Implementation and verification of a conservative,<scp>multi‐species</scp>,<scp>gyro‐averaged</scp>, full‐<i>f</i>,<scp>Lenard‐Bernstein</scp>/Dougherty collision operator in the gyrokinetic code<scp>GENE‐X</scp>

Ulbl, Philipp; Michels, D.; Jenko, F.

doi:10.1002/ctpp.202100180

Cited by 6 publications

(4 citation statements)

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“…2019; Francisquez et al. 2021; Ulbl, Michels & Jenko 2021). Finally, we investigate the convergence properties of the gyromoment approach as a function of relevant physical parameters in different collisionality regimes, analysing the Hermite–Laguerre spectrum of the ITG distribution function and showing that magnetic drifts broaden the gyromoment spectrum significantly in the absence of collisions.…”

Section: Introductionmentioning

confidence: 99%

Local gyrokinetic collisional theory of the ion-temperature gradient mode

2022

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We present a study of the linear properties of the ion-temperature gradient (ITG) modes with collisions modelled for the first time by the linearized gyrokinetic (GK) Coulomb collision operator (Frei et al., J. Plasma Phys., vol. 87, issue 5, 2021, 905870501) in the local limit. The study is based on a Hermite–Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyromoments. We explore the collisionless and high-collisional limits of the gyromoment hierarchy analytically. Parameter scans revealing the dependence of the ITG growth rate on the collisionality modelled using the GK Coulomb operator are reported, showing strong damping at small scales as the collisionality increases and, therefore, the need for a steeper gradient for the ITG onset at high collisionality to overcome the finite Larmor radius (FLR) collisional stabilization. The predictions on the ITG growth rate by the GK Coulomb operator are compared with other collision operator models, such as the Sugama, the Dougherty, as well as the momentum-conserving pitch-angle scattering and the Hirshman–Sigmar–Clarke collision operators derived for the first time in terms of gyromoments. The importance of FLR terms in the collision operators is pointed out by the appearance of a short wavelength ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by FLR collisional effects. Energy diffusion is shown to be important at high collisionality and at small scale lengths. Among the GK collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation compared with the GK Coulomb collision operator, while the largest deviations are found with the GK Dougherty operator. Convergence studies of the gyromoment method are reported and show that the drifts associated with the gradient and curvature of the magnetic field increase the required number of gyromoments at low collisionality. Nevertheless, the low number of gyromoments necessary for convergence at high collisionality constitutes an attractive numerical and analytical feature of the gyromoment approach to study the plasma dynamics in the boundary of fusion devices.

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Section: Introductionmentioning

confidence: 99%

Local gyrokinetic collisional theory of the ion-temperature gradient mode

2022

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“…The same test was recently performed with a finite-volume implementation of the LBO-ET and LBO-EM in GENE-X Ulbl et al. (2021). This means that the initial distribution functions are described by the bi-Maxwellians where T, , , , eV and eV.…”

Section: Benchmarks and Resultsmentioning

confidence: 96%

“…We nevertheless present two slight variations in the following subsections, as was also recently done by Ulbl et al. (2021), in order to provide a point of reference for the LBO-G and comparing against Haack et al. (2017).…”

Section: Multispecies Dougherty Operatorsmentioning

confidence: 96%

“…(2017), where two different BGK operators were proposed which independently attempt to match the FPO's momentum and thermal relaxation rates. These are the LBO-EM and LBO-ET, respectively (these operators were also recently implemented in the GENE-X code Ulbl, Michels & Jenko 2021). We conclude this section with similar formulas for a gyroaveraged multispecies Dougherty operator.…”

Section: Multispecies Dougherty Operatorsmentioning

confidence: 99%

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Improved multispecies Dougherty collisions

et al. 2022

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The Dougherty model Fokker–Planck operator is extended to describe nonlinear full- $f$ ( f is the distribution function) collisions between multiple species in plasmas. Simple relations for cross-species primitive moments are developed which obey conservation laws, and reproduce familiar velocity and temperature relaxation rates. This treatment of multispecies Dougherty collisions, valid for arbitrary mass ratios, avoids unphysical temperatures and satisfies the $H$ -theorem (H is related to the entropy) unlike an analogous Bhatnagar–Gross–Krook operator. Formulas for both a Cartesian velocity space and a gyroaveraged operator are provided for use in Vlasov as well as long-wavelength gyrokinetic models. We present an algorithm for the discontinuous Galerkin discretization of this operator, and provide results from relaxation and Landau damping benchmarks.

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