Propagation of shear Alvén waves in two-ion species plasmas confined by a nonuniform magnetic field

Abstract

Ray tracing calculations are performed for shear Alfvén waves in two-ion species plasmas in which the magnetic field varies with position. Three different magnetic topologies of contemporary interest are explored: a linear magnetic mirror, a pure toroidal field, and a tokamak field. The wave frequency is chosen to lie in the upper propagation band, so that reflection at the ion-ion hybrid frequency can occur for waves originally propagating along the magnetic field direction. Calculations are performed for a magnetic well configuration used in recent experiments [S. T. Vincena et al., Geophys. Res. Lett. 38, L11101 (2011) and S. T. Vincena et al., Phys. Plasmas 20, 012111 (2013)] in the Large Plasma Device (LAPD) related to the ion-ion hybrid resonator. It is found that radial spreading cannot explain the relatively low values of the resonator quality factor (Q) measured in those experiments, even when finite ion temperature is considered. This identifies that a damping mechanism is present that is at least an order of magnitude larger than dissipation due to radial energy loss. Calculations are also performed for a magnetic field with pure toroidal geometry, without a poloidal field, as in experiments being planned for the Enormous Toroidal Plasma Device. In this case, the effects of field-line curvature cause radial reflections. A poloidal field is included to explore a tokamak geometry with plasma parameters expected in ITER. When ion temperature is ignored, it is found that the ion-ion hybrid resonator can exist and trap waves for multiples bounces. The effects of finite ion temperature combine with field line curvature to cause the reflection point to move towards the tritium cyclotron frequency when electron temperature is negligible. However, for ITER parameters, it is shown that the electrons must be treated in the adiabatic limit to properly describe resonator phenomena.

Three dimensional magnetohydrodynamic simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field

“…Note from the movies that, because of existence of exponentially divergent field line regions, initially flat AW fronts became quickly corrugated via wave refraction, because of rather complicated form of the local Alfven speed C A (x, y, z) prescribed by Eq. (4). As in the case of UBMF, in ABC fields, the Gaussian pulse damping is also faster because it is strong localisation along z-coordinate.…”

“…1 and references therein) and Tokamak plasmas. [2][3][4] Phase mixing of harmonic Alfven waves (AW), which propagate in plasma, which has a density inhomogeneity in transverse to the uniform background magnetic field (UBMF) direction, results in their fast damping in the density gradient regions. In this case, the dissipation time scales as s D / S 1=3 , where S ¼ LV=g / 1=g is the Lundquist number, g ¼ 1/(l 0 r) is plasma resistivity, while L and V are characteristic lengthand velocity-scales of the system.…”

The ion-ion hybrid Alfvén resonator in a fusion environment

“…It was shown in Ref. 15 that the curvature of the field lines preferentially increases the component of the wave vector anti-parallel to the curvature of the field line. With the inclusion of FLR effects, this feature causes the reflection point to change as the absolute magnitude of k ?…”

“…14 In a theoretical study that included both the effects of the offdiagonal component of the dielectric tensor and finite-Larmor-radius (FLR) effects, radial convection of the mode was also unable to explain the low quality factors. 15 Due to the variation in magnetic field strength between the outboard and inboard sides of a toroidal device, a resonator configuration is also naturally present in a tokamak. This is shown schematically in Fig.…”

“…A subsequent study applied ray-tracing techniques for parameters relevant to ITER to assess the complicated geometrical effects on the resonator modes. 15 Finite-Larmor-radius effects were included to determine their impact on wave propagation, but damping was excluded from the analysis. It was shown in Ref.…”