Multiscale Finite-Beta Gyrokinetics
Abstract
Finite-β effects on microinstabilities have been investigated by gyrokinetic particles codes using the new double split scheme [Startsev, Lee and Wang, manuscript in preparation]. The scheme requires that F=(1 + ψ) F0+dx||κe.(∇A||xb0)+δg,eq1 so that a new full density gradient, which is set up by the fast electrons transverse to the direction of the full field, is consistent with the condition of b .∇(F0+dx||κe.(∇A||xb0))=0, where b=b0+δB/B0. Here φ is normalized by Te/e, A by cTe/e cs, F is the total distribution function, F0 is the background distribution function, ψ= φ+ (A/ t) d x/c, and φ and A are the perturbed potentials. The finite-β effects on microinstabilities are found to be related to the multiscale equation of the form, (ρs/ λD)^2 [2̂ψ- ψ/ δe^2 ]= -4 πq v <δ(r) > where is the gyro angle based on the ion gyroradius, ρi, and δe is the electron skin depth, which can be an order of magnitude smaller in the tokamak core. To the lowest order, this equation gives rise to the shielding effect as ψ= (q / r) (ρs/ λD) exp(-r/δe). Thus, we have the presence of two distinct spatial scales in the problem. A numerical scheme based on the concept of singular perturbation methods is used and the resulting finite-β effects on drift instabilities, ion temperature gradient drift modes and electron temperature gradient drift modes will be reported.
- Publication:
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APS Division of Plasma Physics Meeting Abstracts
- Pub Date:
- November 2008
- Bibcode:
- 2008APS..DPPGP6099L