Generalized gyroviscous force and its effect on the momentum balance equation
- Department of Nuclear Engineering and Engineering Physics, University of Wisconsin, Madison, Wisconsin 53706-1687 (United States)
The perturbed nonlinear gyroviscous force ({del}{center dot}{tilde {Pi}}{sub {ital g}}, where {tilde {Pi}}{sub {ital g}} is the gyroviscous stress tensor) is calculated through order {delta}{sup 2} ({delta}{similar to}(1/{Omega})({partial derivative}/{partial derivative}{ital t}), {ital k}{sub {perpendicular}}{rho}{similar to}{delta}{sup 1/2}, where {Omega} is the particle gyrofrequency, {ital k}{sub {perpendicular}}{rho} denotes the finite Larmor radius effect) by solving the stress tensor evolution equation. The result shows that {del}{center dot}{tilde {Pi}}{sub {ital g}} mostly cancels the diamagnetic convective term {ital nm}{bold V}{sub *}{center dot}{del}{sub {perpendicular}}{bold {tilde u}} (where {bold V}{sub *} is a generalized total diamagnetic flow) in the momentum balance equation. This formula generalizes the usual, widely used gyroviscous cancellation'' (in which the {del}{center dot}{tilde {Pi}}{sub {ital g}} cancels mostly the total time derivative of the diamagnetic flow ({ital d}{bold {tilde V}}{sub {ital d}}/{ital dt})) to include temperature variations and a perturbed stress tensor drift. It is proved that when temperature variations are neglected, the new formula reduces to the conventional form. When the temperature variations are considered, the new formula is simpler and more rigorous than the conventional one. A new polarization drift formula deduced from the new gyroviscous force is also derived.
- DOE Contract Number:
- FG02-86ER53218
- OSTI ID:
- 7104991
- Journal Information:
- Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 4:7; ISSN 0899-8221; ISSN PFBPE
- Country of Publication:
- United States
- Language:
- English
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