BORAY: An Axisymmetric Ray Tracing Code Supports Both Closed and Open Field Lines Plasmas

Abstract

Ray tracing codes are useful to study the electromagnetic wave propagation and absorption in the geometrical optics approximation. In magnetized fusion plasma community, most ray tracing codes assume the plasma density and temperature be functions of the magnetic flux and study waves only inside the last closed flux surface, which are sufficient for the present day tokamak. However, they are difficult to be used for configurations with open magnetic field line plasmas, such as mirror machine and field-reversed-configuration (FRC). We develop a ray tracing code in cylindrical coordinates (r, φ, z) to support arbitrary axisymmetric configurations with both closed and open field lines plasmas. For wave propagation, the cold plasma dispersion relation is usually sufficient, and we require the magnetic field B(r, z) and species densities n s0 (r, z) profiles as input. For wave absorption, we require a further temperature T s0 (r, z) profile to solve a hot kinetic plasma dispersion relation. In difference to other ray tracing codes which calculate the imaginary part of wave vector k ⊥,i for wave absorption, we calculate the imaginary part of wave frequency ω i , which is shown to be equivalent with the former technique under weak damping approximation. The code can use either numerical or analytical equilibrium. Examples and benchmarks with electron cyclotron wave, lower hybrid wave and ion cyclotron wave for tokamak, spherical tokamak (ST), FRC and mirror machine are shown.

Investigation of the effectiveness of non-inductive `multi-harmonic' electron cyclotron current drive through modeling multi-pass absorptions in the EXL-50 spherical tokamak

“…In another modeling of non-inductive plasma current [35], it was reported, in their terminology, minority hot electrons by the 2nd harmonic ECR power absorption could drive most of the current observed on QUEST. Our recent study of ray-tracing simulation on EXL-50 also confirmed that the single pass absorption ratio of X-to O-wave can be larger than 50% with around 2% energetic electrons of few hundreds keV energy [36]. In all of these studies, various energetic electron parameters -its distribution, temperature and density -are presumed and set through a mathematical function with some informations collected from experiments.…”

Plasma Waves Accessibility Diagrams: A Tutorial to Include the Fluid and Kinetic Thermal Effects

“…There existed several ray tracing codes based on kinetic model for plasma waves heating in 1970s, e.g., for the study of ICRF [21] and ECRF [22]. However, most later ray tracing codes [7][8][9]11] choose the cold plasma model for ray trajectory as default option. The main reasons are that the kinetic calculation is much slower than the calculation in the cold model, and the cold model is found to be valid for most cases.…”

“…Performing the coordinates transformation from (x, y, z, k x , k y , k z ) to (r, φ, z, k r , n φ , k z ), we can have the ray tracing equations [11]…”

“…We use the analytical Solovév equilibrium to demonstrate the results, with R 0 = 2m, R x = 0.8m, q 0 = 3, E = 1.5, τ = 0.8, L ns = 0.9, L T s = 0.8 and n e0 = 5 × 10 19 m −3 . One can refer to BORAY [11] code for details of the ray tracing method and equilibrium model used here. The cold plasma dispersion relation Eq.…”

“…With the use of these figures, the wave accessibility under given plasma parameters can be readily identified. Local cold plasma models are also widely used to study the wave * Email: huashengxie@gmail.com propagation in nonuniform plasma via WKB (Wentzel-Kramers-Brillouin) ray tracing method [7][8][9]11], though the wave absorption or heating requires kinetic models. In experimental wave heating studies, the wave is launched from the outside vacuum region or in low density edge region with a fixed frequency f = ω/2π and some ranges of parallel wave vector k .…”