Solution of the drift-kinetic equation for global plasma modes and finite particle orbit widths

Porcelli, Francesco; Stankiewicz, R.; Kerner, W.; Berk, H. L.

doi:10.1063/1.870792

Cited by 150 publications

(224 citation statements)

References 16 publications

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“…In addition, F j is the equilibrium distribution function for the species j, P φ and E are the toroidal canonical momenta and kinetic energy of a particle. Finally, V jg is the guiding centre velocity for a particle of species j, which also enters into the time derivative of the perturbed Lagrangian, defined as [24]:…”

Section: Exact Zonal Modes Under Kinetic-mhd Modelmentioning

confidence: 99%

Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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The MHD model enables derivation and analysis of the rich structure of geodesic acoustic modes (GAMs) and zonal modes in axisymmetric magnetic confined plasmas. The modes are identifiable from a single dispersion relation as two branches of slow magnetosonic continua. The lower frequency branch can be identified as a zonal flow, which in the simplified limit of static plasmas, has vanishing magnetic component. It is shown in this contribution that axisymmetric, and lesser known nonaxisymmetric, zonal modes can be derived from MHD and kinetic models. The work provides a comprehensive derivation of the GAMs and zonal flow continua in static and stationary toroidally rotating plasmas, and investigates the exact solution and structure of a generalised family of zonal modes.

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Section: Exact Zonal Modes Under Kinetic-mhd Modelmentioning

confidence: 99%

Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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“…is the adiabatic (fluid) contribution, ¼^expðÀin À i!tÞ is the MHD displacement with^¼ P m^m expðÀim Þ, and the nonadiabatic (kinetic) contribution F k can be approximately written as ''bounce time'' b periodic function of time [4,14]:…”

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confidence: 99%

Sawtooth-Control Mechanism using Toroidally Propagating Ion-Cyclotron-Resonance Waves in Tokamaks

et al. 2009

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The sawtooth control mechanism in plasmas employing off-axis toroidally propagating ion cyclotron resonance waves in tokamaks is reinvestigated. The radial drift excursion of energetic passing ions distributed asymmetrically in the velocity parallel to the magnetic field determines stability when the rational q ¼ 1 surface resides within a narrow region centered about the shifted fundamental cyclotron resonance. Magnetohydrodynamic (MHD) stability of plasmas in the presence of energetic ions is a crucial issue for present and future large tokamak experiments. Such ions include 3.5 MeV fusion alpha particles, and energetic minority ions produced by auxiliary heating methods such as from ion cyclotron resonance frequency (ICRF) waves. Ions trapped outside the region of highest magnetic field strength have been shown [1] to stabilize a key core instability known as the sawtooth, located within the q ¼ 1 rational surface, thereby lengthening the period between sequential soft-xray relaxations [2]. Without an effective means of shortening the period of sawteeth, coupling can occur with instabilities located at rational surfaces closer to the tokamak edge. Indeed, interaction of long sawteeth and performance degrading neoclassical tearing modes has been observed [3] in the Joint European Torus (JET), while improved plasma confinement is often found to coincide with small regular sawteeth.Under certain conditions untrapped, or passing, energetic ions can also strongly influence sawteeth. Sawtooth control from energetic ions injected with near tangential unbalanced neutral beams has already been demonstrated analytically, for deeply passing ions [4], numerically and experimentally [5]. The mechanism responsible was found to be due to the contribution on the n ¼ 1 internal kink mode of passing particles intersecting the q ¼ 1 rational surface. An important fast ion effect is obtained when the distribution function of passing ions is asymmetrically distributed in the velocity parallel to the magnetic field. By extending the analysis of Ref.[4] to solve for the internal kink mode across all velocity space, including barely passing trajectories, it is shown in the present contribution that the sawtooth control mechanism responsible for localized off-axis toroidally propagating ICRF waves is essentially the same as for unbalanced neutral beam injection (NBI) scenarios. Moreover, the propagating ICRF waves are more effective than unbalanced NBI because the orbit widths of the energetic ions are larger, and the parallel asymmetry of the distribution function is more strongly radially sheared. Simulations using SELFO [6] for the ICRF wave field and distribution function are applied to a key demonstration JET discharge [7] with localized off-axis ion cyclotron current drive (ICCD) counter to the Ohmic current. Analytical and full numerical calculations [8] of the internal kink mode with the simulated JET ICRF distribution function [9] demonstrate ideal instability when the deposition of the resonating ions is very close to the ...

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“…Setting D = 0 (i.e, C = v b ) and V E = O( ) in (3) and (7) recovers the standard results [4]. We introduce the coordinate system r-θ-φ, where θ is the well-defined poloidal angle.…”

Section: A Solution To the Perturbed Drift Kinetic Equation With Sheamentioning

confidence: 99%

“…We note that the adiabatic response δW f p in (12) reduces to the standard fluid pressure response in the zero-banana-width limit [4].…”

Section: Reformulating the Energy Functional Of Kinetic Resonancementioning

confidence: 99%

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On Kinetic Resistive Wall Mode Theory with Sheared Rotation

Shiraishi

Miyato

Matsunaga

2014

Plasma and Fusion Research

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To study toroidal rotation shear effect on Resistive Wall Mode (RWM) stability, kinetic RWM formulation is extended to include general equilibrium rotation. By starting from the guiding-center Lagrangian with sheared rotation, an energy functional of kinetic resonance is generalized. Based on the generalized energy functional, a new dispersion relation is derived in the large aspect ratio limit. Numerical analysis of the new dispersion relation indicates that the rotation shear can reduce the growth rates of the RWMs.

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Solution of the drift-kinetic equation for global plasma modes and finite particle orbit widths

Cited by 150 publications

References 16 publications

Generalised zonal modes in stationary axisymmetric plasmas

Generalised zonal modes in stationary axisymmetric plasmas

Sawtooth-Control Mechanism using Toroidally Propagating Ion-Cyclotron-Resonance Waves in Tokamaks

On Kinetic Resistive Wall Mode Theory with Sheared Rotation

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