Comparisons and applications of four independent numerical approaches for linear gyrokinetic drift modes

Xie, Huasheng; Li, Y. Y.; Lu, Zhixin; Ou, Weike; Li, B.

doi:10.1063/1.4990435

Cited by 17 publications

(36 citation statements)

References 28 publications

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“…Contrast to previous studies [11,13], this work is valid for all the gyrokinetic orderings, without further approximations. Contrast to previous Z-pinch and ring dipole studies [16,17,25,28], this work demonstrates the importance of the parallel mode structures and finds that the high order eigenstates can be important at some parameters.…”

Section: Discussioncontrasting

confidence: 93%

“…(5) and (6) in Z-pinch with only passing particles using MGK code in Ref. [25], where we can assume v and v ⊥ to be constant along field line. However, to study the physics in dipole configuration, we must treat the particles trapping, i.e., the variation of v and v ⊥ along the field line.…”

Section: Linear Gyrokinetic Modelmentioning

confidence: 99%

“…[28] and more details in Ref. [25], i.e., only two types of unstable electrostatic drift modes in the system, one is mainly driven by electron gradient and propagates in electron diamagnetic direction; and another is mainly driven by ion gradient and propagates in ion direction. However, when considering the mode structures, we find some new physics not existed in Z-pinch configuration, i.e., high order eigenstates of the mode can be more unstable than the ground state in particular parameters.…”

Section: Benchmark and Basic Features Of The Modesmentioning

confidence: 99%

“…However, new unstable modes appear by increasing k ⊥ ρ i in the simulation, and the corresponding mode structures are shown in Fig.17. Due to steep gradient, this mode is 'interchange-like' [25], as ω i → γ 0 = 0 for k ⊥ ρ i → 0. The eigenstate label l here is roughly to fit the mode structure with φ(ξ) = H l (ξ)e −ξ 2 /2 , where H l is l-th Hermite polynomials, with l = 0, 1, 2, · · · .…”

Section: Parameters Scan In Simulationsmentioning

confidence: 99%

“…(16)- (19) are our final equations to solve for local electrostatic drift mode in dipole. Standard δf particle-in-cell (PIC) approach [25,26] is used in this work to do our simulation. If we use adiabatic electron model, i.e., h e = 0 (not g e = 0), the only change is the quasi-neutrality Eq.…”

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confidence: 99%

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Local gyrokinetic study of electrostatic microinstabilities in dipole plasmas

et al. 2017

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A linear gyrokinetic particle-in-cell scheme, which is valid for arbitrary perpendicular wavelength k ⊥ ρi and includes the parallel dynamic along the field line, is developed to study the local electrostatic drift modes in point and ring dipole plasmas. We find the most unstable mode in this system can be either electron mode or ion mode. The properties and relations of these modes are studied in detail as a function of k ⊥ ρi, the density gradient κn, the temperature gradient κT , electron to ion temperature ratio τ = Te/Ti, and mass ratio mi/me. For conventional weak gradient parameters, the mode is on ground state (with eigenstate number l = 0) and especially k ∼ 0 for small k ⊥ ρi. Thus, bounce averaged dispersion relation is also derived for comparison. For strong gradient and large k ⊥ ρi, most interestingly, higher order eigenstate modes with even (e.g., l = 2, 4) or odd (e.g., l = 1) parity can be most unstable, which is not expected by previous studies. High order eigenstate can also easily be most unstable at weak gradient when τ > 10. This work can be particularly important to understand the turbulent transport in laboratory and space magnetosphere.

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Section: Discussioncontrasting

confidence: 93%

Section: Linear Gyrokinetic Modelmentioning

confidence: 99%

Section: Benchmark and Basic Features Of The Modesmentioning

confidence: 99%

Section: Parameters Scan In Simulationsmentioning

confidence: 99%

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confidence: 99%

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Local gyrokinetic study of electrostatic microinstabilities in dipole plasmas

et al. 2017

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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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Moment-based approach to the flux-tube linear gyrokinetic model

Frei,

Hoffmann,

Ricci

et al. 2023

J. Plasma Phys.

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This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

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Comparisons and applications of four independent numerical approaches for linear gyrokinetic drift modes

Cited by 17 publications

References 28 publications

Local gyrokinetic study of electrostatic microinstabilities in dipole plasmas

Local gyrokinetic study of electrostatic microinstabilities in dipole plasmas

Local gyrokinetic collisional theory of the ion-temperature gradient mode

Moment-based approach to the flux-tube linear gyrokinetic model

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