A Modification of the Guiding-Centre Fundamental 1-Form with StrongE×BFlow

Abstract

A modified guiding-centre fundamental 1-form with strong E Â B flow is derived by the phase space Lagrangian Lie perturbation method. Since the symplectic part of the derived 1-form is the same as the standard one without the strong E Â B flow, it yields the standard Lagrange and Poisson brackets. Therefore the guiding-centre Hamilton equations keep their general form even when temporal evolution of the E Â B flow is allowed. Compensation of keeping the standard symplectic structure is paid by complication of the guiding-centre Hamiltonian. However, it is possible to simplify the Hamiltonian in well localised transport barrier regions like a tokamak edge in a high confinement regime and an internal transport barrier in a reversed shear tokamak. The guiding-centre Vlasov and Poisson equations are derived from the variational principle. The conserved energy of the system is obtained from the Noether's theorem. Correspondence to low-frequency fluid equations is shown.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

“…Here, v Ti is the ion thermal velocity and d $ q Ti =L ( 1 represents the ordering parameter defined by the ratio of the ion thermal gyroradius q Ti to the background gradient scale length L. On the other hand, under the high-flow ordering V 0 ¼ Oðv Ti Þ (Hinton and Wong 1985;Catto 1987;Sugama andHorton 1997a, b, 1998;Artun and Tang 1994;Brizard 1995;Hahm 1996;Miyato 2009;Abel et al 2013), the toroidal momentum transport equation which determines the background radial electric field profile can be derived with the same-order accuracy as the particle and energy transport equations. In this paper, we present a novel formulation of collisional and turbulent transport in toroidal plasmas under the high-flow ordering (Sugama et al 2017) by generalizing the previous study to derive governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions which satisfy conservation laws for particles, energy, and toroidal momentum.…”

Nonlinear gyrokinetic theory with polarization drift

“…This can be attributed to the modification of the Jacobian for transformation from the particle phase space to the gyrocenter phase space 17 which was ignored in previous works. [10][11][12] Including the polarization drift explicitly in the gyrocenter equation of motion does not change significantly neither the gyrocenter equation of motion nor the energy invariant. The phase-space Lagrangian Lie-perturbation theory ensures that the gyrokinetic Vlasov-Poisson system has an exact energy conservation law.…”

Fluid Moments in the Reduced Model for Plasmas with Large Flow Velocity

“…We consider a transformation from particle coordinates z = (x, v , w, θ) to guiding-centre coordinates Z = (X, U, μ, ξ) given by [4] …”

“…Hence, extension of the standard model is needed to treat the formation of transport barriers. Several gyrokinetic Lagrangians have been presented to treat this situation [4][5][6][7][8][9][10]. Here we give an account of the underlying representations of the particle density in each of these models.…”

“…Recently a reduced fundamental 1-form (phase space Lagrangian) including a large E × B flow was derived by modifying the standard guiding-centre transformation author's e-mail: miyato.naoaki@jaea.go.jp through the Lie-transform perturbation method [4]. In contrast to conventional models for a flowing plasma [5][6][7][8][9][10], the symplectic part of the Lagrangian is the same as the standard one without flow formally.…”