Geodesic acoustic modes with poloidal mode couplings ad infinitum

Abstract

Geodesic acoustic modes (GAMs) are studied, for the first time, including all poloidal mode (m) couplings using drift reduced fluid equations. The nearest neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number k r . The infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fractions. Convergence study of linear GAM dispersion with respect to k r and the m-spectra confirms that high m couplings become increasingly important with k r . The radially sorted roots overlap with experimentally measured GAM frequency profile in low collisionality shots in Tore Supra thus explaining the reduced frequency of GAM in Tore Supra.

Linear gyrokinetic investigation of the geodesic acoustic modes in realistic tokamak configurations

“…The same effect was observed in Ref. [34], where the GAMs were studied using drift reduced Braginskii equations.…”

“…To describe how the frequency changes with the radial wavenumber, a polynomial has been taken. Moreover, to take into account the frequency saturation for higher wavenumbers [34] we have introduced a function of the form 1/(1 + g 4 k). Here, k = k r ρ i , v T i = q e T i /2m p .…”

Propagation direction of geodesic acoustic modes driven by drift wave turbulence

“…The GAM frequency is given as ω G = √ 2L n /R, which corresponds to √ 2c s /R in the dimensional form, where L n is the density scale length and R is the major radius. We treat ω G as a constant parameter, assuming that the scale length of the temperature is much larger than the system size we consider, and neglecting the linear dispersion effect [31][32][33]. The viscosity for the GAM, µ G , is introduced.…”

A gyro-fluid model of global geodesic acoustic modes supported by finite ion Larmor radius

“…It remains to check how our predictions on the internal global modes will change when this condition is relaxed to λ r ∼ ρ i . Under the latter condition, as has been demonstrated in [37] for GAM continua, an infinite tower of θ-harmonics are coupled together through the geodesic curvature. As one can imagine, in this case it is impossible to obtain a compact analytical radial differential equation for the GGAMs, hence it is better to turn to the direct gyro-fluid or gyro-kinetic simulations.…”

“…37) and equation (B.35) asni = 1 − 2 + τ 2q 2 ω2 − 1 −1 2 iω c B 0 κ g n 0 E (0)r . substituting for j (r) P via equation (B.26) and ĵ(r) D+ + ĵ(r) D− via equation (B.39), equation (B.27) then leads to…”