Linear radial structure of reactive energetic geodesic acoustic modes

Abstract

In this paper we have developed a fluid model to study the radial mode structure of the reactive energetic geodesic acoustic modes (reactive EGAMs), a branch of GAM that becomes unstable in the presence of a cold fast ion beam. We have solved the resulting dispersion relationship, a second order ODE, both analytically in restricted cases and numerically in general. It is found that the reactive EGAM global mode structure is formed with the inclusion of fast ion finite drift orbit effects. In two cases with typical DIII-D parameters but different q profiles, the global EGAM frequency is slightly higher than the local EGAM extremum, located either on axis with a monotonic shear or at mid-radius with a reversed shear. The mode wavelength roughly scales with L 1/2 orbit in the core and L orbit at the edge, though the dependency is more complicated for the reversed shear case when L orbit < 0.06a (L orbit is the fast ion drift orbit width and a the minor radius). Finally, the growth rate of the global mode is boosted by 50% to 100% when switching from co-beam to counter-beam, depending on the fast ion density, which may help to explain the more frequent occurrence of EGAMs with counter-injection in experiments.

Linear properties of global energetic particle induced geodesic acoustic mode with bump-on-tail distribution in tokamak plasmas

“…Since then EGAM has been observed in other tokamaks [7][8][9] as well as in the Large Helical Device (LHD) [10][11]. Extensive theoretical and numerical work has been done on the linear physics of EGAM in the past decade [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The research on EGAM has been reviewed recently in several papers [26][27][28].…”

Geodesic modes driven by plasma fluxes during oblique NB heating in tokamaks

“…[10][11][12][13][14] According to the early theoretical models, in discharges with NB injection, the GAM instability can be driven due to an inhomogeneous dependence on the pitch angle distribution [15][16][17] in velocity space. For the parallel balanced injection, 17 the inverse Landau damping is found to be the origin of instability, but a cold beam model 18,19 of the bump may also reproduce the GAM instability that is named 18 as reactive and it begins without threshold due to the absence of dissipation. Generally, the energetic ion model was used in the form of a slowing down distribution…”

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

“…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. EGAM is important since it can degrade energetic particle confinement as shown in the DIII-D experiments (Nazikian et al.…”

“…2010; Qu et al. 2017), our model considers the situation in which the thermal GAM frequency for thermal particles is close to the energetic-ion toroidal transit frequency, creating the condition when the EGAM frequency is located slightly below it. Although the model of (Qiu et al.…”

“…2010) involves the EGAM source employing a sharp distribution and the model of (Qu et al. 2017) is restricted to the early beam scenario before the slowing down time, the new feature of our model is that the eigenmode is expected to be present after the slowing down time, in cases with reverse safety factor profile, where a small concentration of energetic ions can produce an off-axis maximum in the GAM dispersion relation, which is required for its appearance.…”