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.

中文翻译：

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聚变等离子体边缘随机调制密度界面对射频波的散射

在托卡马克的刮除层和边缘区域，等离子体强烈湍流并散射通过该区域传播的射频 (RF) 电磁波。了解这些散射射频波的光谱特性非常重要，无论是用于诊断还是用于加热和电流驱动。光谱变化会影响对获得的诊断数据以及电流和加热曲线的解释。全波、三维 (3-D) 电磁码 ScaRF（参见 Papadopoulos等。,J.等离子物理学。, 卷。85, issue 3, 2019, 905850309) 已被开发用于研究射频波在湍流等离子体中的传播。ScaRF 是一种有限差分频域 (FDFD) 方法，用于求解麦克斯韦方程组。磁化等离子体通过冷等离子体由各向异性介电常数张量定义。因此，ScaRF 可用于研究任何冷等离子体射频波的散射。还可用于TCV、ASDEX-U、DIII-D等ITER型和中型托卡马克中电子回旋波散射的研究。对于中型托卡马克，有实验证据表明边缘区域存在漂移波和波纹模式（参见 Ritz等。,物理。流体, 卷。27，1984 年第 12 期，第 2956-2959 页）。因此，我们研究了周期性密度界面（等离子体光栅）对射频波的散射，其形式为具有不同周期性和随机幅度的空间模式的叠加（参见 Papadopoulos等。,J.等离子物理学。, 卷。85，2019 年第 3 期，905850309）。针对密度界面的不同实现计算功率反射系数（随机变量）。在这项工作中，功率反射系数的不确定性通过使用多项式混沌展开（参见 Xiu & Karniadakis，暹罗学家科学。计算。, 卷。24, issue 2, 2002, pp. 619–644) 方法与 Smolyak 稀疏网格集成相结合（参见 Papadopoulos等。,应用程序。选择。, 卷。57, issue 12, 2018, pp. 3106–3114), 这就是所谓的 PCE-SG 方法。PCE-SG 方法被证明是准确和更有效的（大约执行时间缩短 2 个数量级) 与蒙特卡洛 (MC) 方法等替代方法进行比较。