Page 2 - Simulations of High Harmonic Fast Wave Heating on the C-2U Advanced Beam-Driven Field-Reversed Configuration Device

EPJ Web of Conferences 157, 03065 (2017) DOI: 10.1051/epjconf/201715703065 22 Topical Conference on Radio-Frequency Power in Plasmas
2 Parameter settings
Ray-tracing code Genray-C is a special version of Genray [8] adapted for plasmas like FRC or mirror machine where toroidal magnetic field can be absent. The C-2U machine configuration can be found in [1]; pure deuterium gas is routinely used in experiments. In our simulations, 5 rays are launched from one point but with different angles, each ray carrying 200 kW power. In this report, the launcher’s z-axial position is fixed at the midplane (z = 0), which is a preferable position for HHFW antenna-plasma coupling and wave penetration; moreover, launching HHFW at the midplane can make antenna physics and engineering design easier. The 2D equilibrium field profile reconstructed from experimental measurements is utilized; Fig. 1 shows its radial profile at the midplane. For feasibility study, the 2D model density profiles are used, matching those from C-2U experimental measurements. Both electrons and ions (D) have the same peak density of 2.4×1019m-3 at the field null point and the same density of 1.5×1019m-3 at the separatrix. In this case, the plasma has an unusually large (comparing to tokamaks) dielectric constant ( pe2/ ce2 > 4000 inside the separatrix layer). The Te and Ti (thermal D ions) in the plasma core are 150 eV and 800 eV, respectively. For simplification the data (density and temperature) on fast ions generated by neutral-beam injection is not included in present calculations. The simulations with fast ions will be performed in future work.
As an example of optimal regimes, Fig. 2 shows HHFW propagation trajectory in C-2U FRC plasmas. The HHFW frequency is at 7 MHz, and the initial n// is in a narrow range between 5 and 7 for the five rays. The background contours show the 2D profile of electron density, which is peaked at magnetic field null or local minimum of |B|. Rays launched at the possible antenna position near the wall (z = 0, r = 55 cm) can penetrate through the separatrix layer and propagate into the FRC plasma core. Figure 3 shows the change of power in each ray channel with the distance of wave propagation. The total distance of the rays’ propagation is about 200 cm, but most of their power is deposited by non-collisional damping in the area between 40 cm to 100 cm (the region marked with shadow); even though rays can continue propagating another 100 cm into the plasma core, the remaining power is very small.
60 40 20
0 -20 -40 -60
50 100 150 1.0e13 1.6e13 2.0e13 (cm-3)
-150 -100 -50 0
Z (cm)
5e11 5.5e12
0.10 0.05 0.00
-0.05
Fig. 2. The propogation trajectory of HHFW (7 MHz) in C-2U plasmas. Background contours show electron density profile.
Separatrix
-0.10 0 20 40 60 R (cm)
Fig. 1. Radial profile of C-2U equilibrium field Bz at midplane. 3 Simulation results
Extensive simulations have been performed in order to find optimal regimes, for which the HHFWs have both good penetration and favourable power damping partition between electrons and ions. The parameters that have been scanned in the process of optimization include frequencies (thus the ratio of / ci[D] at rays’ starting point since equilibrium field profile is fixed), antenna radial positions (the distance between antenna surface and plasma edge), and spectrum of parallel refractive index n// at the antenna position (launch angles). Those parameters can have significant effects on wave coupling, propagation, and penetration, as well as power damping partition between electrons and ions.
0 50
Distance along ray (cm)
100 150 200
2
Fig. 3. The HHFW (7 MHz) power in ray channel along the distance of wave propagation. The initial n// = 5 for blue ray and n// = 7 for purple ray.
The radial profiles of power density for total power absorption, power damping on electrons and ions, and collisional power damping, are shown in Figs. 4(a)-4(d), respectively. The position of rho = 1 corresponds to the location of separatrix layer of FRC plasma, where rho is defined through the square root of poloidal flux. In this report, the area of rho <1 (with closed field lines) defines “plasma core” while the area of rho >1 outlines the region of scrape-off layer (SOL). As shown clearly in Fig. 4(a), single pass absorption efficiency of HHFW power is 100% (total launched power is 1000 kW), and
Power in ray (kW)
0 50 100 150 200
Bz (Tesla)
R (cm)