Page 5 - Combination Doppler backscattering/cross-polarization scattering diagnostic for the C-2W field-reversed configuration

10H116-5 Schmitz et al. 1.5-10 GHz) are used to detect the CPS signals (highlighted in blue here). IV. GEOMETRY AND ALIGNMENT For optimum spatial resolution, the DBS probing beam should be narrow and well focused on the plasma region of interest. Wavenumber resolution would however be improved 20,21 Rev. Sci. Instrum. 89, 10H116 (2018) where the index “n” denotes the density fluctuation wavenum- ber, a0 is the beam radius, and φ0 is the local axial mismatch angle at the turning point (cutoff), which is increased compared to the launch mismatch angle. Accordingly, significant scat- with a larger diameter probing beam. As described in more detail previously,6,21 the wavenumber resolution of the backscattered signal depends, however, also on the toroidal and poloidal curvature of flux surfaces, and optimization for the expected C-2W plasma equilibria requires narrow prob- ing beams with a Gaussian width of 3-6 cm. For these beam parameters and plasma curvature radii of 0.2-0.4 m in C-2W, a wavenumber resolution ∆kθ/kθ ≤ 0.4-0.8 is calculated. FRC plasmas in C-2W are also expected to slowly contract axially on a timescale of several ms, reducing their axial length in the confinement vessel. Since the DBS/CPS diagnostic will be installed close to but not exactly in the axial device midplane, a possible axial misalignment of the probing beam needs to be taken into account. Figure 6(a) shows trajectories of O-mode beams launched with different axial launch mismatch angles φL with respect to the magnetic field direction \[as shown in Fig. 6(a)\]; Fig. 6(b) shows the resulting local axial mismatch angles φ0 of the launched microwave beam inside the plasma vs. radius, for different initial launch mismatch angles φL. To estimate the permissible beam misalignment, the change of the 21 scattered power along the beam path can be expressed as 222 dI 2 kna0 sin (φ0) ∝n˜ (kn,z)exp􏰀− 􏰁, (4) 􏰂􏰃 tered power is still received when the mismatch angle at the √ turning point satisfies |φ0|≤ 2/(2kna0), leading to permis- sible launch misalignment angles φL between ∼8◦ and 1◦ for −1 We would like to acknowledge the support of the entire TAE team in the design and implementation of the DBS/CPS diagnostic. 1M. W. Binderbauer, T. Tajima, L. C. Steinhauer, E. Garate, M. Tuszewski, L. Schmitz, H. Y. Guo, A. Smirnov, H. Gota, D. Barnes et al., Phys. Plasmas 22, 056110 (2015). 2H. Gota, M. W. Binderbauer, T. Tajima, S. Putvinski, M. Tuszewski, E. Garate, S. Korepanov, A. Smirnov, M. C. Thompson, E. Trask, X. Yang, L. Schmitz, Z. Lin et al., Nucl. Fusion 57, 116021 (2017). 3J. C. Hillesheim, W. A. Peebles, T. L. Rhodes, L. Schmitz et al., Rev. Sci. Instrum. 81, 10D907 (2010). 4W. A. Peebles, T. L. Rhodes, J. C. 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Controlled Fusion 33(8), 903 (1991). 14L. Vahala, G. Vahala, and N. Bretz, Phys. Fluids B 4, 619 (1992). 15X. L. Zou, L. Colas, M. Paume, J. M. Chareau et al., Phys. Rev. Lett. 75, 1090–1093 (1995). 16Y. Kogi, A. Mase, L. G. Bruskin, N. Oyama et al., Rev. Sci. Instrum. 70, 991–994 (1999). 17T. L. Rhodes, K. Barada, W. A. Peebles, and N. A. Crocker, Rev. Sci. Instrum. 87, 11E726 (2016). 18N. Rostoker and A. Querushi, Phys. Plasmas 9, 3057 (2002). 19 A. P. Smirnov and R. W. Harvey, “The GENRAY ray tracing code,” CompX Report COMPX-2000-01, 2001. 20E. Blanco, T. Estrada, and J. Sanchez, Plasma Phys. Controlled Fusion 48, 699 (2006). 21J. C. Hillesheim, N. A. Crocker, W. A. Peebles, H. Meyer et al., Nucl. Fusion 55, 073024 (2015). probed toroidal turbulence wavenumbers kθ = 1–8 cm axis adjustability of the focusing mirror allows minimizing the axial beam misalignment, enabling useful data collection once the FRC has axially contracted, in addition to selecting the toroidal launch angle and hence the probed DBS and CPS wavenumber. ACKNOWLEDGMENTS . Two- dz 2 FIG. 6. (a) O-mode ray trajectory in a typical C-2U FRC plasma for different axial launch mismatch angles φL as indicated vs. radius R and coordinate z along the local magnetic field (referenced here to the launch point); (b) local O-mode mismatch angle φ0 vs. radius in the plasma for different launch mismatch angles φL . φ0 is increased substantially compared to φL due to beam refraction in the plasma \[angles appear exaggerated in (a) due to expanded ◦ z-axis scale\]. The toroidal launch angle (defined in Fig. 3) is ζ = 4 .