Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

Abstract

Using ray tracing, a detailed investigation of the lower-hybrid ͑LH͒ wave propagation in presence of toroidal magnetic field ripple is presented. The local ray behavior is first depicted for a cylindrical equilibrium periodically modulated along the axial direction. Variations along ray trajectories in the component of the wave vector parallel to the equilibrium magnetic field are observed, with a maximum relative amplitude that is locally of the order of the ripple level. For the full rippled toroidal equilibrium, a similar local behavior is found when the ray trajectory crosses a high ripple region. Despite the modest amplitude of the local ray perturbation, its global influence on ray trajectories may be strong, as a consequence of the combined effects of toroidal and poloidal inhomogeneities. By coupling ray tracing with a one-dimensional relativistic Fokker-Planck code, simulations of LH experiments have been performed for the TORE SUPRA tokamak ͓Equipe TORE SUPRA, in . It is shown that magnetic ripple may induce significant modifications in the LH power deposition profiles, mainly in the ''few passes'' regime when the wave makes some, but not many, passes inside the plasma before being absorbed. The effect of magnetic ripple leads then to a broadening of the power deposition profile and a shift towards the center of the plasma, and a better coupling with high energy electrons. This behavior may be explained by an increase in the overall ray stochasticity. Taking into account magnetic ripple in LH simulations, a better agreement is found between numerical predictions and experimental observations.

Collisionless fast electron losses in magnetic toroidal ripples during lower hybrid current drive in Tore Supra

“…In consequence, serious damages to inner vessel components may occur for low density plasma and high injected power levels. [2][3][4] Conversely, the knowledge of the ripple induced losses may provide valuable information on the fast electron population, especially those which become trapped by pitch-angle scattering. It is therefore a complementary diagnostic of the fast electron bremsstrahlung tomography in the hard x-ray photon energy range, for characterizing the nonthermal electron dynamics.…”

“…Only electrons entering into the vertical port in which the diagnostic is installed are effectively collected, which represent approximately 70% of the total amount of lost fast electrons. 3 Information about the mean energy of the lost electrons is also estimated from complementary calorimetric measurements, 4 which may provide interesting details on the shape of the tail and its evolution with plasma parameters. 4,6 The purpose of this work is to assess the consistency of experimental observations with a simple modeling of the two-dimensional ͑2D͒ fast electron dynamics in momentum space.…”

“…[1][2][3] The lack of toroidal axisymmetry strongly affects fast electron dynamics in both configuration and momentum spaces during the lower hybrid ͑LH͒ wave current drive experiments. Fast electrons interacting resonantly with the LH wave along the toroidal field direction can be toroidally trapped in local magnetic mirrors between two consecutive coils through pitch angle scattering.…”

High energy electron deposition within vertical ports, during lower hybrid current drive on Tore Supra

“…Even in the core of the plasma, the local magnetic wells are deep enough to trap fast particles. In particular, electrons accelerated up to 200 keV by lower hybrid waves (LH), used to drive the current, can undergo pitch angle scattering, and be trapped between two adjacent toroidal coils in the local magnetic well [2,3].…”

Full Wave Simulation of Lower Hybrid Waves in ITER Plasmas Based on the Finite Element Method

“…Until recently numerical modeling of LHCD has consisted, for the most part, of toroidal ray tracing codes and Fokker Planck (FP) solvers [1][2][3]. Ray tracing approximates the wave as a bundle of rays under the assumption of the validity of Wenzel-Kramers-Brillouin (WKB) approximation, and is used to calculate the path of waves and the evolution of their wave vector.…”