Scattering of radiofrequency waves by randomly modulated density interfaces in the edge of fusion plasmas

In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radiofrequency (RF) electromagnetic waves that propagate through this region. It is important to know the spectral properties of these scattered RF waves, whether used for diagnostics or for heating and current drive. The spectral changes influence the interpretation of the obtained diagnostic data, and the current and heating profiles. A full-wave, three-dimensional (3-D) electromagnetic code ScaRF (see Papadopoulos et al., J. Plasma Phys., vol. 85, issue 3, 2019, 905850309) has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method used for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma by the anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can also be used for the study of the scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U and DIII-D. For the case of medium-sized tokamaks, there is experimental evidence that drift waves and rippling modes are present in the edge region (see Ritz et al., Phys. Fluids, vol. 27, issue 12, 1984, pp. 2956–2959). Hence, we have studied the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes (see Papadopoulos et al., J. Plasma Phys., vol. 85, issue 3, 2019, 905850309). The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion (see Xiu & Karniadakis, SIAM J. Sci. Comput., vol. 24, issue 2, 2002, pp. 619–644) method in conjunction with the Smolyak sparse-grid integration (see Papadopoulos et al., Appl. Opt., vol. 57, issue 12, 2018, pp. 3106–3114), which is known as the PCE-SG method. The PCE-SG method is proven to be accurate and more efficient (roughly a 2-orders of magnitude shorter execution time) compared with alternative methods such as the Monte Carlo (MC) approach.

Влияние металлических масок на согласование нижнего электрода с высокочастотным генератором смещения при реактивно-ионном травлении массивных подложек

The effect of metal masks on the matching of the lower electrode with a high-frequency bias generator during selective reactive-ion etching through the mask of massive substrates in freon-14 has been studied theoretically and experimentally. It is shown that masks with a substrate coating above 30% lead to an increase in the reactive power component at distances from the center close to the substrate radius. The absence of influence on the specific reactive power of the thickness and material of the masks is established. It is experimentally shown that masks with any practically significant coating coefficient of the substrate, connected to the lower electrode through the substrate holder, improve the matching, reducing the power reflection coefficient.

Dielectric anisotropy in ice Ih at 9.7 GHz

Dielectric anisotropy in ice Ih was investigated at 9.7 GHz with the waveguide method. The measurement of dielectric permittivity was made using single crystals collected from Mendenhall Glacier, Alaska. The result of the measurement shows that ϵ′‖c, the real part of dielectric permittivity parallel to the c axis, is larger than ϵ′⊥c the real part of dielectric permittivity perpendicular to the c axis. This tendency is similar to that at low frequencies in the region of the Debye relaxation dispersion. It can be proposed that ϵ′‖c>ϵ′⊥c in the HF, VHF and microwave frequency range. ϵ′‖c and ϵ′‖c depend slightly upon temperature but the dielectric anisotropy, ∆ϵ′=ϵ′‖c-ϵ′⊥c, is constant and becomes 0.037 (±0.007). Based on the present results, a simple caculation indicates that the maximum power reflection coefficient caused by the dielectric anisotropy is about −50 ∼ −80 dB, which is significantly larger than the power reflection coefficient observed in the ice sheet by radio-echo sounding, about −70 ∼ −80 dB. This leads to a conclusion that dielectric anisotropy is one of the dominant causes of internal reflections.

Dielectric anisotropy in ice Ih at 9.7 GHz

Dielectric anisotropy in ice Ih was investigated at 9.7 GHz with the waveguide method. The measurement of dielectric permittivity was made using single crystals collected from Mendenhall Glacier, Alaska. The result of the measurement shows that ϵ′ ‖c , the real part of dielectric permittivity parallel to the c axis, is larger than ϵ′ ⊥c the real part of dielectric permittivity perpendicular to the c axis. This tendency is similar to that at low frequencies in the region of the Debye relaxation dispersion. It can be proposed that ϵ′ ‖c >ϵ′ ⊥c in the HF, VHF and microwave frequency range. ϵ′ ‖c and ϵ′ ‖c depend slightly upon temperature but the dielectric anisotropy, ∆ϵ′=ϵ′ ‖c -ϵ′ ⊥c , is constant and becomes 0.037 (±0.007). Based on the present results, a simple caculation indicates that the maximum power reflection coefficient caused by the dielectric anisotropy is about −50 ∼ −80 dB, which is significantly larger than the power reflection coefficient observed in the ice sheet by radio-echo sounding, about −70 ∼ −80 dB. This leads to a conclusion that dielectric anisotropy is one of the dominant causes of internal reflections.

Scattering of a Love Wave by the Edge of a Thin Surface Layer

The antiplane strain problem of the scattering of an incident Love wave by the edge of a thin surface layer is solved. The effect of the layer is represented by a boundary condition applied at the surface of the substrate. In addition, the condition of vanishing traction on the edge of the layer is explicitly enforced. At large distances from the layer’s edge the scattered field is found to consist of a reflected Love wave and a radiated wave. The power flux identity for the problem is derived, and values of the power reflection coefficient are computed. The power flux identity is verified numerically, and the discrepancy which would arise from a failure to satisfy the condition of vanishing traction on the layer’s edge is evaluated.