Tokamak ripple transport at arbitrary collision frequency

Technical Report · Tue Sep 01 04:00:00 EDT 1987

OSTI ID:6135627

Hitchon, W N.G.; Beidler, C D; Shohet, J L

The bounce-averaged Fokker-Planck equation for the distribution function of ripple-trapped particles in a Tokamak has been solved, for arbitrary collision frequencies, in the 'Tokamak' limit in which ripple wells are localized close to the mid-plane. The equation includes the main terms contributing to collisionless (de)trapping. The solution employs power series expansions for the distribution function in the pitch-angle variable k/sup 2/ and the poloidal angle, theta; the series in k/sup 2/ and theta both terminate. The boundary conditions applied at the trapping-detrapping boundary, that f and (par. deltaf/par. deltak/sup 2/) be continuous, become requirements that in the collisionless limit the derivative with respect to k/sup 2/ reflects the scale length set by the motion in toroidally blocked orbits. The resulting series solutions reduce to the usual expressions in the high collision frequency limit, but are considerably lower than results of previous calculations (which neglect the collisionless detrapping effects), in the low collision frequency limit. Comparison with Monte-Carlo calculations for INTOR parameters shows that the analytic results lie somewhat below the numerical results, in all cases. Since banana-drift diffusion is also present in the Monte-Carlo calculation, this is a partial confirmation of the validity of our theory. 15 refs.

• Research Organization: Wisconsin Univ., Madison (USA). Torsatron/Stellarator Lab.
• DOE Contract Number: FG02-86ER53216; FG02-85ER53201
• OSTI ID: 6135627
• Report Number(s): DOE/ER/53216-T1; TSL-87-3; ON: DE88000687
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700103* -- Fusion Energy-- Plasma Research-- Kinetics
BOUNDARY CONDITIONS
CLOSED PLASMA DEVICES
COLLISIONAL PLASMA
COLLISIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
DISTRIBUTION FUNCTIONS
EQUATIONS
FOKKER-PLANCK EQUATION
FUNCTIONS
INSTABILITY
KINETIC EQUATIONS
MAGNETIC FIELD CONFIGURATIONS
MAGNETIC FIELD RIPPLES
MONTE CARLO METHOD
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
THERMONUCLEAR DEVICES
TOKAMAK DEVICES
TRANSPORT THEORY
TRAPPED-PARTICLE INSTABILITY