Excitation of Geodesic Acoustic Modes by External Fields

It is planned to use external magnetic perturbations at acoustic frequencies at the DIII-D tokamak to attempt to drive geodesic acoustic modes (GAM) to modify the turbulent transport. We show that this might not only be possible—despite the well-known electrostatic nature of the GAMs—but might be a viable and efficient method to generate GAMs in magnetically confined plasmas, by developing an elegant analytic method which allows us to couple numerical dynamic equilibrium calculations with massively parallel non-Boussinesq turbulence code runs and yields practical estimates of the effectivity of the method.

Figure 1

GAM pressure perturbation, associated poloidal projection of magnetic drift and return currents (“Pfirsch-Schlüter current”), and external quadrupole current.

Figure 2

Linear displacement and flux surface perturbation visualized for hypothetical quadrupole perturbation current $I=90\mathrm{kA}$) for DIII-D plasma configuration from discharge no. 119527, including the effect of screening currents in the limiter structures (not shown). Light gray: Unperturbed separatrix. Red (bright) and blue (dark) toroidal loops: Position of positive and negative perturbation current relative to the plasma current, respectively. Red and blue (bright and dark) shells: Volume traversed by positive and negative radial displacement of flux surfaces, respectively. Yellow arrows in cross section: Poloidal displacement component. White arrows: Total displacement tangential to flux surfaces. Flux surfaces are repulsed by negative currents. The radial displacement is particularly strong close to magnetic nulls and to the perturbation current. The resulting poloidal displacement according to the incompressibility condition (4c) is amplified by the nozzle effect of close flux surface spacing at the midplane. For the outermost shown flux surface displacement $\delta B_{\mathrm{pol}}\sim 25\mathrm{mT}$, $|{\xi }_{\mathrm{rad},\max }|\sim 4.8\mathrm{cm}$ $|{\xi }_{\mathrm{pol}}|\sim 13\mathrm{cm}$, nozzle effect $\max (|\nabla \psi |)/\min (|\nabla \psi |)\sim 2.9$. The displacement diverges at the separatrix.

Figure 3

GAM excitation in a turbulent nonlocal resistive ballooning scenario in a thin shell at the edge of a circular tokamak discharge. (a) Flux surface averaged poloidal flow velocity with resonance. (b) Shearing of turbulence fluctuations: top, cut from outboard midplane; bottom, steepening of ion temperature profile.