Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

Xu, X. Q.; Xiong, Z.; Gao, Zhe; Nevins, W. M.; McKee, G. R.

doi:10.1103/physrevlett.100.215001

Cited by 68 publications

(109 citation statements)

References 11 publications

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“…They numerically evaluated the influence of toroidal Mach number on the Landau damping rate by considering from 2nd to 5th FOW resonance effect, respectively. Similar to the case without toroidal rotation [5,6,10], they found that the damping rate was significantly enhanced by 3rd resonance and the damping rate with 3rd resonance and the one with 4th * Electronic address: hjren@ustc.edu.cn or 5th resonance are almost the same with each other. In this Letter, theoretical investigation on the collisionless damping of GAM in a toroidally rotating tokamak plasma is performed.…”

supporting

confidence: 66%

“…When only the 2-nd resonance is taken into account, a recent NEMORB simulation [8] performed a good agreement with the analytical result to the 2-nd FOW effects for about q < 3.5 [2]. It was shown that for q > 3.5, the discrepancy between the theoretical result with 2nd harmonics and the TEMPEST simulation data becomes remarkable [6]. That means higher-order resonance should be considered.…”

supporting

confidence: 59%

“…The numerical evaluation performed by Gao et al [5] shows that the damping rate with 3-rd resonance and the one with 4-th resonance have only slight discrepancy when q is about greater than 7. Meanwhile, Xu et al numerically found that the damping rate with 4-th order resonance is almost the same as the rate with 10-th resonance [6].In a recent work[9], Guo and co-authors investigated the collisionless damping rate of GAM by taking into account the toroidal rotation. They numerically evaluated the influence of toroidal Mach number on the Landau damping rate by considering from 2nd to 5th FOW resonance effect, respectively.…”

mentioning

confidence: 99%

“…The classical Landau damping rate of GAM is found to be ∝ e −q 2 Ω 2 and independent of δ i , where Ω is the GAM frequency normalized by R/v T i with major radius R and ions thermal velocity v T i . Later, some theoretical analysis[2-4], numerical evaluation [5], and simulation [6,7] all indicate that the high-order FOW effect plays a key role in the collisionless damping of GAM, specifically in the large q region. The resonant damping rate is sensitive to and significantly enhanced by k r ρ i , where k r is the radial wave number.…”

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confidence: 99%

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Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma

Ren

2016

Nucl. Fusion

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The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating tokamak plasma is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical result is shown to agree well with the numerical solution. The dependence of the damping rate on the toroidal Mach number M relies on krρi. For sufficiently small krρi, the damping rate monotonically decreases with M . For relatively large krρi, the damping rate increases with M until approaching the maximum and then decreases with M .In the kinetic framework, keeping terms to the 1st order finite-Larmor-radius (FLR) effect, which represents the leading order polarization, and the 1st order finiteorbit-width (FOW) effect of passing particles δ i ∼ qρ i , where q is the safety factor of tokamaks and ρ i is the ion gyroradius, the dispersion relation of geodesic acoustic mode (GAM) [1] is derived. The classical Landau damping rate of GAM is found to be ∝ e −q 2 Ω 2 and independent of δ i , where Ω is the GAM frequency normalized by R/v T i with major radius R and ions thermal velocity v T i . Later, some theoretical analysis[2-4], numerical evaluation [5], and simulation [6,7] all indicate that the high-order FOW effect plays a key role in the collisionless damping of GAM, specifically in the large q region. The resonant damping rate is sensitive to and significantly enhanced by k r ρ i , where k r is the radial wave number. When only the 2-nd resonance is taken into account, a recent NEMORB simulation [8] performed a good agreement with the analytical result to the 2-nd FOW effects for about q < 3.5 [2]. It was shown that for q > 3.5, the discrepancy between the theoretical result with 2nd harmonics and the TEMPEST simulation data becomes remarkable [6]. That means higher-order resonance should be considered. The numerical evaluation performed by Gao et al. [5] shows that the damping rate with 3-rd resonance and the one with 4-th resonance have only slight discrepancy when q is about greater than 7. Meanwhile, Xu et al. numerically found that the damping rate with 4-th order resonance is almost the same as the rate with 10-th resonance [6].In a recent work[9], Guo and co-authors investigated the collisionless damping rate of GAM by taking into account the toroidal rotation. They numerically evaluated the influence of toroidal Mach number on the Landau damping rate by considering from 2nd to 5th FOW resonance effect, respectively. Similar to the case without toroidal rotation [5,6,10], they found that the damping rate was significantly enhanced by 3rd resonance and the damping rate with 3rd resonance and the one with 4th * Electronic address: hjren@ustc.edu.cn or 5th resonance are almost the same with each other. In this Letter, theoretical investigation on the collisionless damping of GAM in a toroidally rotating tokamak plasma is performed. We derive the analytical expression for the Landau damping rate by considering the FOW resonance effect to the 3rd order. Good agreement is found between our...

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supporting

confidence: 66%

supporting

confidence: 59%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma

Ren

2016

Nucl. Fusion

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“…Radial propagation of geodesic acoustic modes (GAMs) [1], and GAM eigenmodes have been discussed in recent literature [2][3][4]. The existence and properties of global GAM eigenmodes, which are influenced by the GAM group velocity, might be relevant for the efficiency of GAM excitation [4,5].…”

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confidence: 99%

Radial propagation of geodesic acoustic modes in up-down asymmetric magnetic geometries

Hager

Hallatschek

2010

Physics of Plasmas

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The energy approach to the analysis of the propagation of geodesic acoustic modes presented in Physics of Plasmas 16, 072503 (2009) is generalized to up-down asymmetric magnetic geometries including a model for single-null configuration. By removing the neoclassical cancellation effects, updown asymmetry can trigger a non-vanishing group velocity at zero radial wavenumber. Theoretical insight in this effect is provided by analytical calculations combined with numerical gyrokinetic and two-fluid studies. Thereby, an useful estimate of the group velocity at zero radial wavenumber is derived within a two-fluid framework.

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Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

et al. 2018

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Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this paper, we propose an implicitexplicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the -implicit additive Runge-Kutta methods in COGENT, a finite-volume gyrokinetic code for mapped, multiblock grids and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.Keywords IMEX time integration · plasma physics · gyrokinetic simulations · Vlasov-Fokker-Planck equations IntroductionThe purpose of this paper is to describe the application and performance of a semiimplicit time integration algorithm for the solution of a system of Vlasov-Fokker-Planck equations, motivated by the goal of simulating the edge plasma region of tokamak fusion reactors. Plasma dynamics in the tokamak edge region is an unsteady multiscale phenomenon, characterized by a large range of spatial and temporal scales due to the density and temperature variations. Figure 1 shows the cross-section of a typical tokamak fusion reactor. The geometry is defined by the magnetic flux surfaces that contain the plasma, and the core and the edge regions are marked. Within the edge region, as the temperature decreases from the hot near-core region to the cold outeredge region, there are three scale regimes. The hot and dense plasma in the inner edge region adjacent to the core plasma is weakly collisional, and the mean free paths of the particles are significantly larger than the density and temperature gradient length scales [20,26,25]. Near the separatrix that separates the closed magnetic field lines from the open ones, the plasma is moderately collisional, and the mean free paths are comparable to the density and temperature gradient scales. At the outer edge (near the material surfaces), the cold plasma is strongly collisional. In this region, the particle mean free paths are significantly smaller than the density and temperature length scales.Due to the weak collisionality near the core, a kinetic description with an appropriate collision model is required to model accurately the perturbations to the velocity distribution from the Maxwellian distribution. The Vlasov-Fokker-Planck (VFP) equation governs the evolution of the distribution function of each charged particle in the position and velocity space [80]. In the presence of a strong, externally-applied magnetic field, the ionized particles gyrate around the magnetic fiel...

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Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

Cited by 68 publications

References 11 publications

Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma

Energetic particle driven geodesic acoustic mode in a toroidally rotating tokamak plasma

Radial propagation of geodesic acoustic modes in up-down asymmetric magnetic geometries

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

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