Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

Abstract

Theoretical and numerical studies of wave-packet propagation are presented to analyze the time varying 2D mode structures of electrostatic fluctuations in tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave equations directly, the solution of the initial value problem is used to obtain the 2D mode structure, following the propagation of wave-packets generated by a source and reconstructing the time varying field. As application, the 2D WKB method is applied to investigate the shaping effects (elongation and triangularity) of tokamak geometry on the lower hybrid wave propagation and absorbtion. Meanwhile, the mode structure decomposition (MSD) method is used to handle the boundary conditions and simplify the 2D problem to two nested 1D problems. The MSD method is related to that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)], when spatial scale separation applies. This method is used to investigate the time varying 2D electrostatic ITG mode structure with a mixed WKB-fullwave technique. The time varying field pattern is reconstructed and the time asymptotic structure of the wave-packet propagation gives the 2D eigenmode and the corresponding eigenvalue. As a general approach to investigate 2D mode structures in tokamak plasmas, our method also applies for electromagnetic waves with general source/sink terms, either by an internal/external antenna or nonlinear wave interaction with zonal structures.

Particle simulation of lower hybrid wave propagation in fusion plasmas

“…A WKB simulation [8,9] gives similar results to the LH wave propagation in the toroidal geometry as shown in figure 6(a). In the WKB simulation, two identical rays are launched along the clockwise and counter-clockwise directions at the same time, respectively.…”

“…In order to investigate the LH wave propagation in cylindrical plasmas, we apply an antenna as a source term to generate wave-packets at the outer boundary [8,33] with all the information including the amplitude and initial phase.…”

“…Wide varieties of linear and quasi-linear simulation models, e.g., the WentzelKramers-Brillouin (WKB, i.e., ray tracing) [4][5][6][7], mixed WKB-full-wave [8,9], beam tracing [10,11] and full-wave methods [12,13] have been constructed to study the RF wave propagation and absorption in fusion plasmas during last two decades. However, with the availability of high RF power, the nonlinear phenomena of RF waves become important to heating and current drive.…”

The mixed WKB-full-wave approach and its application to lower hybrid wave propagation and absorption

“…Then, as higher order correction, the anti-Hermitian part can be taken into account to describe the absorption's effect in the amplitude equation. Considering straight field line tokamak magnetic flux coordinates, (r,θ , ζ ), where r,θ and ζ are the radiallike, poloidal-like and toroidal-like variables, respectively, with the Jacobian defined as J = (∇r · ∇ζ × ∇θ ) −1 , the wave propagation equation becomes [13] L H (r,…”

“…More recently, with the great progress of super computer capabilities, full wave solvers have been developed to investigate the LHW problem in tokamak plasmas [8,9,10]. Another approach, based on asymptotic analysis, consists in a mixed WKB-full-wave method, adopted for analytical as well as numerical studies [11,12,13]. During wave-packet propagation, parallel mode structure is formed before a significant radial propagation of the wave-packet if v g⊥ v g , where v g⊥ and v g are group velocities in the perpendicular and parallel directions with respect to the magnetic field.…”