Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

Lakhin, V. P.; Sorokina, E. A.

doi:10.1016/j.physleta.2013.12.008

Cited by 16 publications

(37 citation statements)

References 17 publications

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“…The result found for the eigenfunction is similar to previous calculations for GAM in MHD, numerically (Berk et al. 2006) and analytically (Lakhin & Sorokina 2014), showing strong coupling to the dispersion relation near its maximum. In our case, instead of a Dirac function for , the solution is spatially distributed.…”

Section: Maximum Off Axis – Radial Profile For the Egam Oscillationsupporting

confidence: 89%

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Description of global EGAM in the maximum of local frequency during current ramp-up discharges in DIII-D

et al. 2022

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Energetic-particle-induced geodesic acoustic modes, EGAMs (Fu, Phys. Rev. Let., vol. 101, 2008, pp. 185002), driven by neutral beam injection (NBI), have been observed in many DIII-D tokamak experiments (Nazikian et al., Phys. Rev. Lett., vol. 101, 2008, pp. 185001). This mechanism has been theoretically investigated in (Qiu et al., Plasma Phys. Control. Fusion, vol. 52, 2010, pp. 095003), using a sharp energetic particle distribution function, and in (Qu et al., Plasma Phys. Control. Fusion, vol. 59, 2017, pp. 055018), where the dispersion relation and eigenmode behaviour were obtained for the situation of early beam scenario, that is, for times smaller than the beam slowing down time. In this work, we extend these studies determining the eigenmode for beyond the slowing down time, in a scenario with reverse safety factor $q$ profile, where a small concentration of energetic ions can produce an off-axis maximum in the GAM dispersion relation. The characteristics of EGAM are analytically studied with the drift kinetic equation together with the MHD code NOVA. The toroidal energetic ion transit frequency, coupled with the GAM frequency, produces the maximum in the dispersion relation where the eigenmode can be found. The quantitative correspondence of experimental results with the predictions of the proposed model is analysed.

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Section: Maximum Off Axis – Radial Profile For the Egam Oscillationsupporting

confidence: 89%

“…2002; Heidbrink 2008) or geodesic modes (Berk et al. 2006; Lakhin & Sorokina 2014). In recent studies, it was proposed that the EGAM can also lie on the extrema of the dispersion relation in early beam discharges (Qu, Hole & Fitzgerald 2017), before energetic particles are completely slowed down.…”

Section: Introductionmentioning

confidence: 99%

Description of global EGAM in the maximum of local frequency during current ramp-up discharges in DIII-D

et al. 2022

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“…Geodesic Acoustic Modes (GAMs) are M ¼ 0, N ¼ 0 axisymmetric modes combined with M ¼ 61, 62 poloidal sidebands with frequency 1 x 2 G % ð7T i =2 þ 2T e Þ=R 2 0 m i in hot plasmas, where T e;i are the electron or ion temperatures in energy units, R 0 is the major radius of the plasma column, and m i is the ion mass. Geodesic eigenmodes have been experimentally observed in tokamak Ohmic discharges 2,3 and also detected during ion cyclotron resonance heating (ICRH) 4 and Neutral Beam Injection (NBI) [5][6][7][8][9] heating discharges in tokamaks. These modes attract attention due to accompanied energetic ion loss observed in experiments [3][4][5][6][7] and modification of the plasma transport, as discussed in theoretical models.…”

Section: Introductionmentioning

confidence: 99%

“…These modes attract attention due to accompanied energetic ion loss observed in experiments [3][4][5][6][7] and modification of the plasma transport, as discussed in theoretical models. 8,9 In the ICRH 4 and NBI heating 6,7 experiments, geodesic mode instabilities are usually driven by trapped 4 and untrapped fast ions, respectively. 6,7 According to models 10,11 of the instability in discharges with NBI, the energetic particle GAM (EGAM) instability is defined by the pitch angle dependence in velocity space with a slowing-down energy distribution that is finished at the critical energy.…”

Section: Introductionmentioning

confidence: 99%

Geodesic modes driven by untrapped resonances of NB energetic ions in tokamaks

2019

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Geodesic modes are typically excited by a minor concentration of energetic ions, but unstable mode frequencies are substantially different from Geodesic Acoustic Modes (GAMs) and are named EGAM (Energetic particle GAM). The EGAM instability driven by Neutral Beam Injection (NBI) has been observed in DIII-D tokamak experiments. The problem of the geodesic mode instability is analytically studied using a full drift kinetic equation. To analyze the instability condition, an ionization NBI location is assumed to be on the high field side of tokamaks. A minority NBI ion distribution is modeled by an energetic ion tail in the untrapped-passing region that remains between a magnetic axis and the trapped NBI boundary. The EGAM instability condition is defined by the parallel NBI ion velocity v||≈(1.2−1.5)ωR0q0 that has to be above the effective EGAM phase velocity. In this case, the EGAM frequency is ≈50% below the standard stable GAM frequency, which is reduced by a small concentration of energetic NBI ions. Qualitative comparison of the developed geodesic mode theory with NBI heating experiments in the midregion of the tokamak plasma is discussed.

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“…Since the early works of Winsor 2 and Mikhailoviskii 21 , several fluid [22][23][24][25] and kinetic 9,[26][27][28][29] models have been developed to improve the theoretical prediction of the GAMs frequencies. Numerous corrections on the dynamics of these modes were included to account for realistic conditions observed in experiments and, among these corrections, those due to electromagnetic effects [30][31][32][33][34] may be essential to predict correctly not only the value of the higher frequency of GAMs, f GAM ∼ T e /m i R 0 (hereafter referred simply as the GAM frequency), but also the parallel current density ( j ). Here T e is the electron temperature, m i is the ion mass and R 0 is the major radius of the tokamak.…”

Section: Introductionmentioning

confidence: 99%

Drift effects on electromagnetic geodesic acoustic modes

Sgalla

2015

Physics of Plasmas

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A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ r ∼ 25 cm, i. e., an order of magnitude higher than the usual value for zonal flows (ZFs).

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Geodesic acoustic eigenmode for tokamak equilibrium with maximum of local GAM frequency

Cited by 16 publications

References 17 publications

Description of global EGAM in the maximum of local frequency during current ramp-up discharges in DIII-D

Description of global EGAM in the maximum of local frequency during current ramp-up discharges in DIII-D

Geodesic modes driven by untrapped resonances of NB energetic ions in tokamaks

Drift effects on electromagnetic geodesic acoustic modes

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