Full-wave calculation of sheared poloidal flow driven by high-harmonic ion Bernstein waves in tokamak plasmas

A full-wave, one-dimensional spectral model is developed to study sheared poloidal flow driven by high-harmonic ion Bernstein waves (IBWs) in tokamak plasmas. The local plasma conductivity is corrected to lowest order in $\mathrm{\rho /L}$ where ρ is the ion Larmor radius and L is the equilibrium scale length. This correction takes into account gradients in equilibrium quantities and is necessary for conservation of energy. It is equivalent to the “odd-order derivative” terms in finite difference models. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength, and results are applicable to all orders in $k_{\perp }\rho$ where $k_{\perp }$ is the perpendicular wave number. Previous numerical results for flow drive have relied on expansions in $k_{\perp }\mathrm{\rho ,}$ and are thus limited to cyclotron harmonics of two and below. In this article, we consider higher-harmonic cases corresponding to recent IBW flow drive experiments on the Tokamak Fusion Test Reactor [B. P. LeBlanc, R. E. Bell, S. Bernabei et al., Phys. Rev. Lett. 82, 331 (1999)] and the Frascati Tokamak Upgrade [R. Cesario, C. Castaldo, V. Pericoli-Ridolfini et al., “Recent Results of the Ion Bernstein Wave Heating Experiment on FTU,” in Proceedings of the 13th Topical Conference on Radio Frequency Power in Plasmas, 1999, Annapolis, MD, edited by S. Bernabei and F. Paoletti (American Institute of Physics, New York, 1999), p. 100]. In these cases, a directly launched high-harmonic IBW is used to drive poloidal flow near the fourth- and fifth-harmonic ion cyclotron layers. Other applications include high-harmonic fast wave heating in low aspect ratio tokamaks such as the National Spherical Torus Experiment [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)].