Gyrokinetic theory of turbulent acceleration and momentum conservation in tokamak plasmas

Wang, Lu; Peng, Shuitao; Diamond, P. H.

doi:10.1088/2058-6272/aab5bc

Cited by 7 publications

(9 citation statements)

References 31 publications

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“…The argument was made [56,57,58,59] that in experimental measurements the parallel velocity u ∥ is measured and not the parallel momentum density nu ∥ . It was concluded that therefore u ∥ respectively ⟨u ∥ ⟩ should be the quantity that theoretical work should focus on when discussing intrinsic rotation.…”

Section: Comparison To Parallel Accelerationmentioning

confidence: 99%

“…Also, recall that even though it is not technically wrong to compute ⟨u ∥ ⟩ the fluxsurface average (7) is a volume average and should be taken over density like quantities (like nu ∥ ). Finally, what comes out of a gyro-kinetic moment expansion (as performed in [56,57,58,59]) is the gyro-fluid parallel velocity U ∥ , not the actually measured fluid velocity u ∥ . As we discuss in Sec.…”

Section: Comparison To Parallel Accelerationmentioning

confidence: 99%

“…As collectively generated, internal forces neither the pressure gradient nor the electric field can be the source of an intrinsic rotation profile. We point out here that the only external force that is able to make a contribution, the mirror force term ⟨p ⊥ ∇ ∥ ln B⟩, was neglected in [56,57,58,59].…”

Section: Comparison To Parallel Accelerationmentioning

confidence: 99%

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Angular momentum and rotational energy of meanflows in toroidal magnetic fields

Wiesenberger¹,

Held²

2020

Preprint

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We derive the balance equation for the Favre averaged angular momentum in toroidal not necessarily axisymmetric magnetic field equilibria. These include tokamaks, stellarators, the reversed field pinch and field-reversed configurations. We find that the components of angular momentum are given by the covariant poloidal and toroidal components of E×B and parallel flow velocities and we separately identify all relevant stress tensors, torques and source terms for each of these components. Our results feature the Favre stress generalisations of previously found Reynolds stresses like the diamagnetic or parallel E × B stress. Further, we identify the magnetic shear as a source of poloidal E × B angular momentum and discuss the mirror and the Lorentz force. Here, we find that the geodesic transfer term, the Stringer-Winsor spin-up term and the ion-orbit loss term are all part of the Lorentz force and are in fact one and the same term.Discussing the relation to angular velocity we build the inertia tensor with the help of the first fundamental form of a flux-surface. In turn, the inertia tensor is used to construct a flux-surface averaged rotational energy for E × B surface flows of the plasma. The evolution of this rotational energy features a correction of previous results due to the inertia tensor. In particular, this correction suggests that density sources on the high-field side contribute much more to zonal flow energy generation than on the low field side.Our derivation is based on a full-F, electromagnetic, gyro-kinetic model in a long-wavelength limit. The results can be applied to gyro-kinetic as well as gyrofluid theories and can also be compared to drift-kinetic and drift-fluid models. Simplified cases for the magnetic field geometry including the axisymmetric purely toroidal and purely poloidal magnetic fields are discussed, as are the angular momentum balance of the electromagnetic fields, the ion-orbit loss mechanism and the parallel acceleration.

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Section: Comparison To Parallel Accelerationmentioning

confidence: 99%

Section: Comparison To Parallel Accelerationmentioning

confidence: 99%

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Angular momentum and rotational energy of meanflows in toroidal magnetic fields

Wiesenberger¹,

Held²

2020

Preprint

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“…Here, ∥ is the parallel current density, In this work, we focus on the intrinsic current drive which is independent of the mean parallel current density or its gradient. This is analogous to the intrinsic rotation drive by the residual stress, kinetic stress, and turbulent source [26][27][28].…”

Section: Quasi-linear Estimate For Intrinsic Parallel Current Densitymentioning

confidence: 99%

Intrinsic current driven by electromagnetic electron drift wave turbulence in the tokamak pedestal region

He¹,

Wang²,

Zhuang³

2019

Plasma Phys. Control. Fusion

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The local intrinsic parallel current density driven by electron drift wave (DW) turbulence including electromagnetic (EM) effects is analytically studied. The scalings of the ratios of intrinsic current density driven by residual turbulent flux and by turbulent source to the bootstrap current density with electron density and temperature are predicted to be e 3 4 ⁄ i e ⁄ and e i e ⁄ , respectively. Based on the typical parameters in DIII-D pedestal region, the local intrinsic current density driven by both the residual turbulent flux and the turbulent source is negligible. However, despite the negligible turbulent source driven current, the residual turbulent flux driven local intrinsic current density by EM DW turbulence can reach about 66% of the bootstrap current density for ITER pedestal parameters due to much lower collisionality in ITER than in DIII-D. Moreover, the contributions from adiabatic ES parts, non-adiabatic ES parts and non-adiabatic EM parts of the plasma response to electromagnetic fluctuations are analyzed. It is found that there exists strong cancelation between non-adiabatic ES response and the non-adiabatic EM response for the ITER pedestal case, and thus the kinetic stress contributed by the adiabatic ES response of parallel electron pressure dominates the intrinsic current drive. This is different from the ES electron DW case. Therefore, the EM effects on turbulence driven intrinsic current density should be carefully considered in the future reactor with high ratio of electron pressure to the magnetic pressure and steep pressure profile. 2

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“…The topic of an exact gyrokinetic momentum conservation law gained crucial importance in the context of the momentum transport (Waltz et al 2007; Parra & Catto 2010 a ; Abiteboul et al 2011; Peeters et al 2011) and intrinsic toroidal rotation (Wang, Peng & Diamond 2018; Stoltzfus-Dueck 2019) in axisymmetric tokamak plasmas. In particular, the phenomenon of intrinsic toroidal rotation, which is observed in the absence of external torque, must be investigated within the context of toroidal angular momentum conservation.…”

Section: Introductionmentioning

confidence: 99%

Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

Brizard

2021

J. Plasma Phys.

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The exact energy and angular momentum conservation laws are derived by the Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov–Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocentres and the perturbed electromagnetic fields, in which the crucial roles played by gyrocentre polarization and magnetization effects are highlighted. In addition to yielding an exact angular momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries.

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Gyrokinetic theory of turbulent acceleration and momentum conservation in tokamak plasmas

Cited by 7 publications

References 31 publications

Angular momentum and rotational energy of meanflows in toroidal magnetic fields

Angular momentum and rotational energy of meanflows in toroidal magnetic fields

Intrinsic current driven by electromagnetic electron drift wave turbulence in the tokamak pedestal region

Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

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