Multiscale modelling for tokamak pedestals

Abel, Ian; Hallenbert, A.

doi:10.1017/s0022377818000326

Cited by 3 publications

(3 citation statements)

References 61 publications

(159 reference statements)

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“…As a final remark, we note that, to solve the field equations, a plasma vorticity equation can be used, which generalizes the ones commonly solved in drift and long wavelength models (Zeiler et al 1997;Ricci et al 2012;Jorge et al 2017;Abel & Hallenbert 2018). The plasma vorticity equation can be obtained from the quasineutrality condition in (7.11).…”

Section: δA δφmentioning

confidence: 99%

A gyrokinetic model for the plasma periphery of tokamak devices

2020

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A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated. †

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Section: δA δφmentioning

confidence: 99%

A gyrokinetic model for the plasma periphery of tokamak devices

2020

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“…The inclusion of the finite gradient and curvature of the magnetic field – in addition to the conventional slab geometry (see, e.g., Howes et al. 2006) – is motivated by recent evidence (Abel & Hallenbert 2018; Parisi et al. 2020) that the modes mediated by these equilibrium quantities can often be the fastest-growing ones in steep-gradient regions of the plasma (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…To this end, in this paper, we consider electromagnetic instabilities and turbulence driven by the ETG in a local slab model of a tokamak-like plasma, with constant equilibrium gradients, including magnetic drifts but not magnetic shear. The inclusion of the finite gradient and curvature of the magnetic field -in addition to the conventional slab geometry (see, e.g., Howes et al 2006) -is motivated by recent evidence (Abel & Hallenbert 2018;Parisi et al 2020) that the modes mediated by these equilibrium quantities can often be the fastest-growing ones in steep-gradient regions of the plasma (e.g. the pedestal), and thus significant in determining its nonlinear saturated state.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic instabilities and plasma turbulence driven by electron-temperature gradient

et al. 2022

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Electromagnetic (EM) instabilities and turbulence driven by the electron-temperature gradient (ETG) are considered in a local slab model of a tokamak-like plasma. Derived in a low-beta asymptotic limit of gyrokinetics, the model describes perturbations at scales both larger and smaller than the electron inertial length $d_e$ , but below the ion Larmor scale $\rho _i$ , capturing both electrostatic and EM regimes of turbulence. The well-known electrostatic instabilities – slab and curvature-mediated ETG – are recovered, and a new instability is found in the EM regime, called the thermo-Alfvénic instability (TAI). It exists in both a slab version (sTAI, destabilising kinetic Alfvén waves) and a curvature-mediated version (cTAI), which is a cousin of the (electron-scale) kinetic ballooning mode. The cTAI turns out to be dominant at the largest scales covered by the model (greater than $d_e$ but smaller than $\rho _i$ ), its physical mechanism hinging on the fast equalisation of the total temperature along perturbed magnetic field lines (in contrast to kinetic ballooning mode, which is pressure balanced). A turbulent cascade theory is then constructed, with two energy-injection scales: $d_e$ , where the drivers are slab ETG and sTAI, and a larger (parallel system size dependent) scale, where the driver is cTAI. The latter dominates the turbulent transport if the temperature gradient is greater than a certain critical value, which scales inversely with the electron beta. The resulting heat flux scales more steeply with the temperature gradient than that due to electrostatic ETG turbulence, giving rise to stiffer transport. This can be viewed as a physical argument in favour of near-marginal steady-state in electron-transport-controlled plasmas (e.g. the pedestal). While the model is simplistic, the new physics that is revealed by it should be of interest to those attempting to model the effect of EM turbulence in tokamak-relevant configurations with high beta and large ETGs.

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Transport theory of phase space zonal structures

Falessi

Zonca

2019

Physics of Plasmas

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A set of equations is derived that describes the transport of particles and energy in a thermonuclear plasma on the energy confinement timescale. The equations thus derived allow to study collisional and turbulent transport self-consistently retaining the effect of magnetic field geometry without assuming any scale separation between fluctuations and the reference state. In a previous article [1], transport equations holding on the reference state lengthscale have been derived using the moment approach introduced in [2]. Furthermore it has been shown how this approach is not suitable for the description of smaller length-scales. In this work, this analysis is extended to micro-and meso-scales adopting the framework of phase space zonal structure theory [3, 9]. Previous results are recovered in the long wavelength limit and, in the general case, transport equations in the phase space for particles and energy are obtained that correctly take into account meso-scale structures.

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Multiscale modelling for tokamak pedestals

Cited by 3 publications

References 61 publications

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model for the plasma periphery of tokamak devices

Electromagnetic instabilities and plasma turbulence driven by electron-temperature gradient

Transport theory of phase space zonal structures

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