Generalized gyroviscous force and its effect on the momentum balance equation
- Univ. of Wisconsin, Madison, WI (United States)
The perturbed nonlinear gyroviscous force (∇ • $$\tilde{Π}$$g, where $$\tilde{Π}$$g is the gyroviscous stress tensor) is calculated through order δ2 [δ~(1/Ω)(∂/∂t), k ⊥ρ~δ1/2, where Ω is the particle gyrofrequency, k⊥ρ denotes the finite Larmor radius effect] by solving the stress tensor evolution equation. The result shows that ∇ • $$\tilde{Π}$$g mostly cancels the diamagnetic convective term $$\mathrm{nmV}$$* • ∇ ⟂$$\tilde{u}$$ (where V* is a generalized total diamagnetic flow) in the momentum balance equation. This formula generalizes the usual, widely used ‘‘gyroviscous cancellation’’ [in which the ∇ • $$\tilde{Π}$$g cancels mostly the total time derivative of the diamagnetic flow ($$\mathrm{d}$$$$\tilde{V}$$ d/ $$\mathrm{dt}$$)] 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. Importantly, a new polarization drift formula deduced from the new gyroviscous force is also derived.
- Research Organization:
- Wisconsin Univ., Madison, WI (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- FG02-86ER53218
- OSTI ID:
- 5541234
- Alternate ID(s):
- OSTI ID: 7104991
- Report Number(s):
- UW-CPTC-91-3; ON: DE91013344
- Journal Information:
- Physics of Fluids. B, Plasma Physics, Journal Name: Physics of Fluids. B, Plasma Physics Journal Issue: 7 Vol. 4; ISSN 0899-8221
- Publisher:
- American Institute of PhysicsCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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