Pablant N A, Bell R E, Bitter M, Delgado-Aparicio L, Hill K W, Lazerson S, Morita S
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA.
National Institute for Fusion Science, Toki 509-5292, Gifu, Japan.
Rev Sci Instrum. 2014 Nov;85(11):11E424. doi: 10.1063/1.4891977.
Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at the Large Helical Device. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICS can provide profile measurements of the local emissivity, temperature, and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modified Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example, geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.
精确的层析反演对于仿星器和托卡马克上的诊断系统很重要，这些系统依赖于线积分发射光谱的测量。本文描述了一种基于样条优化并施加约束的层析反演技术，即使在输入数据有噪声或不完整的情况下，该技术也能产生独特且符合物理实际的反演结果。这种反演技术经常用于分析安装在大型螺旋装置上的X射线成像晶体谱仪（XICS）的数据。XICS诊断系统记录等离子体中杂质的线积分发射光谱的一维图像。通过使用多普勒光谱学和层析反演，XICS可以提供局部发射率、温度和等离子体流的剖面测量。层析反演需要假设这些测量量是通量表面函数，并且有已知的等离子体平衡重建结果。在低信号水平或等离子体横截面部分空间覆盖的情况下，利用矩阵反演和线性正则化的标准反演技术通常无法产生独特且符合物理实际的解。添加物理约束，如参数范围、导数方向和边界条件，可以可靠地找到唯一解。这里描述的约束反演技术使用了一种改进的Levenberg-Marquardt优化方案，该方案通过选择性减少搜索方向引入了一种条件避免机制。约束反演技术还允许添加更复杂的参数依赖性，例如，由于快速旋转导致的等离子体密度不对称引起的发射率的几何依赖性。本文讨论了这种约束反演技术的准确性，重点强调了其对等离子体覆盖有限的系统的适用性。
