Collisionless damping of short wavelength geodesic acoustic modes

Qiu, Zhiyong; Chen, Liu; Zonca, F.

doi:10.1088/0741-3335/51/1/012001

Cited by 89 publications

(143 citation statements)

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“…The GAM is usually driven nonlinearly by plasma microturbulence. There is much linear study on GAM's damping due to collision and ion Landau resonance [8][9][10][11][12][13][14][15][16] and on GAM's radial propagation due to finite thermal ion gyroradius and plasma temperature profile inhomogeneity [13,14]. Nonlinear studies found that that GAM can be driven by plasma microturbulence [13,[17][18][19], consistent with experimental observation of GAM in the plasma edge region [20][21][22].…”

Section: Introductionsupporting

confidence: 53%

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

Fu¹

2010

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It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

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Section: Introductionsupporting

confidence: 53%

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

Fu¹

2010

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“…The procedure is almost the same as described in Ref. 23, but can still be simply outlined here with the expressions in Eqs. ͑6͒-͑8͒ for the sake of clarity and completeness.…”

Section: B the Solution In The Large Orbit Drift Width Limitmentioning

confidence: 99%

“…For nonresonant ions, the large orbit drift width limit can be relaxed more in the expansion. 23 We only need t / ϳ 1 / q Ӷ 1 and also d / ϳ k ti Ӷ 1. Without losing the generality, we can put these two terms into the same order.…”

Section: B the Solution In The Large Orbit Drift Width Limitmentioning

confidence: 99%

“…Later, a new method based on the large orbit drift width expansion is developed. This method was initialed by Zonca and Chen 22 and clearly presented by Qiu et al 23 Under the large orbit drift width assumption, the magnetic drift term is larger than the parallel transit term and then the magnetic drift frequency resonance ϳ d ϵ k · v d is considered first, where k and v d are the wave vector of the zonal potential ͑in the radial direction͒ and the magnetic drift velocity ͑in the vertical direction͒, respectively. It returns to a clear picture of Landau damping.…”

Section: Introductionmentioning

confidence: 99%

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Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit

Gao

2010

Physics of Plasmas

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Plasma shaping effects on the geodesic acoustic mode ͑GAM͒ are revisited analytically in the large orbit drift width limit. Comparing with results from the small orbit drift width expansion method ͓Z. Gao et al., Phys. Plasmas 15, 074502 ͑2008͔͒ the behavior of the real frequency is almost the same but the effect on the damping rate is different due to the change of dominant resonant mechanism, from low order harmonic transit resonance to high order harmonic resonance, or equivalently, to the magnetic drift resonance. As a result, although the GAM frequency decreases with an increasing elongation by dependence of ͓2 / ͑ 2 +1͔͒ 1/2 , the damping is weakened mildly in the large orbit drift width limit, which is quite different from the result in the low small orbit drift limit, where the damping is enhanced exponentially with the decrease in frequency. Also, in the large orbit drift width limit, the dependence of the GAM damping rate on inverse aspect ratio is analytically obtained for the first time. As increases, the frequency behaves as a weakly decreasing parabola function of , and the damping rate increases parabolically, but more rapidly than the frequency decreases. The GAM with longer radial wavelength is more easily damped by the finite aspect ratio effect. It is also found that the Shafranov shift gradient has the similar effect as the inverse aspect ratio.

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“…There is no fluctuations on the curves. As a comparison, we then let k = 0.1375 as done in the TEM-PEST simulation [6], COGENT simulation [7] and theoretical calculation [10,16]. It is found that in this condition, the damping rate increases with M first.…”

mentioning

confidence: 99%

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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Collisionless damping of short wavelength geodesic acoustic modes

Cited by 89 publications

References 13 publications

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

Plasma shaping effects on the geodesic acoustic mode in the large orbit drift width limit

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

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