# Review of Advanced Implementation of Doppler Backscattering Method in Globus-M
## 2 Doppler Backscattering on Globus-M  
### DBS Systems  
Doppler backscattering (DBS), also known as Doppler reflectometry, is a type of Thomson's collective microwave scattering. The method is based on recording the backscattered microwave radiation with an oblique incidence of the microwave beam. Scattering mainly occurs near the cutoff of the microwave beam on plasma fluctuations with a selected wave vector \(\mathrm{k}_{\perp}\), which satisfies the Bragg condition for backscattering--\(\mathrm{k}_{\perp}=2\ \mathrm{k}_{\mathrm{i}}\). Here \(\mathrm{k}_{\mathrm{i}}\) is the wave vector of the incident wave in the cutoff region and it is oriented in the direction of the electron or ion diamagnetic drift. When scattering fluctuations move in the diamagnetic direction with a certain velocity \(\mathrm{V}_{\perp}\), a Doppler frequency shift of backscattered radiation appears--\(\mathrm{\Delta}\omega_{\mathrm{D}}=\mathrm{k}_{\perp}\ \mathrm{V}_{\perp}\). The Doppler frequency shift \(\mathrm{\Delta}\omega_{\mathrm{D}}\) needed for the calculation of the perpendicular velocity \(\mathrm{V}_{\perp}\) can be obtained as the position of the 'center of gravity' of the complex signal I(t) + iQ(t) spectral density, or the derivative of the phase of the complex signal [30]. The sign and magnitude of the shift allow us to determine the sign and magnitude of the velocity of fluctuations in the diamagnetic direction \(\mathrm{V}_{\perp}\). The first implementation of DBS on a spherical tokamak was carried out on Globus-M [31]. There are specific requirements for DBS application in a spherical tokamak that is characterized by a significant pitch angle (more than 20\({}^{\circ}\)) at the low magnetic field side. To satisfy the Bragg condition, the antenna has to be tilted not only poloidally but also toroidally. To evaluate the required antenna tilt angles, ray tracing of the incident beam was performed for the actual three-dimensional (3D) geometry of the Globus-M flux surfaces [32]. To determine the investigated area of each DBS channel, experimental electron density profiles obtained by Thomson diagnostics and magnetic surface reconstruction data obtained using the EFIT code were used. An example of the performed ray tracing is presented in Figure 1. The locations of the ports available for the installation of the DBS systems are also indicated. The first Globus-M DBS system was based on a monostatic antenna scheme, which allowed one to probe the plasma by O-mode microwaves in the frequency band 18-26 GHz (system #1 in Table 1). It was possible to change the incident frequency from shot to shot. The tilt angles of the incident beam were chosen as 7\({}^{\circ}\) in the poloidal and 3\({}^{\circ}\) in the toroidal direction. The relevant wavelength of the scattering plasma fluctuations was in the range of 1.1-1.8 cm. The cutoff position was in the vicinity of the separatrix at high \(q\)-values. The radial resolution of the method was estimated to be about 0.5 cm. Dual homodyne detection was employed to receive the backscattered radiation [1]. The DBS system #1 was used successfully to study peripheral transport processes as well as to obtain measurements near the separatrix. Due to the usefulness of the diagnostics, the physics research program on the Globus-M tokamak required the expansion of the measured region into the area of the formation of the pedestal. Accordingly, an additional  
Figure 1: Ray tracing for the geometry of the Globus-M tokamak.