Collisionless damping of zonal flows in helical systems

Abstract

Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode ͑GAM͒ in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.

Geodesic Acoustic Eigenmodes

“…The extension to a more general profile of temperature T (r) is possible. When T e comes closer to T i , the screening owing to the finite-gyroradius effect also appears inJ D,r as was explained in [12][13][14][15], so that the coefficient to k 2 ρ 2 i in Eq. (1) becomes smaller (i.e., the radial wavelength becomes shorter).…”

“…The dispersion relation of GAMs, ω = ω G , is derived by balancing the cross-field currentJ D,r (due to the magnetic field curvature) and the ion polarization currentJ p,r under the imposition of an electrostatic perturbation that has a formφ exp(ikr − iωt) in the leading order [12][13][14][15]. In order to study the radial eigenmode with analytic transparency, we take a simple collisionless limit with T e T i…”

“…where the lowest order finite-gyroradius correction is included (see [12][13][14][15][16] for a more detailed derivation). We consider the case in which the temperature decreases in radius, and choose the radius r 0 where ω 2 = ω 2 G (r 0 ) holds.…”

A New Simulation Method of Geodesic Acoustic Mode in Toroidal Plasmas by Using Band-Limited White Noise in a δf Neoclassical Transport Code

“…One possibility to explain it is the magnetic field structure. Theoretical studies on GAMs in non-axisymmetric magnetic field based on the gyrokinetic model by Sugama and Watanabe 22) have shown that the GAM frequency and damping rate depend on the magnetic field spectrum, and the collisionless damping of GAM oscillation in helical plasma is faster than that in a comparable scale tokamaks. To verify the analytic expectation of GAM in LHD magnetic configurations, we have carried out a simulation study of the dependence of GAM frequency and damping rate using FORTEC-3D.…”

“…Next, the peak frequencies and peak amplitudes of the power spectrum of Γ D i and E r are compared with the gyrokinetic theory, 22) which takes into account of the helical magnetic ripples of LHD configurations. Analytic solutions of ω G and γ G for the gyrokinetic analysis in the T e /T i → 0 drift-kinetic limit is shown in Eqs.…”