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

Abstract

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...

Geodesic acoustic modes in magnetic confinement devices

“…Similar behaviour was obtained from GK theory [86,90], and from an extended fluid model with Grad type evolution equations for the heat flux [89,91]. The effects of plasma anisotropy in combination with toroidal rotation have also been considered [88,92]. Centrifugal and Coriolis forces further modify the plasma equilibria, thus affecting the perturbations.…”

“…More accurate results can be obtained by using the 21-moment system [84], which also includes the relaxation of the higher order (energy weighted) viscosity tensor, π * in notations of [84]. In the latter case, the coefficient 6/5 in equation (92), and respectively in (93), has to be replaced with another coefficient 6/5 → 6 × 178/(5 × 205) = 1.042, which will slightly modify the results (94) and (95). The accuracy of the fluid results obtained with Landau collision operator for the relaxation of the viscosity and energy weighted viscosity tensor is expected to be higher than those employing the reduced forms of the Krook collision operators [131,132].…”

Kinetic theory of geodesic acoustic modes in toroidal plasmas: a brief review

“…GAM branch was carried out [78,80]. Corrections to EGAM local dispersion relation due to electromagnetic effects [93], kinetic electrons [64,94] and toroidal rotation [95], were also investigated. Readers interested in these works may refer to the original papers for more details.…”

Summary of the 6th asia-pacific transport working group (APTWG) meeting

“…Theoretical studies of energetic particle transport were also presented in the conference. Ren presented results of an analytical investigation on energetic particle-driven geodesic acoustic modes (EGAM) [68] in a toroidally rotating tokamak plasma by using a kinetic-fluid hybrid model and gyrokinetic equations [69]. He found the co-existence of two branches, i.e.…”