Page 2 - Combination Doppler backscattering/cross-polarization scattering diagnostic for the C-2W field-reversed configuration

10H116-2 Schmitz et al. cut-off layer. In addition to backscattering (exploited for density fluctuation measurements via DBS), a fraction of the incident radiation scatters into the opposite (X-mode) polar- ization. In principle, backscattering and CPS occur along the entire beam trajectory; however, several effects localize the backscattering and CPS response to the cut-off layer, includ- ing the reduction of the incident radial wavenumber as the 3–5 In this paper, we describe a combination DBS/CPS diagnostic planned for the C-2W FRC, which has recently completed construction at TAE Technologies, Inc. The paper is organized as follows: in Sec. II, calculations of the cut-off layer radii for X-mode and O-mode incident polarization are shown. GENRAY ray tracing calculations have been carried out, showing the trajectories of incident and back-scattered microwave beams for different repre- sentative expected plasma parameters in C-2W. The beam optics setup and microwave signal detection and process- ing are discussed in Sec. III. In Sec. IV, limiting geometry Rev. Sci. Instrum. 89, 10H116 (2018) considerations and the requirements for beam alignment are discussed. II. GENRAY RAY TRACING RESULTS FOR DBS AND CPS BEAM TRAJECTORIES A thorough understanding of the trajectories of incident and scattered microwave beams, including the cross-polarized feature, is required to evaluate the probed wavenumber and the radial/toroidal location of the cut-off layer. For the initial plasma parameters in C-2W \[with external field Be ∼ 0.1 T and total (electron + ion) temperature T tot = T e + T i ≤ 1 keV\], the X-mode and O-mode cutoff radii are located very closely together, as shown in Fig. 1(a). A rigid-rotor equilibrium,18 with external field Be = 0.1 T and total temperature T tot = T e + T i = 1 keV, was used to calculate the cut-off radii. The X-mode and O-mode cutoff locations track very closely in the FRC core, as shown in Fig. 1(a). As C-2W reaches its maximum expected ion energy and external magnetic field \[Fig. 1(b)\], the X-mode and O-mode cut-off radii separate, in particular in the SOL outside the separatrix (R ≥ Rs). The effects of a further projected performance increase for a follow-up exper- iment are indicated in Fig. 1(c). Here, the X- and O-mode cut-off radii are separated considerably in the SOL and in the FRC core plasma. It will be shown in the following Fig. 2, for launched O-mode and initial C-2W parameters, that the cross-polarized X-mode emission can be detected with only minor re-alignment of the (dedicated) receiving X-mode horn antennas, within a few cm off the optical axis. Beam trajec- tories are calculated with the GENRAY beam tracing code,19 using the cold plasma dispersion relation, which is adequate for electron temperatures below ∼4 keV, well above the pro- jected C-2W electron temperature. Figure 2 shows the results of ray tracing calculations for launched O-mode radiation at different frequencies and toroidal launch angles ζ. The O-mode beam (shown in red) is launched here for simplicity in the C-2W midplane. Within the available launch frequency range of 26-60 GHz, the SOL and the FRC core plasma between the separatrix and the field-null region can be accessed up to beam approaches cutoff. early C-2W plasma parameters, the calculated O-mode and X-mode cut-off locations are relatively close together, as demonstrated in Fig. 1(a). This is due to the fact that the plasma frequency, ωpe, is substantially above the electron cyclotron frequency ωce across the FRC core plasma and most of the SOL. In C-2U and with the expected FIG.1. (a)Cut-offfrequencyfortheX-mode(fcx)andO-mode(fco)vs.radius R, for the initial plasma parameters in C-2W, (b) for expected advanced plasma parameters, and (c) for expected plasma parameters in a future higher–field FRC. The electron cyclotron frequency fce is also shown. The calculations are 18 . The O-mode radia- tion backscattered from the O-mode cut-off layer is detected via monostatic beam optics for DBS (the launch antenna is also used as a receive antenna, and directional couplers are used to separate out the backscatter return). Cross-polarized radiation emission is expected to be most prominent near the X-mode cut-off layer, which is just outside the O-mode cutoff. We focus on backscattering because it allows using monos- tatic detection for DBS for a large range of toroidal launch angles, providing the toroidal turbulence wavenumber spec- trum. The corresponding outbound CPS X-mode ray paths are shown in green and follow a slightly different trajectory than the incoming O-mode due to the higher X-mode refrac- tive index. Dedicated X-mode receive antennas are used that can be independently positioned off-center with respect to the O-mode optical axis via adjustable xyz stages. Ray tracing for a range of toroidal launch angles demonstrates that the maximum expected deviation of backscattered X-mode radi- ation from the optical axis is <5 cm at the detection location. The probed turbulence wavenumber is predominantly toroidal based on rigid-rotor equilibria. 19 −3 a density maximum of 4.4 × 10 m