Nonlinear gyrokinetic equations for turbulence in core transport barriers
- Princeton University, Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States)
An energy-conserving set of the nonlinear electrostatic gyrokinetic Vlasov and Poisson equations is derived for the first time in the presence of equilibrium {bold E{times}B} velocity {ital u}{sub {ital E}}{approximately}{ital v}{sub {ital Ti}}, via phase-space Lagrangian Lie-perturbation theory. In this general formulation, only the basic small parameter {epsilon} with {omega}/{Omega}{approximately}{ital k}{sub {parallel}}/{ital k}{sub {perpendicular}}{approximately}{epsilon} and {delta}{ital n}/{ital n}{sub 0}{approximately}1/{ital k}{sub {perpendicular}}{ital L}{approximately}{epsilon}, is used, while no device-specific expansion has been made. Here, {ital L} is the equilibrium scale length. For application to microturbulence in tokamak core transport barriers, an additional small ordering parameter {delta}{sub {ital B}}{equivalent_to}{ital B}{sub {theta}}/{ital B}{lt}1 is utilized. This leads to a useful form of the nonlinear gyrokinetic system which is applicable to a realistic situation in which the gradient lengths of the equilibrium radial electric field and pressure are of the same order as the ion poloidal gyroradius. The ordering for fluctuations is also modified to {delta}{ital n}/{ital n}{sub 0}{approximately}{epsilon}{delta}{sub {ital B}}{lt}1/{ital k}{sub {perpendicular}}{ital L}{approximately}{delta}{sub {ital B}} for a better description of sub-mixing-length level fluctuations. {ital u}{sub {ital E}}/{ital v}{sub {ital Ti}}{approximately}{delta}{sub {ital B}} and {rho}{sub {theta}{ital i}}{approximately}{ital L}{sub {ital p}} put the pressure-gradient contribution to {ital E}{sub {ital r}} and the toroidal-flow contribution to {ital E}{sub {ital r}} at the same order. {delta}{sub {ital B}}{approximately}{epsilon} is shown to be a maximal ordering for studying the {bold E{times}B} flow shear suppression of turbulence. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 397524
- Journal Information:
- Physics of Plasmas, Vol. 3, Issue 12; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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