Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Xiao, Yong; Catto, Peter J.; Dorland, W.

doi:10.1063/1.2718519

Cited by 41 publications

(81 citation statements)

References 23 publications

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“…If higher accuracy is warranted, it is straightforward to use Eq. (6), which is valid down to kδ r = O(1), at the expense of making the integrals more complicated [7].…”

Section: Landau Dampingmentioning

confidence: 99%

Oscillations of zonal flows in stellarators

Helander¹,

Mishchenko²,

Kleiber³

et al. 2011

Plasma Phys. Control. Fusion

108

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The linear response of a collisionless stellarator plasma to an applied radial electric field is calculated, both analytically and numerically. Unlike in a tokamak, the electric field and associated zonal flow develop oscillations before settling down to a stationary state, the so-called Rosenbluth-Hinton flow residual. These oscillations are caused by locally trapped particles with radially drifting bounce orbits. These particles also cause a kind of Landau damping of the oscillations that depends on the magnetic configuration. The relative importance of geodesic acoustic modes and zonal-flow oscillations therefore varies among different stellarators.

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“…If higher accuracy is warranted, it is straightforward to use Eq. (6), which is valid down to kδ r = O(1), at the expense of making the integrals more complicated [7].…”

Section: Landau Dampingmentioning

confidence: 99%

Oscillations of zonal flows in stellarators

Helander¹,

Mishchenko²,

Kleiber³

et al. 2011

Plasma Phys. Control. Fusion

108

View full text Add to dashboard Cite

show abstract

“…An accurate collision operator is important for calculation of neoclassical transport 1,2 and the growth rate of instabilities such as trapped electron modes, 3,4 dissipative drift waves, [5][6][7] and microtearing modes 8 in moderate collisionality regimes. Collisions can also affect the damping of zonal flows 9 and other modes that provide a sink for turbulent energy. In their absence, arbitrarily fine scales can develop in phase space, [10][11][12][13][14] which can in some cases pose challenges for discrete numerical algorithms, especially in the long-time limit; 15,16 even a modest amount of collisions can make accurate numerical calculation much easier.…”

Section: Introductionmentioning

confidence: 99%

Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests

et al. 2009

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A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical ͑real-space͒ diffusion. The numerical implementation in the continuum gyrokinetic code GS2 ͓Kotschenreuther et al., Comput. Phys. Comm. 88, 128 ͑1995͔͒ is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation.

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“…This unified approach highlights intricacies of the previous investigations, thereby forming a firm basis for how these kinetic calculations are best performed. In particular, we present a general method of treating finite electric field effects on ion orbits that allows us to solve a reduced kinetic equation for the pedestal modifications to the results of the usual evaluations of neoclassical transport in the banana and plateau regimes [6][7][8], and the residual zonal flow calculation [9,10]. The emphasis herein is on the steps that differ from the usual neoclassical and residual zonal flow treatments.…”

Section: Introductionmentioning

confidence: 99%

A unified treatment of kinetic effects in a tokamak pedestal

Catto¹,

Kagan²,

Landreman³

et al. 2011

Plasma Phys. Control. Fusion

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We consider the effects of a finite pedestal radial electric field on ion orbits using a unified approach. We then employ these modified orbit results to retain finite E×B drift departures from flux surfaces in an improved drift kinetic equation. The procedure allows us to make clear distinction between transit averages and flux surface averages when solving this kinetic equation. The technique outlined here is intended to clarify and unify recent evaluations of the banana regime decrease and plateau regime alterations in the ion heat diffusivity, the reduction and possible reversal of the poloidal flow in the banana regime and its augmentation in the plateau regime, the increase in the bootstrap current, and the enhancement of the residual zonal flow regulation of turbulence.

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Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Cited by 41 publications

References 23 publications

Oscillations of zonal flows in stellarators

Oscillations of zonal flows in stellarators

Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests

A unified treatment of kinetic effects in a tokamak pedestal

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