DATA
ELECTRIC FIELDS
HARTMANN NUMBER
INFORMATION
MAGNETIC FIELDS
MASS TRANSFER
MATHEMATICAL MODELS
NUMERICAL DATA
PARTICLE KINEMATICS
PINCH EFFECT
PLASMA
REVERSE-FIELD PINCH
REYNOLDS NUMBER
STOCHASTIC PROCESSES
THEORETICAL DATA
TRANSPORT THEORY